The document studies small excitonic complexes in a disk-shaped quantum dot using the Bethe-Goldstone equation. It examines systems with up to 12 electron-hole pairs. For symmetric configurations where the number of electrons equals the number of holes, it finds:
1) The triexciton and four-exciton system show weak binding or possible unbinding in the weak confinement regime.
2) Higher complexes beyond four pairs exhibit binding in the weak confinement regime.
3) The Bethe-Goldstone approach provides better energies than the BCS variational method in the weak confinement regime.
This document provides an introduction to photonic crystals, including:
- Photonic crystals are periodic electromagnetic structures that can possess photonic band gaps where light cannot propagate, analogous to electronic band gaps in solids.
- The propagation of electromagnetic waves in periodic media is governed by Bloch's theorem and results in photonic band structures and gaps similar to electronic band structures.
- Introducing defects in photonic crystals allows for localized electromagnetic states like waveguides and cavities, allowing the crystal to confine and control light.
1) The document discusses travelling wave solutions for pulse propagation in negative index materials (NIMs) in the presence of an external source.
2) It obtains fractional-type solutions containing trigonometric and hyperbolic functions by using a fractional transform to map the governing equation to an elliptic equation.
3) Specific solutions include dark/bright solitary waves described by a sech-squared profile, as well as periodic solutions.
1) The document discusses travelling wave solutions for pulse propagation in negative index materials (NIMs) in the presence of an external source.
2) It obtains fractional-type solutions containing trigonometric and hyperbolic functions by using a fractional transform to map the governing equation to an elliptic equation.
3) Specific solutions include periodic solutions and bright/dark solitary wave solutions, with the intensity profiles of the bright solitary wave shown.
The document summarizes key aspects of the Standard Model of particle physics. It describes how the Standard Model accounts for fundamental particles like quarks and leptons that interact via four fundamental forces - gravitation, electromagnetism, weak force, and strong force. These interactions are mediated by exchange of spin-1/2 bosons. The Standard Model has been very successful in explaining experimental observations, but questions remain like incorporating gravity and the origin of particle masses.
Investigation of Steady-State Carrier Distribution in CNT Porins in Neuronal ...Kyle Poe
In this work, the carrier distribution of a carbon nanotube inserted into the spinal ganglion neuronal membrane is examined. After primary characterization based on previous work, the nanotube is approximated as a one-dimensional system, and the Poisson and Schrödinger equations are solved using an iterative finite-difference scheme. It was found that carriers aggregate near the center of the tube, with a negative carrier density of ⟨ρn⟩ = 7.89 × 10^13 cm−3 and positive carrier density of ⟨ρp⟩ = 3.85 × 10^13 cm−3. In future work, the erratic behavior of convergence will be investigated.
- The document discusses strongly interacting atoms in optical lattices and lattice-induced Feshbach resonances.
- It presents exact calculations of two atoms in a 1D lattice and finds avoided crossings between molecular bands and continuum states that depend on the lattice quasimomentum.
- An effective Hamiltonian is constructed that qualitatively captures these effects and introduces a momentum-dependent atom-dimer coupling parameter.
Introduction to the phenomenology of HiTc superconductors.ABDERRAHMANE REGGAD
1. The document provides an introduction to the phenomenology of high-temperature superconductors (HiTc).
2. It discusses the basic physics of doped Mott insulators and experimental methods used to study HiTc superconductors such as thermodynamic measurements, transport properties, neutron scattering, and ARPES.
3. It also covers topics such as the pseudo-gap phase, the one-hole problem, properties at small doping levels, and properties of the superconducting state.
This document provides a summary of quantum mechanical concepts and solid state physics. It begins with a review of quantum mechanics and the Schrodinger equation. It then discusses the wave nature of electrons and how the Schrodinger equation describes the wavefunction and probability of finding an electron. It also covers energy band diagrams and how the periodic potential in solids leads to the formation of allowed energy bands. It discusses these concepts for isolated atoms, silicon crystals, and the one-dimensional Kronig-Penny model.
This document provides an introduction to photonic crystals, including:
- Photonic crystals are periodic electromagnetic structures that can possess photonic band gaps where light cannot propagate, analogous to electronic band gaps in solids.
- The propagation of electromagnetic waves in periodic media is governed by Bloch's theorem and results in photonic band structures and gaps similar to electronic band structures.
- Introducing defects in photonic crystals allows for localized electromagnetic states like waveguides and cavities, allowing the crystal to confine and control light.
1) The document discusses travelling wave solutions for pulse propagation in negative index materials (NIMs) in the presence of an external source.
2) It obtains fractional-type solutions containing trigonometric and hyperbolic functions by using a fractional transform to map the governing equation to an elliptic equation.
3) Specific solutions include dark/bright solitary waves described by a sech-squared profile, as well as periodic solutions.
1) The document discusses travelling wave solutions for pulse propagation in negative index materials (NIMs) in the presence of an external source.
2) It obtains fractional-type solutions containing trigonometric and hyperbolic functions by using a fractional transform to map the governing equation to an elliptic equation.
3) Specific solutions include periodic solutions and bright/dark solitary wave solutions, with the intensity profiles of the bright solitary wave shown.
The document summarizes key aspects of the Standard Model of particle physics. It describes how the Standard Model accounts for fundamental particles like quarks and leptons that interact via four fundamental forces - gravitation, electromagnetism, weak force, and strong force. These interactions are mediated by exchange of spin-1/2 bosons. The Standard Model has been very successful in explaining experimental observations, but questions remain like incorporating gravity and the origin of particle masses.
Investigation of Steady-State Carrier Distribution in CNT Porins in Neuronal ...Kyle Poe
In this work, the carrier distribution of a carbon nanotube inserted into the spinal ganglion neuronal membrane is examined. After primary characterization based on previous work, the nanotube is approximated as a one-dimensional system, and the Poisson and Schrödinger equations are solved using an iterative finite-difference scheme. It was found that carriers aggregate near the center of the tube, with a negative carrier density of ⟨ρn⟩ = 7.89 × 10^13 cm−3 and positive carrier density of ⟨ρp⟩ = 3.85 × 10^13 cm−3. In future work, the erratic behavior of convergence will be investigated.
- The document discusses strongly interacting atoms in optical lattices and lattice-induced Feshbach resonances.
- It presents exact calculations of two atoms in a 1D lattice and finds avoided crossings between molecular bands and continuum states that depend on the lattice quasimomentum.
