This document summarizes a PhD thesis talk on strongly interacting fermions in optical lattices. The outline discusses chapters on the Hubbard and Heisenberg models, cooling into the Néel state, and imbalanced antiferromagnets. The introduction provides background on realizing the Hubbard model experimentally and the goal of achieving the Néel state. It also discusses imbalanced Fermi gases and how imbalance may affect the Néel state.
Published papers:
Buckyball quantum computer: realization of a quantum gate , M.S. Garelli and F.V. Kusmartsev, European Physical Journal B, Vol. 48, No. 2, p. 199, (2005)
Fast Quantum Computing with Buckyballs, M.S. Garelli and F.V. Kusmartsev, Proceedings of SPIE, Vol. 6264, 62640A (2006)
Theoretical Realization of Quantum Gates Using Interacting Endohedral Fullerene Molecules:
We have studied a physical system composed of two interacting endohedral fullerene molecules for quantum computational purposes. The mutual interaction between these two molecules is determined by their spin dipolar interaction. The action of static magnetic fields on the whole system allow to encode the qubit in the electron spin of the encased atom.
We herein present a theoretical model which enables us to realize single-qubit and two-qubit gates through the system under consideration. Single-qubit operations can be achieved by applying to the system resonant time-dependent microwave fields. Since the dipolar spin interaction couples the two qubit-encoding spins, two-qubit gates are naturally performed by allowing the system to evolve freely. This theoretical model is applied to two realistic architectures of two interacting endohedrals. In the first realistic system the two molecules are placed at a distance of $1.14 nm$. In the second design the two molecules are separated by a distance of $7 nm$. In the latter case the condition $\Delta\omega_p>>g(r)$ is satisfied, i.e. the difference between the precession frequencies of the two spins is much greater than the dipolar coupling strength. This allows us to adopt a simplified theoretical model for the realization of quantum gates.
The realization of quantum gates for these realistic systems is provided by studying the dynamics of the system. In this extent we have numerically solved a set of Schr{\"o}dinger equations needed for reproducing the respective gate, i.e. phase-gate, $\pi$-gate and CNOT-gate. For each quantum gate reproduced through the realistic system, we have estimated their reliability by calculating their related fidelity.
Finally, we present new ideas regarding architectures of systems composed of endohedral fullerenes, which could allow these systems to become reliable building blocks for the realization of quantum computers.
Quantum Nanomagnetism and related phenomena
Professor Javier Tejada presented on topics related to quantum nanomagnetism including: (1) exchange and anisotropy energies that determine magnetic behavior on small scales; (2) single domain particles whose magnetic moments behave collectively; (3) molecular magnets that exhibit quantum tunneling of magnetization and resonant spin tunneling; and (4) phenomena such as quantum magnetic deflagration and potential evidence of superradiance observed in molecular magnet experiments using pulsed magnetic fields. Future directions may explore stabilizing molecular magnets above liquid nitrogen temperatures and their potential applications in memory and quantum computing.
1) The rotational Doppler effect describes a change in the resonant frequency of a system due to relative rotation between the emitter and observer. (Beginning sentence)
2) For magnetic resonance systems like ESR, NMR, and FMR, the resonant frequency is sensitive to magnetic fields and will shift due to the rotational Doppler effect caused by particle rotation.
3) For free magnetic nanoparticles with rotation rates of around 100 kHz, the rotational Doppler shift of around 100 kHz is measurable and on the same order as the linewidth for ESR and FMR, allowing determination of the maximum position with 100 kHz accuracy.
Spin qubits for quantum information processingGabriel O'Brien
This chapter reviews manipulating spin qubits for quantum information processing. It describes the history of spin manipulation techniques dating back to the 1940s. An electron spin can be manipulated faster than a nuclear spin, making it suitable for a quantum processor qubit, while a nuclear spin has a longer coherence time, making it suitable for a quantum memory qubit. The chapter discusses how to manipulate single electron and nuclear spins with alternating magnetic fields and transfer information between them using hyperfine coupling.
This document discusses the spin and orbital angular momentum of photons. It begins by introducing Maxwell's equations and quantizing the electromagnetic field operators. It then derives expressions for the linear momentum and total angular momentum operators in terms of creation and annihilation operators. It shows that the linear momentum operator is constant, while the total angular momentum operator changes in time due to its spin component. Finally, it decomposes the total angular momentum into orbital angular momentum and spin parts.