- An effective Hamiltonian is constructed that qualitatively captures these effects and introduces a momentum-dependent atom-dimer coupling parameter.
Introduction to the phenomenology of HiTc superconductors.ABDERRAHMANE REGGAD
1. The document provides an introduction to the phenomenology of high-temperature superconductors (HiTc).
2. It discusses the basic physics of doped Mott insulators and experimental methods used to study HiTc superconductors such as thermodynamic measurements, transport properties, neutron scattering, and ARPES.
3. It also covers topics such as the pseudo-gap phase, the one-hole problem, properties at small doping levels, and properties of the superconducting state.
This document provides a summary of quantum mechanical concepts and solid state physics. It begins with a review of quantum mechanics and the Schrodinger equation. It then discusses the wave nature of electrons and how the Schrodinger equation describes the wavefunction and probability of finding an electron. It also covers energy band diagrams and how the periodic potential in solids leads to the formation of allowed energy bands. It discusses these concepts for isolated atoms, silicon crystals, and the one-dimensional Kronig-Penny model.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
This document discusses characterization of countably normed nuclear spaces. It begins by defining countably normed spaces and providing an example using Kothe sequence spaces. It then proves that a nuclear Frechet space is countably normed if and only if it is isomorphic to a subspace of a nuclear Kothe space with a continuous norm. This nuclear Kothe space can be chosen to be a quotient of the space (s). The proof constructs a Kothe space K(a) and shows that the original space can be continuously embedded as a subspace of K(a).
This document is a physics problem set from MIT's 8.044 Statistical Physics I course in Spring 2004. It contains 5 problems related to statistical physics and probability distributions. Problem 1 considers the probability distribution and properties of the position of a particle undergoing simple harmonic motion. Problem 2 examines the probability distribution of the x-component of angular momentum for a quantum mechanical system. Problem 3 analyzes a mixed probability distribution describing the energy of an electron. Problem 4 involves finding and sketching the time-dependent probability distribution for the position of a particle given its wavefunction. Problem 5 concerns Bose-Einstein statistics and calculating properties of the distribution that describes the number of photons in a given mode.
This document analyzes extensions of the Standard Model that naturally accommodate tiny neutrino masses through the exchange of heavy particles. It discusses how neutrino masses are generated at tree-level by seesaw mechanisms involving fermionic singlets/triplets or scalar triplets. Dimension-six operators are also explored, as they may allow observable low-energy effects even with suppressed dimension-five operators. Phenomenological consequences are then analyzed, with a focus on charged lepton flavor violating processes and constraints from rare decays.
This document discusses density functional theory (DFT) and exact exchange methods. It provides background on DFT, the Kohn-Sham equations, and common exchange-correlation functionals like the local density approximation (LDA) and generalized gradient approximations (GGA). It then introduces exact exchange (EXX) methods, which neglect correlation and use the Hartree-Fock exchange energy. Calculating the functional derivative of the exchange energy is discussed to obtain the exchange potential within the Kohn-Sham scheme for EXX.
Apartes de la Conferencia de la SJG del 14 y 21 de Enero de 2012: Hubble diag...SOCIEDAD JULIO GARAVITO
This document discusses using gamma-ray bursts (GRBs) to test cosmological predictions of the Gurzadyan-Xue (GX) model of dark energy. It calibrates GRBs as standard candles using empirical relations between their observed characteristics. It then uses 3 samples of GRB data spanning redshifts up to 7 to generate Hubble diagrams and compare them to the predictions of GX models and the standard ΛCDM model. The analysis shows GX models are compatible with one GRB sample but more data is needed to clarify the issues of GRBs as standard candles and the physics underlying the empirical relations.
1. This document contains 6 problems related to statistical mechanics and quantum gases. The problems cover topics like the energy states of an ideal quantum gas, properties of white dwarf stars, compressibility of metals, virial expansions, Gibbs free energy differences between normal and superconducting states, and Monte Carlo simulations.
2. The document provides detailed multi-part physics problems and asks the reader to calculate various properties of quantum gases and condensed matter systems using statistical mechanics concepts and equations of state. Hints or guidance are given for some problems.
3. The problems progressively increase in complexity, starting with basic calculations for an ideal quantum gas and ending with Monte Carlo simulation techniques and properties of superconducting phase transitions.
1. This chapter discusses electrostatic fields, beginning with Coulomb's law and electric field intensity.
2. Coulomb's law describes the force between two point charges, and electric field intensity is defined as the force per unit charge.
3. Examples show how to calculate the electric force and field given point charge configurations using Coulomb's law and the superposition principle.
This document summarizes elementary particles in physics. It describes how particles are classified into leptons and hadrons. Leptons include electrons, muons, taus and their neutrinos. Hadrons include baryons like protons and neutrons, and mesons. Interactions are also classified, including the electromagnetic, weak, and strong interactions. The electromagnetic interaction between charged leptons and photons is described based on local gauge invariance, resulting in a theory of quantum electrodynamics that agrees well with experiments.
This document provides an overview of near-dissociation expansion (NDE) theory for quantizing energy levels of diatomic molecules near dissociation. Section 1 introduces the topic and outlines subsequent sections. Section 2 discusses the historical motivation of using the Birge-Sponer method to determine dissociation energies from spectroscopic data before NDE theory. Section 3 outlines the assumptions of NDE theory, including the Wentzel-Kramers-Brillouin approximation and representing the long-range potential as a dispersion expansion involving inverse powers of the internuclear separation.
1) This chapter discusses electromagnetic wave propagation based on Maxwell's equations. It will derive wave motion in free space, lossless dielectrics, lossy dielectrics, and good conductors.
2) A wave is a function of both space and time that transports energy or information from one point to another. Electromagnetic waves include radio waves, light, and more.
3) Key wave characteristics include amplitude, wavelength, frequency, period, phase, and velocity. The velocity is the frequency multiplied by the wavelength based on a fixed relationship between them.
1. Diluted magnetic semiconductors aim to integrate semiconductor processing and ferromagnetic data storage on a single chip. Magnetic semiconductors are classes of materials that exhibit both semiconducting and magnetic properties.
2. The lecture discusses the theoretical picture of magnetic impurities in semiconductors based on the Zener model and mean-field theory. It also covers disorder, transport properties, and the anomalous Hall effect in diluted magnetic semiconductors.
3. The final sections discuss magnetic properties in the presence of disorder and recent developments, as well as open questions for the future of magnetic semiconductors.