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.
Ap physics b_-_electric_fields_and_forcesArvenz Gavino
Electric fields are produced by electric charges and describe the interaction between charges. There are two types of charges - positive and negative - and like charges repel while opposite charges attract. An electric field is a vector quantity that describes the force that would be experienced by a hypothetical positive test charge placed at a point in space. The electric field near a point charge is calculated using the equation E = kQ/r^2, where k is a constant, Q is the charge producing the field, and r is the distance from the charge. The direction of the electric field points away from a positive charge and toward a negative charge.
This document provides an overview of plasma physics concepts. It defines an ionized gas and explains how the Saha equation describes ionization equilibrium. It also discusses how an ionized gas can become a plasma if it exhibits collective behavior and quasineutrality. Additionally, it introduces the Maxwellian velocity distribution and kinetic equations like the Boltzmann and Vlasov equations that govern plasma behavior.
Published papers:
Buckyball quantum computer: realization of a quantum gate , M.S. Garelli and F.V. Kusmartsev, European Physical Journal B, Vol. 48, No. 2, p. 199, (2005)
Fast Quantum Computing with Buckyballs, M.S. Garelli and F.V. Kusmartsev, Proceedings of SPIE, Vol. 6264, 62640A (2006)
Theoretical Realization of Quantum Gates Using Interacting Endohedral Fullerene Molecules:
We have studied a physical system composed of two interacting endohedral fullerene molecules for quantum computational purposes. The mutual interaction between these two molecules is determined by their spin dipolar interaction. The action of static magnetic fields on the whole system allow to encode the qubit in the electron spin of the encased atom.
We herein present a theoretical model which enables us to realize single-qubit and two-qubit gates through the system under consideration. Single-qubit operations can be achieved by applying to the system resonant time-dependent microwave fields. Since the dipolar spin interaction couples the two qubit-encoding spins, two-qubit gates are naturally performed by allowing the system to evolve freely. This theoretical model is applied to two realistic architectures of two interacting endohedrals. In the first realistic system the two molecules are placed at a distance of $1.14 nm$. In the second design the two molecules are separated by a distance of $7 nm$. In the latter case the condition $\Delta\omega_p>>g(r)$ is satisfied, i.e. the difference between the precession frequencies of the two spins is much greater than the dipolar coupling strength. This allows us to adopt a simplified theoretical model for the realization of quantum gates.
The realization of quantum gates for these realistic systems is provided by studying the dynamics of the system. In this extent we have numerically solved a set of Schr{\"o}dinger equations needed for reproducing the respective gate, i.e. phase-gate, $\pi$-gate and CNOT-gate. For each quantum gate reproduced through the realistic system, we have estimated their reliability by calculating their related fidelity.
Finally, we present new ideas regarding architectures of systems composed of endohedral fullerenes, which could allow these systems to become reliable building blocks for the realization of quantum computers.
Quantum Nanomagnetism and related phenomena
Professor Javier Tejada presented on topics related to quantum nanomagnetism including: (1) exchange and anisotropy energies that determine magnetic behavior on small scales; (2) single domain particles whose magnetic moments behave collectively; (3) molecular magnets that exhibit quantum tunneling of magnetization and resonant spin tunneling; and (4) phenomena such as quantum magnetic deflagration and potential evidence of superradiance observed in molecular magnet experiments using pulsed magnetic fields. Future directions may explore stabilizing molecular magnets above liquid nitrogen temperatures and their potential applications in memory and quantum computing.
1) The rotational Doppler effect describes a change in the resonant frequency of a system due to relative rotation between the emitter and observer. (Beginning sentence)
2) For magnetic resonance systems like ESR, NMR, and FMR, the resonant frequency is sensitive to magnetic fields and will shift due to the rotational Doppler effect caused by particle rotation.
3) For free magnetic nanoparticles with rotation rates of around 100 kHz, the rotational Doppler shift of around 100 kHz is measurable and on the same order as the linewidth for ESR and FMR, allowing determination of the maximum position with 100 kHz accuracy.
Spin qubits for quantum information processingGabriel O'Brien
This chapter reviews manipulating spin qubits for quantum information processing. It describes the history of spin manipulation techniques dating back to the 1940s. An electron spin can be manipulated faster than a nuclear spin, making it suitable for a quantum processor qubit, while a nuclear spin has a longer coherence time, making it suitable for a quantum memory qubit. The chapter discusses how to manipulate single electron and nuclear spins with alternating magnetic fields and transfer information between them using hyperfine coupling.
This document discusses the spin and orbital angular momentum of photons. It begins by introducing Maxwell's equations and quantizing the electromagnetic field operators. It then derives expressions for the linear momentum and total angular momentum operators in terms of creation and annihilation operators. It shows that the linear momentum operator is constant, while the total angular momentum operator changes in time due to its spin component. Finally, it decomposes the total angular momentum into orbital angular momentum and spin parts.
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.
Ap physics b_-_electric_fields_and_forcesArvenz Gavino
Electric fields are produced by electric charges and describe the interaction between charges. There are two types of charges - positive and negative - and like charges repel while opposite charges attract. An electric field is a vector quantity that describes the force that would be experienced by a hypothetical positive test charge placed at a point in space. The electric field near a point charge is calculated using the equation E = kQ/r^2, where k is a constant, Q is the charge producing the field, and r is the distance from the charge. The direction of the electric field points away from a positive charge and toward a negative charge.
This document provides an overview of plasma physics concepts. It defines an ionized gas and explains how the Saha equation describes ionization equilibrium. It also discusses how an ionized gas can become a plasma if it exhibits collective behavior and quasineutrality. Additionally, it introduces the Maxwellian velocity distribution and kinetic equations like the Boltzmann and Vlasov equations that govern plasma behavior.
Simulation of Magnetically Confined Plasma for Etch Applicationsvvk0
The document describes computational optimization of plasma uniformity in a magnetically enhanced capacitively coupled plasma (CCP) reactor for disk etch applications. Initial simulations using a two-dimensional hybrid plasma equipment model (HPEM) showed non-uniform electron density and radical distributions in a CFP plasma with the magnet placed 125 mm from the substrate. The distance between the magnet and substrate was increased to 113 mm, which improved the uniformity of the electron density, CFx radical densities, and plasma potential above the substrate. Further simulations varying the magnet distance found that plasma density and F radical density decreased with smaller magnet-substrate gaps. The study demonstrates optimization of plasma uniformity through computational modeling of magnetic field and plasma transport parameters.
This document discusses electron spin resonance (ESR), which is similar in principle to nuclear magnetic resonance (NMR). It derives the magnetic moment of an electron's spin and shows that a spin placed in a constant magnetic field will precess around the field at the Larmor frequency. When an additional oscillating magnetic field is applied at the Larmor frequency, the spin will rotate at the Rabi frequency in the rotating frame. This rotation appears as oscillations between the spin states on the Bloch sphere in the lab frame.
Existence of Hopf-Bifurcations on the Nonlinear FKN ModelIJMER
This document discusses Hopf bifurcations, which occur when the stability of an equilibrium point in a nonlinear dynamical system changes as a parameter is varied, resulting in the emergence of periodic solutions. It first provides background on limit cycles and the Hopf bifurcation theorem. It then determines the indicator k, whose sign indicates whether a Hopf bifurcation is supercritical (k<0) or subcritical (k>0). The analysis is extended to three-dimensional systems by reducing them to a two-dimensional system near the equilibrium point. Finally, the document applies this analysis to the Field-Körös-Noyen (FKN) chemical reaction model to determine its supercritical and subcritical Hopf bifurcations.
Spectroscopic ellipsometry is a technique for investigating the optical properties and electrodynamics of materials. It has several advantages over other optical techniques:
1) It provides an exact numerical inversion with no need for Kramers-Kronig transformations, allowing consistency checks.
2) Measurements are non-invasive and highly reproducible as they do not require reference samples.
3) It is very sensitive to thin film properties due to its ability to measure at oblique angles of incidence.
Ellipsometry has been used to study phenomena like superconductivity in cuprates and pnictides by measuring changes in spectral weight, and collective charge ordering in oxide superlattices.
The document discusses the field of magnetism from 1990-2010, including topics such as quantum magnetism, single-domain particles, molecular magnets, magnetic deflagration, and the rotational Doppler effect in magnetic resonance systems which can be used to detect the rotation of nanoparticles.
This document discusses trions, which are charged exciton-electron complexes, and their properties. It covers:
1. Trions can exist in singlet or triplet spin states at low electron densities. Modulation doping is used to control electron density in quantum wells.