This document presents a new preon model with three fundamental spin-1/2 preons (α, β, δ) that can combine to form nine leptons, nine quarks, and nine heavy vector bosons. The preons have charges of +e/3, -2e/3, and +e/3. Quarks and leptons are composed of combinations of one spin-1/2 preon and one spin-0 "dipreon" made of two spin-1/2 preons. This model aims to address shortcomings of the standard model such as the large number of fundamental particles and mixings between particles, through a more fundamental layer of preons with an underlying symmetry.
(1) Biot-Savart's law states that the magnetic field intensity produced at a point P by a differential current element is proportional to the product of the current and the sine of the angle between the element and the line joining P to the element, and inversely proportional to the square of the distance between P and the element.
(2) The magnetic field intensity due to different current distributions such as line, surface, and volume currents can be determined using Biot-Savart's law.
(3) Example problems demonstrate applying Biot-Savart's law to calculate the magnetic field intensity at a point due to straight and semi-infinite current filaments.
The document discusses the Schrodinger equation and its applications in quantum mechanics. It covers:
1. The postulates of quantum mechanics including that systems are described by wavefunctions and observables are represented by Hermitian operators.
2. Examples of operators for observables like position, momentum, energy.
3. The time-independent Schrodinger equation for a time-independent potential and its solution for an infinite square well potential.
4. Other examples like an infinite square well potential trapping an electron and calculating its energy levels and wavefunctions.
In this second lecture, I will discuss how to calculate polarization in terms of Berry phase, how to include GW correction in the real-time dynamics and electron-hole interaction.
Using the two forms of Fish-Bone potential (I and II), a self-consistent calculations are carried out to perform the analysis of binding energies, root mean square radii and form factors using different configuration symmetries of 20Ne nucleus. A computer simulation search program has been introduced to solve this problem. The Hilbert space was restricted to three and four dimensional variational function space spanned by single spherical harmonic oscillator orbits. A comparison using Td and D3h configuration symmetries are carried out.
(1) The document discusses electric fields in material spaces and summarizes some key properties of conductors and dielectrics.
(2) Conductors have an abundance of free electrons that allow conduction current to flow according to Ohm's law, while dielectrics have few free electrons.
(3) A perfect conductor cannot contain an electric field within it due to the migration and accumulation of free charges on its surface when an external field is applied.
The document discusses the Bethe-Salpeter equation (BSE) which accounts for electron-hole interactions beyond the independent particle approximation. It summarizes that the BSE is derived from the equation of motion for the response function and results in an effective two-particle Hamiltonian that describes electron-hole excitations when diagonalized. Solving the BSE for lithium fluoride improves agreement with experimental optical spectra by including excitonic effects neglected by the independent particle picture.
The document discusses holographic soliton automata using a causal crystal approach. It proposes that spacetime may be fundamentally discrete and composed of causal sets. This leads to the idea of modeling soliton cellular automata using tensorial crystals and box-ball solitons. The automata would evolve according to the rules of the underlying causal Lorentz manifold, which is decomposed into an intelligent crystal behaving as an automaton.
Passivation Of Ga As Surface With Sa Ms Finalrkjean
1. The document discusses the passivation of a GaAs semiconductor surface using self-assembled monolayers (SAMs) of redox-active ruthenium-based molecules and non-redox active molecules.
2. Characterization techniques like FTIR, CV, and XPS showed that a mixed monolayer of ruthenium molecules inserted into a matrix of OPE1 molecules provided better surface coverage than a ruthenium SAM alone.
3. The optimal deposition times were 3 hours for OPE1 and 6 hours for inserting ruthenium molecules into the OPE1 matrix. ODT provided the most effective passivation of the GaAs surface.
El documento discute los desafíos que enfrentan los sistemas de salud, incluyendo el envejecimiento de la población, el aumento de costos y la introducción de nuevas tecnologías. También destaca la importancia de basar las decisiones clínicas en evidencia científica para mejorar la calidad y reducir la variabilidad en la atención. Propone el uso de guías de práctica clínica fundamentadas en evidencia para lograr estos objetivos.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
This document discusses characterization of countably normed nuclear spaces. It begins by defining countably normed spaces and providing an example using Kothe sequence spaces. It then proves that a nuclear Frechet space is countably normed if and only if it is isomorphic to a subspace of a nuclear Kothe space with a continuous norm. This nuclear Kothe space can be chosen to be a quotient of the space (s). The proof constructs a Kothe space K(a) and shows that the original space can be continuously embedded as a subspace of K(a).
This document is a physics problem set from MIT's 8.044 Statistical Physics I course in Spring 2004. It contains 5 problems related to statistical physics and probability distributions. Problem 1 considers the probability distribution and properties of the position of a particle undergoing simple harmonic motion. Problem 2 examines the probability distribution of the x-component of angular momentum for a quantum mechanical system. Problem 3 analyzes a mixed probability distribution describing the energy of an electron. Problem 4 involves finding and sketching the time-dependent probability distribution for the position of a particle given its wavefunction. Problem 5 concerns Bose-Einstein statistics and calculating properties of the distribution that describes the number of photons in a given mode.
This document analyzes extensions of the Standard Model that naturally accommodate tiny neutrino masses through the exchange of heavy particles. It discusses how neutrino masses are generated at tree-level by seesaw mechanisms involving fermionic singlets/triplets or scalar triplets. Dimension-six operators are also explored, as they may allow observable low-energy effects even with suppressed dimension-five operators. Phenomenological consequences are then analyzed, with a focus on charged lepton flavor violating processes and constraints from rare decays.
This document discusses density functional theory (DFT) and exact exchange methods. It provides background on DFT, the Kohn-Sham equations, and common exchange-correlation functionals like the local density approximation (LDA) and generalized gradient approximations (GGA). It then introduces exact exchange (EXX) methods, which neglect correlation and use the Hartree-Fock exchange energy. Calculating the functional derivative of the exchange energy is discussed to obtain the exchange potential within the Kohn-Sham scheme for EXX.
Apartes de la Conferencia de la SJG del 14 y 21 de Enero de 2012: Hubble diag...SOCIEDAD JULIO GARAVITO
This document discusses using gamma-ray bursts (GRBs) to test cosmological predictions of the Gurzadyan-Xue (GX) model of dark energy. It calibrates GRBs as standard candles using empirical relations between their observed characteristics. It then uses 3 samples of GRB data spanning redshifts up to 7 to generate Hubble diagrams and compare them to the predictions of GX models and the standard ΛCDM model. The analysis shows GX models are compatible with one GRB sample but more data is needed to clarify the issues of GRBs as standard candles and the physics underlying the empirical relations.