2. Trions appear in optical spectra and their binding energy depends on the quantum well width. Magnetic fields affect the trion energy levels and allow determination of electron concentration.
3. At high electron densities, combined exciton-electron and trion-electron processes influence photoluminescence spectra. Trion Zeeman splitting also occurs in magnetic fields.
TWO-POINT STATISTIC OF POLARIMETRIC SAR DATA TWO-POINT STATISTIC OF POLARIMET...grssieee
This document discusses using wavelet transforms to analyze two-point statistics of polarimetric synthetic aperture radar (PolSAR) data. It introduces wavelet variance and kurtosis as metrics that can be applied to PolSAR data transformed using a wavelet frame. It then provides an example of applying this analysis to ALOS PALSAR data over Hawaii's Papau Seamount to characterize sea surface features.
Branislav K. Nikoli
ć
Department of Physics and Astronomy, University of Delaware, U.S.A.
PHYS 624: Introduction to Solid State Physics
http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html
Gravitation al field_equations_and_theory_of_dark matter_and_dark_energySérgio Sacani
1) The document derives new gravitational field equations and establishes a unified theory of dark matter and dark energy.
2) The key ideas are that the energy-momentum tensor need not be divergence-free, and the field equations obey the Euler-Lagrange equation of the Einstein-Hilbert functional under a divergence-free constraint on the metric.
3) The new field equations introduce a scalar potential φ. The scalar potential energy density represents a new type of energy that accounts for dark matter and dark energy based on the distribution of matter.
The document summarizes the metal-insulator transition in VO2, which occurs at 340K. In the metallic phase, VO2 exhibits bad metal behavior with short electron mean free paths. The insulating phase has two possible structures - M1 and M2. M1 involves pairing of V atoms and splitting of orbitals. M2 involves formation of zig-zag V chains. The transition may involve both Mott-Hubbard localization and a Peierls instability driven by soft phonon modes near the R point of the Brillouin zone. Precise values are estimated for the electronic parameters characterizing the insulating M1 phase, including Hubbard U, spin gap Δσ, and charge gap Δρ.
Dr. Mukesh Kumar (NITheP/Wits) TITLE: "Top quark physics in the Vector Color-...Rene Kotze
This document presents a vector color-octet model to explain anomalies observed in top quark physics measurements at the Tevatron collider. The model introduces new vector color-octet resonances that can contribute to top quark pair production and give rise to asymmetries. Observables related to the top quark like the forward-backward asymmetry, charge asymmetry, and single top production are discussed. Constraints on the masses of the new vector resonances from LHC data are also presented. Simulation tools like MadGraph are used to study predictions of the model.
This paper presents the study of the dynamics and control of an axial variable structure satellite (asymmetric platform and an axisymmetric rotor). Inertia moments of the rotor change slowly over time. The dynamics of the satellite is described by using ordinary differential equations with Serret-Andoyer canonical variables. For undisturbed motion, the stationary solutions are found, and their stability is studied. The control law is obtained for the satellite with variable structure on the basis of the stationary solutions. By means of computer numerical simulations, we have shown that the motion of the satellite controlled by founded internal torque is stable.
Instantons and Chern-Simons Terms in AdS4/CFT3: Gravity on the Brane?Sebastian De Haro
1) The document discusses instanton solutions in AdS4/CFT3 duality that probe non-conformal vacuums.
2) It constructs an explicit instanton solution for a conformally coupled scalar field with a quartic interaction in an AdS4 background.
3) Holographically, this instanton describes the decay of the AdS4 vacuum via tunneling, mediated by dressing with a non-zero scalar field. The decay rate is computed.
The document discusses the attitude dynamics of a re-entry vehicle (RV) in planetary atmospheres. It presents the following:
1) Equations of motion for the RV's angular momentum, unit vectors describing its orientation, and acceleration due to aerodynamic and gravitational forces.
2) Equations of motion for the RV's mass center in terms of its velocity, altitude, trajectory inclination angle, and dynamic pressure.
3) Solutions to the undisturbed equations of motion, including an energy integral and general solutions involving elliptic functions for different forms of the restoring aerodynamic moment.
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.
"Squeezed States in Bose-Einstein Condensate"Chad Orzel
1. The document discusses the formation of squeezed quantum states in Bose-Einstein condensates trapped in optical lattices. By slowly ramping up the depth of the optical lattice, the atoms can be prepared in a number-squeezed state.
2. Releasing the atoms from the lattice allows their wavefunctions to overlap and interfere, providing a way to probe the quantum phase state of the atoms. Number-squeezed states are observed to produce interference patterns with higher contrast than coherent states.
3. Variational calculations of the quantum state dynamics during lattice ramping and dephasing agree qualitatively with experimental observations of the transition between coherent and squeezed states.
The document summarizes research on the imbalanced antiferromagnet in an optical lattice. Key points:
1) A mean-field analysis of the Fermi-Hubbard model at half filling predicts a Mott insulator phase transition and Néel antiferromagnetic ordering below a critical temperature.
2) Introducing spin imbalance splits the spin-wave dispersion and leads to three phases in the mean-field phase diagram: Néel, canted, and Ising phases.
3) Topological excitations called merons are predicted at low temperatures, whose unbinding drives a Kosterlitz-Thouless transition lowering the critical temperature compared to mean-field theory.
Simulation of Magnetically Confined Plasma for Etch Applicationsvvk0
The document describes computational optimization of plasma uniformity in a magnetically enhanced capacitively coupled plasma (CCP) reactor for disk etch applications. Initial simulations using a two-dimensional hybrid plasma equipment model (HPEM) showed non-uniform electron density and radical distributions in a CFP plasma with the magnet placed 125 mm from the substrate. The distance between the magnet and substrate was increased to 113 mm, which improved the uniformity of the electron density, CFx radical densities, and plasma potential above the substrate. Further simulations varying the magnet distance found that plasma density and F radical density decreased with smaller magnet-substrate gaps. The study demonstrates optimization of plasma uniformity through computational modeling of magnetic field and plasma transport parameters.
This document discusses electron spin resonance (ESR), which is similar in principle to nuclear magnetic resonance (NMR). It derives the magnetic moment of an electron's spin and shows that a spin placed in a constant magnetic field will precess around the field at the Larmor frequency. When an additional oscillating magnetic field is applied at the Larmor frequency, the spin will rotate at the Rabi frequency in the rotating frame. This rotation appears as oscillations between the spin states on the Bloch sphere in the lab frame.
Existence of Hopf-Bifurcations on the Nonlinear FKN ModelIJMER
This document discusses Hopf bifurcations, which occur when the stability of an equilibrium point in a nonlinear dynamical system changes as a parameter is varied, resulting in the emergence of periodic solutions. It first provides background on limit cycles and the Hopf bifurcation theorem. It then determines the indicator k, whose sign indicates whether a Hopf bifurcation is supercritical (k<0) or subcritical (k>0). The analysis is extended to three-dimensional systems by reducing them to a two-dimensional system near the equilibrium point. Finally, the document applies this analysis to the Field-Körös-Noyen (FKN) chemical reaction model to determine its supercritical and subcritical Hopf bifurcations.
Spectroscopic ellipsometry is a technique for investigating the optical properties and electrodynamics of materials. It has several advantages over other optical techniques:
1) It provides an exact numerical inversion with no need for Kramers-Kronig transformations, allowing consistency checks.
2) Measurements are non-invasive and highly reproducible as they do not require reference samples.
3) It is very sensitive to thin film properties due to its ability to measure at oblique angles of incidence.
Ellipsometry has been used to study phenomena like superconductivity in cuprates and pnictides by measuring changes in spectral weight, and collective charge ordering in oxide superlattices.
The document discusses the field of magnetism from 1990-2010, including topics such as quantum magnetism, single-domain particles, molecular magnets, magnetic deflagration, and the rotational Doppler effect in magnetic resonance systems which can be used to detect the rotation of nanoparticles.
This document discusses trions, which are charged exciton-electron complexes, and their properties. It covers:
1. Trions can exist in singlet or triplet spin states at low electron densities. Modulation doping is used to control electron density in quantum wells.
2. Trions appear in optical spectra and their binding energy depends on the quantum well width. Magnetic fields affect the trion energy levels and allow determination of electron concentration.
3. At high electron densities, combined exciton-electron and trion-electron processes influence photoluminescence spectra. Trion Zeeman splitting also occurs in magnetic fields.