1. This document contains 6 problems related to statistical mechanics and quantum gases. The problems cover topics like the energy states of an ideal quantum gas, properties of white dwarf stars, compressibility of metals, virial expansions, Gibbs free energy differences between normal and superconducting states, and Monte Carlo simulations.
2. The document provides detailed multi-part physics problems and asks the reader to calculate various properties of quantum gases and condensed matter systems using statistical mechanics concepts and equations of state. Hints or guidance are given for some problems.
3. The problems progressively increase in complexity, starting with basic calculations for an ideal quantum gas and ending with Monte Carlo simulation techniques and properties of superconducting phase transitions.
1. This chapter discusses electrostatic fields, beginning with Coulomb's law and electric field intensity.
2. Coulomb's law describes the force between two point charges, and electric field intensity is defined as the force per unit charge.
3. Examples show how to calculate the electric force and field given point charge configurations using Coulomb's law and the superposition principle.
This document summarizes elementary particles in physics. It describes how particles are classified into leptons and hadrons. Leptons include electrons, muons, taus and their neutrinos. Hadrons include baryons like protons and neutrons, and mesons. Interactions are also classified, including the electromagnetic, weak, and strong interactions. The electromagnetic interaction between charged leptons and photons is described based on local gauge invariance, resulting in a theory of quantum electrodynamics that agrees well with experiments.
This document provides an overview of near-dissociation expansion (NDE) theory for quantizing energy levels of diatomic molecules near dissociation. Section 1 introduces the topic and outlines subsequent sections. Section 2 discusses the historical motivation of using the Birge-Sponer method to determine dissociation energies from spectroscopic data before NDE theory. Section 3 outlines the assumptions of NDE theory, including the Wentzel-Kramers-Brillouin approximation and representing the long-range potential as a dispersion expansion involving inverse powers of the internuclear separation.
1) This chapter discusses electromagnetic wave propagation based on Maxwell's equations. It will derive wave motion in free space, lossless dielectrics, lossy dielectrics, and good conductors.
2) A wave is a function of both space and time that transports energy or information from one point to another. Electromagnetic waves include radio waves, light, and more.
3) Key wave characteristics include amplitude, wavelength, frequency, period, phase, and velocity. The velocity is the frequency multiplied by the wavelength based on a fixed relationship between them.
1. Diluted magnetic semiconductors aim to integrate semiconductor processing and ferromagnetic data storage on a single chip. Magnetic semiconductors are classes of materials that exhibit both semiconducting and magnetic properties.
2. The lecture discusses the theoretical picture of magnetic impurities in semiconductors based on the Zener model and mean-field theory. It also covers disorder, transport properties, and the anomalous Hall effect in diluted magnetic semiconductors.
3. The final sections discuss magnetic properties in the presence of disorder and recent developments, as well as open questions for the future of magnetic semiconductors.
This document presents a new preon model with three fundamental spin-1/2 preons (α, β, δ) that can combine to form nine leptons, nine quarks, and nine heavy vector bosons. The preons have charges of +e/3, -2e/3, and +e/3. Quarks and leptons are composed of combinations of one spin-1/2 preon and one spin-0 "dipreon" made of two spin-1/2 preons. This model aims to address shortcomings of the standard model such as the large number of fundamental particles and mixings between particles, through a more fundamental layer of preons with an underlying symmetry.
(1) Biot-Savart's law states that the magnetic field intensity produced at a point P by a differential current element is proportional to the product of the current and the sine of the angle between the element and the line joining P to the element, and inversely proportional to the square of the distance between P and the element.
(2) The magnetic field intensity due to different current distributions such as line, surface, and volume currents can be determined using Biot-Savart's law.
(3) Example problems demonstrate applying Biot-Savart's law to calculate the magnetic field intensity at a point due to straight and semi-infinite current filaments.
The document discusses the Schrodinger equation and its applications in quantum mechanics. It covers:
1. The postulates of quantum mechanics including that systems are described by wavefunctions and observables are represented by Hermitian operators.
2. Examples of operators for observables like position, momentum, energy.
3. The time-independent Schrodinger equation for a time-independent potential and its solution for an infinite square well potential.
4. Other examples like an infinite square well potential trapping an electron and calculating its energy levels and wavefunctions.
In this second lecture, I will discuss how to calculate polarization in terms of Berry phase, how to include GW correction in the real-time dynamics and electron-hole interaction.
Using the two forms of Fish-Bone potential (I and II), a self-consistent calculations are carried out to perform the analysis of binding energies, root mean square radii and form factors using different configuration symmetries of 20Ne nucleus. A computer simulation search program has been introduced to solve this problem. The Hilbert space was restricted to three and four dimensional variational function space spanned by single spherical harmonic oscillator orbits. A comparison using Td and D3h configuration symmetries are carried out.
(1) The document discusses electric fields in material spaces and summarizes some key properties of conductors and dielectrics.
(2) Conductors have an abundance of free electrons that allow conduction current to flow according to Ohm's law, while dielectrics have few free electrons.
(3) A perfect conductor cannot contain an electric field within it due to the migration and accumulation of free charges on its surface when an external field is applied.
The document discusses the Bethe-Salpeter equation (BSE) which accounts for electron-hole interactions beyond the independent particle approximation. It summarizes that the BSE is derived from the equation of motion for the response function and results in an effective two-particle Hamiltonian that describes electron-hole excitations when diagonalized. Solving the BSE for lithium fluoride improves agreement with experimental optical spectra by including excitonic effects neglected by the independent particle picture.
The document discusses holographic soliton automata using a causal crystal approach. It proposes that spacetime may be fundamentally discrete and composed of causal sets. This leads to the idea of modeling soliton cellular automata using tensorial crystals and box-ball solitons. The automata would evolve according to the rules of the underlying causal Lorentz manifold, which is decomposed into an intelligent crystal behaving as an automaton.
Passivation Of Ga As Surface With Sa Ms Finalrkjean
1. The document discusses the passivation of a GaAs semiconductor surface using self-assembled monolayers (SAMs) of redox-active ruthenium-based molecules and non-redox active molecules.
2. Characterization techniques like FTIR, CV, and XPS showed that a mixed monolayer of ruthenium molecules inserted into a matrix of OPE1 molecules provided better surface coverage than a ruthenium SAM alone.