TWO-POINT STATISTIC OF POLARIMETRIC SAR DATA TWO-POINT STATISTIC OF POLARIMET...grssieee
This document discusses using wavelet transforms to analyze two-point statistics of polarimetric synthetic aperture radar (PolSAR) data. It introduces wavelet variance and kurtosis as metrics that can be applied to PolSAR data transformed using a wavelet frame. It then provides an example of applying this analysis to ALOS PALSAR data over Hawaii's Papau Seamount to characterize sea surface features.
Branislav K. Nikoli
ć
Department of Physics and Astronomy, University of Delaware, U.S.A.
PHYS 624: Introduction to Solid State Physics
http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html
Gravitation al field_equations_and_theory_of_dark matter_and_dark_energySérgio Sacani
1) The document derives new gravitational field equations and establishes a unified theory of dark matter and dark energy.
2) The key ideas are that the energy-momentum tensor need not be divergence-free, and the field equations obey the Euler-Lagrange equation of the Einstein-Hilbert functional under a divergence-free constraint on the metric.
3) The new field equations introduce a scalar potential φ. The scalar potential energy density represents a new type of energy that accounts for dark matter and dark energy based on the distribution of matter.
The document summarizes the metal-insulator transition in VO2, which occurs at 340K. In the metallic phase, VO2 exhibits bad metal behavior with short electron mean free paths. The insulating phase has two possible structures - M1 and M2. M1 involves pairing of V atoms and splitting of orbitals. M2 involves formation of zig-zag V chains. The transition may involve both Mott-Hubbard localization and a Peierls instability driven by soft phonon modes near the R point of the Brillouin zone. Precise values are estimated for the electronic parameters characterizing the insulating M1 phase, including Hubbard U, spin gap Δσ, and charge gap Δρ.
Dr. Mukesh Kumar (NITheP/Wits) TITLE: "Top quark physics in the Vector Color-...Rene Kotze
This document presents a vector color-octet model to explain anomalies observed in top quark physics measurements at the Tevatron collider. The model introduces new vector color-octet resonances that can contribute to top quark pair production and give rise to asymmetries. Observables related to the top quark like the forward-backward asymmetry, charge asymmetry, and single top production are discussed. Constraints on the masses of the new vector resonances from LHC data are also presented. Simulation tools like MadGraph are used to study predictions of the model.
This paper presents the study of the dynamics and control of an axial variable structure satellite (asymmetric platform and an axisymmetric rotor). Inertia moments of the rotor change slowly over time. The dynamics of the satellite is described by using ordinary differential equations with Serret-Andoyer canonical variables. For undisturbed motion, the stationary solutions are found, and their stability is studied. The control law is obtained for the satellite with variable structure on the basis of the stationary solutions. By means of computer numerical simulations, we have shown that the motion of the satellite controlled by founded internal torque is stable.
Instantons and Chern-Simons Terms in AdS4/CFT3: Gravity on the Brane?Sebastian De Haro
1) The document discusses instanton solutions in AdS4/CFT3 duality that probe non-conformal vacuums.
2) It constructs an explicit instanton solution for a conformally coupled scalar field with a quartic interaction in an AdS4 background.
3) Holographically, this instanton describes the decay of the AdS4 vacuum via tunneling, mediated by dressing with a non-zero scalar field. The decay rate is computed.
The document discusses the attitude dynamics of a re-entry vehicle (RV) in planetary atmospheres. It presents the following:
1) Equations of motion for the RV's angular momentum, unit vectors describing its orientation, and acceleration due to aerodynamic and gravitational forces.
2) Equations of motion for the RV's mass center in terms of its velocity, altitude, trajectory inclination angle, and dynamic pressure.
3) Solutions to the undisturbed equations of motion, including an energy integral and general solutions involving elliptic functions for different forms of the restoring aerodynamic moment.
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.
"Squeezed States in Bose-Einstein Condensate"Chad Orzel
1. The document discusses the formation of squeezed quantum states in Bose-Einstein condensates trapped in optical lattices. By slowly ramping up the depth of the optical lattice, the atoms can be prepared in a number-squeezed state.
2. Releasing the atoms from the lattice allows their wavefunctions to overlap and interfere, providing a way to probe the quantum phase state of the atoms. Number-squeezed states are observed to produce interference patterns with higher contrast than coherent states.
3. Variational calculations of the quantum state dynamics during lattice ramping and dephasing agree qualitatively with experimental observations of the transition between coherent and squeezed states.
The document summarizes research on the imbalanced antiferromagnet in an optical lattice. Key points:
1) A mean-field analysis of the Fermi-Hubbard model at half filling predicts a Mott insulator phase transition and Néel antiferromagnetic ordering below a critical temperature.
2) Introducing spin imbalance splits the spin-wave dispersion and leads to three phases in the mean-field phase diagram: Néel, canted, and Ising phases.
3) Topological excitations called merons are predicted at low temperatures, whose unbinding drives a Kosterlitz-Thouless transition lowering the critical temperature compared to mean-field theory.
The document discusses Bose-Einstein condensation in weakly interacting gases. It defines BEC as a phase of matter formed by bosons cooled below a critical temperature into a coherent quantum state. It describes how scientists achieved BEC through techniques like laser trapping and cooling atoms with lasers, magnetic confinement with anti-Helmholtz coils, and evaporative cooling to overcome the Doppler limit. It notes the landmark experiments by Cornell, Wieman, and Ketterle in 1995 that first produced BEC in rubidium and sodium vapors, earning them the 2001 Nobel Prize.
1) The document discusses Bose-Einstein condensation (BEC), a state of matter that can be created by cooling a dilute gas of bosons to near absolute zero. This causes the bosons to occupy the lowest quantum state and form a condensate with superfluid properties.
2) Creating a BEC involves using laser cooling and evaporative cooling techniques to reduce the temperature of trapped atoms. When the de Broglie wavelength of the atoms is comparable to their spacing, they form a BEC below a critical temperature.
3) The document also briefly discusses fermionic condensates formed by pairs of fermions, and how ultra-slow light can be achieved by passing light through a
There are five states of matter: solids, liquids, gases, plasmas, and Bose-Einstein condensates. Solids have tightly packed particles that vibrate in a fixed position and definite shape and volume. Liquids also have tightly packed particles, but they can slide over one another and have indefinite shape but definite volume. Gases have particles far apart that move freely with indefinite shape and volume. Plasmas are ionized gases that conduct electricity and are affected by magnetic fields. Bose-Einstein condensates occur at temperatures near absolute zero where atoms can no longer be distinguished as individuals and must act identically.
The 5th state of matter - Bose–einstein condensate y11hci0255
The document discusses Bose-Einstein condensates (BECs), a state of matter that occurs when bosons are cooled to near absolute zero. BECs have unusual properties like flowing without friction. They were first theorized in the 1920s but were not produced in a lab until 1995 using lasers, magnets and evaporative cooling. Potential applications of BECs include precision etching due to their coherent properties when formed into beams.
Bose-Einstein condensates are a state of matter formed by cooling a gas to near absolute zero, causing the atoms to behave as a single super atom. They were first theorized in the 1920s but were not produced in a lab until 1995. BECs represent a fifth phase of matter beyond solids, liquids, gases and plasma, with the atoms becoming indistinguishable from one another and flowing without friction. Potential applications of BECs include precision etching and manipulating light at slow speeds.
Talk given at Physics@FOM Veldhoven 2009. Powerpoint source and high-resolution images available upon request.
Journal reference: Phys. Rev. A 77, 023623 (2008) [arXiv:0711.3425]
Electron configurations 1a presentationPaul Cummings
The document discusses electron configuration, which is the arrangement of electrons around an atom's nucleus. It describes the quantum mechanical model developed in the 1920s using quantum numbers like the principal quantum number n, angular momentum quantum number l, and magnetic quantum number m. Electrons occupy specific orbitals within energy sublevels based on these quantum numbers. There are rules for building electron configurations, including the Aufbau principle, Pauli exclusion principle, and Hund's rule. Electron configurations are written using standard or shorthand notation.
Talk given at Cambridge DAMTP on Friday, 20 June 2008. Describes recent work on understanding what is necessary to embed accelerating cosmology in higher-dimensional theory.
1. The document discusses quantum spin systems in copper minerals, focusing on geometrically frustrated lattices that can exhibit novel quantum phases like spin liquids.
2. It summarizes experiments on the S=1/2 kagome lattice material vesignieite, which shows plateaus in its magnetization curve and spin liquid behavior.
3. Future plans include further investigating the magnetic state of a distorted vesignieite material around half saturation and synthesizing larger crystals of the perfect kagome lattice vesignieite.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
The document provides an overview of the electronic band structure of solids from both the Sommerfeld and Bloch perspectives. It discusses key concepts such as:
1) Quantum numbers that label the eigenenergies and eigenfunctions of the Hamiltonian.