3. The optimal deposition times were 3 hours for OPE1 and 6 hours for inserting ruthenium molecules into the OPE1 matrix. ODT provided the most effective passivation of the GaAs surface.
El documento discute los desafíos que enfrentan los sistemas de salud, incluyendo el envejecimiento de la población, el aumento de costos y la introducción de nuevas tecnologías. También destaca la importancia de basar las decisiones clínicas en evidencia científica para mejorar la calidad y reducir la variabilidad en la atención. Propone el uso de guías de práctica clínica fundamentadas en evidencia para lograr estos objetivos.
1) El síndrome de ovarios poliquísticos (SOP) es una enfermedad heterogénea con componente genético demostrado por casos familiares. La mayoría de los estudios muestran una transmisión autosómica dominante.
2) En el SOP, la síntesis de esteroides está sobrerregulada en las células de la teca del ovario, lo que sugiere una anomalía genética que afecta las vías de señalización que controlan la expresión de genes relacionados con los esteroides.
3)
Evaluación de productos de nueva formulación con esteroles incorporados, aplicables a controlar trastornos metabólicos asociados con factores de riesgo cardiovascular.
El documento resume varias novedades normativas en materia tributaria, contable y laboral que afectan a clientes de Eurosega. Se informa sobre la presentación telemática obligatoria de impuestos trimestrales y anuales, los requisitos para la inscripción en el Registro Andaluz de Caza, los trámites para exámenes de patrones de embarcaciones de recreo, la transformación de sociedades profesionales y la deducción de la segunda parte de los 400 euros por declaración de la renta.
This document discusses a proposed spin filter device consisting of a ferromagnetic scanning tunneling microscope (STM) tip above a metallic surface containing a Kondo adatom.
The combined effects of the Kondo screening, quantum interference between tunneling paths, and the tip magnetism are studied theoretically. It is found that for certain tip-adatom distances and bias voltages, the tunneling current can be nearly 100% spin polarized, making this a potential spin filter or polarizer.
The conductance formula is derived taking into account the Fano lineshape from quantum interference and the splitting of the Kondo resonance into two spin components from the exchange interaction with the tip. For an optimized configuration, one spin channel is suppressed,
The document discusses a nutritional system and exercise. It appears to be about a nutritional and exercise program, but provides no other details on the specific goals, components, or recommendations of the system and exercise in the limited text presented.
This document discusses surface electromyography (sEMG) scans, which allow chiropractors to detect elevated or imbalanced muscle activity that may be associated with spinal subluxations. The sEMG scan technology uses normative databases and statistical analysis of minute muscle measurements to provide an image of back muscle activity. Chiropractors can identify areas of elevated muscle activity along the spine and imbalances across the spine. Repeated sEMG scans during treatment allow monitoring of patient progress by comparing readings over time. The results help chiropractors provide more effective treatment and documentation.
This document describes an intelligent functional electrical stimulation (INTFES) system that uses a multi-pad electrode for grasp rehabilitation. The system includes a multi-pad electrode with multiple conductive pads, stimulation hardware, and control software. The multi-pad electrode allows for asynchronous stimulation of specific forearm muscles to enable hand grasping and releasing motions. The system provides advantages over single-pad electrodes such as applicability for telerehabilitation and delayed muscle fatigue.
El virus de Epstein-Barr pertenece a la familia de los Herpesvirus. Causa la mononucleosis infecciosa al infectar células permanentemente y expresar antígenos virales. Su estructura incluye ADN de doble hebra, cápside proteica, tegumento y envoltura. Puede causar infecciones agudas o latentes que se activan ocasionalmente. La mononucleosis se caracteriza por linfadenopatías, hepatoesplenomegalia y fatiga, y suele resolverse espontáneamente. Rar
This study compared energy intake reported from 4-day multimedia diet records to total energy expenditure measured by doubly labeled water in 53 middle-aged and elderly women. The women underreported their food intake compared to their measured energy needs, with a mean reporting accuracy of 76%. Reported energy intake was significantly lower than total energy expenditure in each age group. While the multimedia diet records aimed to improve reporting accuracy over traditional methods, the women still underreported their food consumption compared to their actual energy requirements.
1995 analysis of piezo actuators in translation constructionspmloscholte
1) A translation stage using piezo stacks as actuators was developed to generate displacements with nanometer accuracy over a dynamic range of 10 micrometers. Capacitive sensors were able to measure displacements with subnanometer resolution.
2) Using the high precision measurements from the capacitive sensors, the displacement properties of the piezo actuator in the translation stage could be characterized with great accuracy when different voltages were applied.
3) A model is presented to describe the general behavior of a piezo actuator in a translation stage, and the hysteresis behavior observed in the piezo actuator is found to have point symmetry properties and branches that can be described by third-order polynomials.
Zetia Reprint Holder Atorvastatin Corbett Work Sample Crystal Kaczkowski Wate...ckaczk
ZETIA (ezetimibe) when initiated concurrently with atorvastatin 10 mg provided dramatically more LDL-C ("bad cholesterol") reduction than higher doses of atorvastatin alone. A clinical trial found that ZETIA + atorvastatin 10 mg reduced LDL-C by 53%, significantly more than atorvastatin doses of 20 mg or 40 mg. Dual inhibition of cholesterol absorption and production provides greater reduction of LDL-C than statin therapy alone. Contraindications for ZETIA include hypersensitivity and active liver disease.
Este documento presenta a siete gatos del refugio Barcelona Gat i Gos que tienen una enfermedad crónica pero no contagiosa para los humanos llamada inmunidad. Explica que a pesar de su enfermedad y edad pueden llevar una vida saludable y larga si son bien cuidados, y pide la adopción para cada uno para hacer posible un milagro de navidad. Proporciona detalles sobre la personalidad y características de cada gato.
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Astute Business Solutions | Oracle Cloud Partner |
Phys e8(2000)1
1. Physica E 8 (2000) 91–98
www.elsevier.nl/locate/physe
Small excitonic complexes in a disk-shaped quantum dot
Ricardo PÃ reza; b; ∗ , Augusto Gonzalezb
e
a Centro de Matemà ticas y FÃsica Teà rica, Calle E No. 309, Ciudad Habana, Cuba
a à o
b Universidad de Antioquia, A.A. 1226, MedellÃn, Colombia
Ã
Received 28 October 1999; accepted 18 November 1999
Abstract
Conÿned excitonic complexes in two dimensions, consisting of Ne electrons and Nh holes, are studied by means of Bethe–
Goldstone equations. Systems with up to 12 pairs, and asymmetric conÿgurations with Ne = Nh are considered. The weak
conÿnement regime gives indication of weak binding or even unbinding in the triexciton and the four-exciton system, and
binding in the higher complexes. ? 2000 Elsevier Science B.V. All rights reserved.
PACS: 71.35.E.e; 78.65.−w
Keywords: Quantum dots; Electron–hole systems; Bethe–Goldstone equations
1. Introduction citon peaks in photoluminescence have been identi-
ÿed in quantum dots [2– 4]. Recently, a confocal mi-
Although the excitonic matter as a research object croscopy technique has been applied to resolve the
has already a relatively long history, dating back to luminescence coming from a single self-assembled
pioneer theoretical ideas in the 1960s [1], the study quantum dot [5]. The power of the excitation laser is
of small excitonic complexes conÿned in regions of such that up to six pairs are excited simultaneously in
nanometer scale became possible only recently, and is the dot. Clearly distinct lines coming from transitions
closely related to dramatic advances in semiconductor between multiexcitonic complexes are identiÿed.
technology. The calculations presented in our paper, although
Due to the smallness of the exciton lifetime in semi- unrealistic, are inspired by the experimental work [5].
conductors (hundreds of picoseconds, sometimes even We address a di erent question, i.e. the dependence
greater), signatures of excitonic complexes are looked of the ground-state energy on the number of pairs.
for mainly in optical experiments. Exciton and biex- From this dependence, the lowest optical absorption
line related to the creation of an electron–hole pair
∗ Correspondence address. Centro de Matemà ticas y FÃsica
in the background of N photo-excited pairs may be
a
Teà rica, Calle E No. 309, Ciudad Habana, Cuba.
o
extracted.
E-mail addresses: rperez@cidet.icmf.inf.cu (R. PÃ rez), agon-
e On the other hand, small excitonic systems have
zale@cidet.icmf.inf.cu (A. Gonzalez). been widely studied theoretically in order to describe
1386-9477/00/$ - see front matter ? 2000 Elsevier Science B.V. All rights reserved.
PII: S 1 3 8 6 - 9 4 7 7 ( 9 9 ) 0 0 3 2 7 - 6
2. 92 R. PÃ rez, A. Gonzalez / Physica E 8 (2000) 91–98
e
the optical properties of bulk and low-dimensional ductor, ÿ = Ec =(˜!0 ), and Ec = me4 =(Ä3 ˜2 ) is the
semiconductors. To the best of our knowledge, one of characteristic Coulomb energy.
the most complete studies is the paper [6], in which The only parameter entering Hamiltonian (1) is
a variational approach is used to compute the prop- ÿ, which may be thought of as the inverse of the
erties of two- and tri-dimensional free (not conÿned) conÿnement strength. In the ÿ = 0 limit, we have
excitons with up to ÿve particles. Our work has also a picture of non-interacting fermions whose energy
a close connection with that paper. levels and one-particle quantum states are those
By using the Bethe–Goldstone (BG) equation to of the 2D harmonic oscillator. The electron (hole)
compute the ground-state energies, we are able to rise states are grouped into shells with “magic numbers”
the number of particles in the complex from a max- Ne ; Nh = 2; 6; 12; : : : : As ÿ grows, correlations be-
imum of ÿve in the variational approach [6] to 24. tween particles become more and more important and
Asymmetric systems with Ne = Nh are studied as well. the previous picture is modiÿed.
In the weak conÿnement regime, we can also address One way to go beyond the independent-particle pic-
the question about the stability of the free complexes. ture is the independent-pair approximation in which
And in fact, our results give indications that the free an exact treatment of the two-body correlations is
triexciton and the four-exciton system are unstable (or made. Its main component is the Bethe–Goldstone
weakly bound), whereas the higher complexes are sta- (BG) equation, extensively used in nuclear matter and
ble. These properties have a distinct trace in the optical ÿnite nucleus calculations [8,9].
absorption, and may be conÿrmed by the experiments. The BG equation applies only to fermionic sys-
The present paper is complementary to Ref. [7], in tems. It describes the motion of an independent pair
which a BCS variational approach is used to study of fermions in the system. The rest of the particles ex-
intermediate-size complexes, containing from 12 to erts an indirect in uence on the pair motion through
180 particles. For those sizes where both approaches the Pauli principle. The equation takes the form
overlap, as a rule BCS gives lower energy values for
strong conÿnement, whereas BG gives better energies (T1 + T2 + Q V ) =E ; (2)
in the weak conÿnement regime.
where and label the states of each fermion in the
pair. These states are below the Fermi level. The Ti
2. The Bethe–Goldstone equation are the one-particle terms in the Hamiltonian, V is the
two-body interaction potential (Coulomb), and Q is
We will study a two-dimensional model of Ne elec- a projection operator given by
trons and Nh holes conÿned by a parabolic potential in
the plane of motion, and interacting via pure Coulomb Q = | )( | + | )( |; (3)
;
potentials. Only one conduction and one valence band,
both ideally parabolic, will be considered, and the where the sum runs over states above the Fermi level.
masses of holes and electrons will be supposed to be Q projects a given function onto states over the Fermi
equal. By choosing the scales of distances and ener- level. (r1 r2 | ) is the unsymmetrized product of two
gies as ˜=m!0 and ˜!0 , we get the dimensionless non-interacting one-particle eigenfunctions (we use
Hamiltonian the notation given in Ref. [10]). E is the pair energy,
Ne pi2 r2 Nh pi2 r2 and – its wave function.
H= + i + + i
i=1 2 2 i=1 2 2 Eq. (2) is formally similar to a pair scattering equa-
tion, except for the presence of the projection opera-
Ne 1 Nh 1 Ne Nh 1 tor (and the fact that all of the states in the external
+ÿ + − ; (1) quadratic potential are bound states). The pair wave
i¡j rij i¡j rij i j rij
function is looked for in the form
where the ri are in-plane coordinates for the particles,
rij = |ri − rj |; !0 is the frequency of the conÿning =| )+ C | ) (4)
potential, Ä is the dielectric constant of the semicon- ;
3. R. PÃ rez, A. Gonzalez / Physica E 8 (2000) 91–98
e 93
and the total energy is computed from 700 unknowns each, and 15 nonlinear equations for
(0) the pair energies are solved.
E= + ; (5)
¡
where = E − (0) − (0) . The corrections coming 3. Symmetric (Ne = Nh ) systems
from the BG equations are proven to be equiva-
lent to summing up all the ladder diagrams in the In this section we present the results obtained for
linked-cluster expansion for the energy [11]. symmetric systems, where Ne = Nh = N . The param-
Multiplying Eq. (2) from the left by ( | or ( |, eter ÿ is varied in the interval (0; 2:5).
we get The ÿrst step in our Bethe–Goldstone calculation is
(0) (0) to deÿne ÿlled and empty levels, i.e the Fermi surface.
( + − E )C + ( |V | )C
; To this end, a Hartree–Fock (HF) calculation was im-
plemented. The harmonic-oscillator states were ÿlled
=−( |V | ); (6) in accordance with the HF results. We show them in
spectroscopic (nuclear) notation in Table 1. 2p− , for
(0) (0)
E = + + ( |V | ) example, means the second level with lz = −1. Se , and
Sh refer to the total electron and hole spins respec-
+ ( |V | )C : (7) tively, and L is the total angular momentum (along the
;
z-axis).
Eq. (6) may be seen as a linear system of equa-
tions for the coe cients C , from which we obtain 3.1. The biexciton
C = C (E ). Then, the transcendental equation (7)
is solved for E . For the biexciton, our starting conÿguration is one
One shall note that the Coulomb interaction does in which the ÿrst harmonic oscillator shell is ÿlled for
not change either the angular momentum of the pair both electron and holes (see Table 1). This state has
or the spin of the particles. The matrix elements are zero total angular momentum and total spin. In order
real and have the following properties: to write down the Bethe–Goldstone equations we shall
identify all possible pairs below the Fermi level. In
( |V | ) = ( |V | )=( |V | ): (8)
the e–e and h–h sectors there is only one pair, but we
Due to these properties, the matrix entering the linear have 4 e–h pairs. For a given initial pair, the number of
system is symmetric. ÿnal pair states above the Fermi level depends on the
In order to solve the BG equation we have to iden- number of harmonic oscillator shells, Nshell , included
tify, given an initial pair, all the possible ÿnal states in the calculations. Fig. 1 shows the results for the
above the Fermi level perserving angular momentum energy as a function of ÿ and Nshell . The solid line is
and spin. Then we solve the linear system and the tran- a two-point Padà approximant, which construction is
e
scendental equation to get the pair energy. One shall described below.
take into account that there are three kinds of pairs in A few remarks shall be made at this point. First,
the system, namely e–e, h–h and e–h. In the second the convergence is slow. Second, the BG results do
term of Eq. (5), ¡ means that for identical parti- not exactly reproduce the perturbative energies at
cles (e–e and h–h) a state | ) should be counted only small values of ÿ. It means simply that the charac-
once. For e–h pairs, however, we should take into ac- teristic distances are much smaller than the charac-
count the two possibilities, i.e. | e h ) and | h e ). teristic pair dimensions, and thus the independent
In our calculations, up to 272 harmonic-oscillator pair approximation breaks down. Fortunately, in this
one-particle states (16 shells) are included. Whenever strong-conÿnement regime the energy is dominated
possible, the e–h, spatial inversion and time-reversal by the one-particle energies, which are properly ac-
symmetries are used to reduce the actual number of counted for by the BG approach. Finally, the BG
equations to solve. For example, in the Ne = Nh = 6 energies seem to overestimate the actual binding
problem, 15 systems of linear equations with roughly energies at large ÿ.
4. 94 R. PÃ rez, A. Gonzalez / Physica E 8 (2000) 91–98
e
Table 1
Occupied electron and hole states for the BG calculations
Ne Nh Electrons Holes Se Sh L
2 2 1s2 1s2 0 0 0
1 1
3 3 1s2 1p1
+ 1s2 1p1
− 2 2
0
4 4 1s2 1p1 1p1
+ − 1s2 1p1 1p1
+ − 1 1 0
1 1
5 5 1s2 1p2 1p1
+ − 1s2 1p1 1p2
+ − 2 2
0
6 6 1s2 1p2 1p2
+ − 1s2 1p2 1p2
+ − 0 0 0
12 12 1s2 1p2 1p2 2s2 1d+ 1d−
+ −
2 2 1s2 1p2 1p2 2s2 1d+ 1d−
+ −
2 2 0 0 0
4 2 2 1p1 1p1
1s + − 1s 2 1 0 0
6 2 1s2 1p2 1p2
+ − 1s2 0 0 0
Fig. 1. Convergence of the biexciton energy as a function of the number of harmonic-oscillator shells included in the calculations.
The two-point Padà approximant for the ground-state
e oscillation, contributing with a one to the ground-state
energy is constructed in the following way [12,13]. energy.
The asymptotic expansions The two-point approximant is a rational function
interpolating between Eqs. (9) and (10):
E|ÿ→0 = b0 + b1 ÿ + b2 ÿ2 + O(ÿ3 ); (9)
b2 ÿ2 + p3 ÿ3 + p4 ÿ4
P(ÿ) = b0 + b1 ÿ + : (11)
1 + q1 ÿ + q2 ÿ2
E|ÿ→∞ = a0 ÿ2 + a2 + O(1=ÿ2 ) (10)
The values of the parameters are the following,
are used, where b0 = 4; b1 = −2:50662; b2 = p3 = 0:525372; p4 = −2:06239; q1 = 0:83554 and
−2:92 [7], and a0 = −2:1928 [6], a2 = 1. a0 is the q2 = 0:940527.
ground-state energy of the free biexciton in two di- As for electron quantum dots [13,14] or conÿned
mensions, and a2 comes from the center of mass charged bosons [15], we expect the error of the PadÃ
e
5. R. PÃ rez, A. Gonzalez / Physica E 8 (2000) 91–98
e 95
Fig. 2. HF, an improved BCS, and BG energies of the 6-exciton complex.
Fig. 3. Energies of the N -exciton systems as a function of ÿ.
6. 96 R. PÃ rez, A. Gonzalez / Physica E 8 (2000) 91–98
e
Fig. 4. Energy di erences EN +1 − EN for the smallest clusters studied.
approximant to be lower than a few percents, typically BG estimate slightly fails for small ÿ, as mentioned
3–5%. Thus, our BG estimate seems to reproduce the above. The relative error, however, is not signiÿcant.
actual biexciton energy. And, what is more important, this small-ÿ region cor-
responds to very strong conÿnements, i.e. very small
3.2. N = 3; 4; 5; 6 and 12 dot sizes, in which a basic assumption of our model
like the e ective mass approximation breaks down.
Next, we present results for N = 3; 4; 5; 6 and In the more physically interesting region, ÿ¿1, the
12, computed with Nshell = 16. The occupied BG approximation gives the lowest energies, mean-
harmonic-oscillator states are indicated in Table 1. ing that it takes proper account of two-particle corre-
Note that, in some cases, the HF approximation does lations.
not suggest a unique state, thus we performed BG The BG results are drawn in Fig. 3 in a “scaled”
calculations with di erent occupations, and select the form, i.e. Egs =N 3=2 versus ÿ=N 1=4 . This scaling comes
one corresponding to the minimal energy. For exam- from the dependence b0 ≈ 4 N 3=2 , b1 ≈ −0:96N 5=4 ,
3
ple, in the N = 3 system we performed calculations b2 ≈ −1:65N and a0 ≈ −N for large N [7], but it is
also for a conÿguration very similar to the one given nicely satisÿed even for the smallest systems. In this
in Table 1, but with total momentum L = 2. scaled drawing, the N = 4 cluster clearly distinguishes
To test the quality of our BG calculations in these as the less bound one.
larger systems, we show in Fig. 2 three di erent ap- The results at the largest values of ÿ, i.e. in the
proximations for the energy of the N = 6 complex. weak conÿnement regime, can be taken as indica-
The highest curve corresponds to the HF results. The tions of stability or instability of the free clusters. The
curve denoted BCS is in fact a Lipkin–Nogami calcu- triexciton seems to be unbound (like in three dimen-
lation with exact projection onto the N -pair sector by sions [16]), and the four-exciton system – evidently
means of a Monte-Carlo algorithm [7]. Note that the unbound. However, the larger clusters are likely to
7. R. PÃ rez, A. Gonzalez / Physica E 8 (2000) 91–98
e 97
Fig. 5. Energies of the Ne = 4; Nh = 2, and Ne = 6; Nh = 2 systems.
be stable. The situation may be analogous to nuclei, 4. Asymmetric cases
where there is a small instability island around atomic
number ÿve. We also studied non-symmetric or non-neutral
The di erences EN +1 − EN are shown in Fig. 4. We systems, in which Ne = Nh . In particular, the cases
note that these di erences enter in the expression Ne = 4, Nh = 2 and Ne = 6; Nh = 2. The results for
their ground-state energies are shown in Fig. 5.In a
e h
h = Egap + Ez + Ez + EN +1 − EN (12) non-neutral system, the energy is an increasing func-
tion of ÿ for low ÿ values, as for electrons [14], but
for weaker conÿnement the −ÿ2 biexcitonic contri-
for the frequency of light creating a new electron– bution dominates over the ÿ2=3 repulsion. A biexciton
hole pair in the background of N pairs. Egap is the plus remaining electrons shall be seen at very large ÿ.
semiconductor gap, and Ez h are the electron (hole)
e;
The Ne = 6, Nh = 2 system clearly reveals the change
conÿnement energies in the z-direction. in slope.
As follows from Fig. 4, the absorption peak corre-
sponding to Eq. (12) will exhibit an interesting be-
haviour as a function of the number of photoexcited 5. Conclusions
pairs, N . High values of N can be reached by rising
the laser excitation power. When N is around four, we In the present paper, we have shown that the
shall observe a highly blue-shifted line, followed by a Bethe–Goldstone equations may be used as a power-
red-shifted one as the power is further increased. The ful method to study small conÿned excitonic clusters.
conclusions coming from our oversimpliÿed model Pure electronic quantum dots may be studied as well,
have only a qualitative predictive power. The e ect and external electric and magnetic ÿelds can be eas-
is so pronounced, however, that we expect it may be ily included in the calculations. Larger unbalanced
observed in experiments. systems with only one exciton may be studied to
8. 98 R. PÃ rez, A. Gonzalez / Physica E 8 (2000) 91–98
e
obtain the optical absorption and photoluminescence [3] H. Drexler, D. Leonard, W. Hansen, J.P. Kotthaus,
of small electronic quantum dots. P.M. Petro , Phys. Rev. Lett. 73 (1994) 2252.
Our numerical results suggest a small instability [4] A. Kuther, M. Bayer, A. Forchel, A. Gorbunov,
V.B. Timofeev, F. Schafer, J.P. Reithmaier, Phys. Rev. B 58
island for the free clusters around Ne = Nh = 4. We (1998) 7508.
showed that this instability causes the appearance of [5] E. Dekel, D. Gershoni, E. Ehrenfreund, D. Spektor,
distinct absorption peaks as the laser excitation power J.M. Garcia, P.M. Petro , Phys. Rev. Lett. 80 (1998) 4991.
is raised. [6] J. Usukura, Y. Suzuki, K. Varga, Phys. Rev. B 59 (1999)
More realistic calculations, closely related to the 5652.
[7] B.A. Rodriguez, A. Gonzalez, L. Quiroga, R. Capote,
experimental results [5], are in progress. F.J. Rodriguez, Int. J. Mod. Phys. B 14 (2000) 71.
[8] H.A. Bethe, Ann. Rev. Nucl. Sci. 21 (1971) 93.
[9] A. de Shalit, H. Feshbach, Theoretical Nuclear Physics, Vol.
Acknowledgements 1, Wiley, New York, 1974.
[10] J.P. Blaizot, G. Ripka, Quantum Theory of Finite Systems,
The authors acknowledge support from the Univer- MIT Press, Cambridge, 1986.
[11] B.D. Day, Rev. Mod. Phys. 39 (1967) 719.
sidad de Antioquia, Medellin. Part of this work was [12] A.H. MacDonald, D.S. Ritchie, Phys. Rev. B 33 (1986) 8336.
done during a visit to the Abdus Salam ICTP under the [13] A. Gonzalez, J. Phys.: Condens. Matter 9 (1997) 4643.
Associateship Scheme and the Visiting Young Student [14] A. Gonzalez, B. Partoens, F.M. Peeters, Phys. Rev. B
Programme. Useful discussions with E. Lipparini are 56 (1997) 15 740.
also acknowledged. [15] A. Gonzalez, B. Partoens, A. Matulis, F.M. Peeters, Phys.
Rev. B 59 (1999) 1653.
[16] K. Varga, Y. Suzuki, Phys. Rev. A 53 (1996) 1907.
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