2) Bloch's theorem which describes the wavefunction of an electron as a plane wave modulated by a periodic function with the periodicity of the crystal lattice.
3) The band structure and energy levels that arise from Bloch's treatment, which has no simple explicit form unlike Sommerfeld's free electron model.
4) Key differences between the Sommerfeld and Bloch approaches regarding concepts like the density of states, Fermi surface, and wavefunctions
Hidden Symmetries and Their Consequences in the Hubbard Model of t2g ElectronsABDERRAHMANE REGGAD
(1) The Hubbard model for t2g electrons in transition metal oxides possesses novel hidden symmetries that have significant consequences.
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Similar to Strongly interacting fermions in optical lattices (20)
2. Outline
• Topics covered in this talk:
Chapter 2: introduction to Hubbard and Heisenberg models
Chapter 3: cooling into the Néel state
Chapter 4: imbalanced antiferromagnets in optical lattices.
• Topics in the thesis but not covered in this talk:
Chapter 1: Introduction (mainly historical)
Chapter 6: BEC-BCS crossover for fermions in an optical lattice
Chaoter 7: Analogy of the BEC-BCS crossover for bosons
Juicy details
2
3. Introduction
• Fermions in an optical lattice
• Described by the Hubbard model
• Realised experimentally [Esslinger ’05], fermionic Mott
insulator recently seen [Esslinger ’08, Bloch ’08]
• There is currently a race to create the Néel state
— How to achieve the Néel state in an optical lattice?
• Imbalanced Fermi gases
• Experimentally realised [Ketterle ’06, Hulet ’06]
• High relevance to other areas of physics (particle physics,
neutron stars, etc.)
— How does imbalance affect the Néel state?
3
4. Fermi-Hubbard Model
P P P
H = −t c† cj 0 ,σ
j,σ +U c† c† cj,↓ cj,↑
j,↑ j,↓
σ hjj 0 i j
Sums depend on:
Filling N
Dimensionality (d=3)
On-site interaction: U Tunneling: t
Consider nearest-neighbor tunneling only.
The positive-U (repulsive) Fermi-Hubbard Model, relevant
to High-Tc SC
4
5. Quantum Phases of the Fermi-Hubbard Model
• Positive U (repulsive on-site interaction):
Conductor
1
Filling Fraction
Band Insulator
Conductor
0.5
Conductor Mott Insulator (need large U)
0
• Negative U: Pairing occurs — BEC/BCS superfluid at all fillings.
5
6. Mott insulator: Heisenberg Model
• At half filling, when U À t and kB T ¿ U we are deep in the Mott phase.
hopping is energetically supressed
only spin degrees of freedom remain (no transport)
• Integrate out the hopping fluctuations, then the Hubbard model reduces to the
simpler Heisenberg model:
J X
H= S j · Sk
2
hjki
Spin ½ operators: S = 1 σ z 1³ † †
´
2 Si = ci,↑ ci,↑ − ci,↓ ci,↓
2
Si =c† ci,↓
+
i,↑
Si =c† ci,↑
−
i,↓
4t2
Superexchange constant (virtual hops): J=
U
6
7. Néel State
• The Néel state is the antiferromagnetic ground state for J > 0
• Néel order parameter 0 ≤ h|n|i ≤ 0.5
measures amount of “anti-alignment”: 0.5
nj = (−1)j hSj i
〈n〉
h|n|i
• Below some critical temperature Tc,
we enter the Néel state and h|n|i
becomes non-zero.
0
0 T Tc
7
8. How to reach the Néel state: Step 1
Start with trapped 2-component fermi gas of cold atoms. The entropy is:
T
2
SFG = N kB π
TF
Total number of particles: N
Fermi temperature in the harmonic trap: kB TF = (3N )1/3 ~ω
Trapping potential:
1
V = mω 2 r2
2
8
9. How to reach the Néel state: Step 2
Adiabatically turn on the optical lattice. We enter the Mott phase: 1 particle per site.
Entropy remains constant: temperature changes!
9
10. How to reach the Néel state: Step 3
Final temperature is below Tc : we are in the Néel state. The entropy remained
constant throughout.
To reach the Néel state:
Prepare the system so
that the initial entropy in
the trap equals the final
entropy below Tc in the
lattice:
SFG (Tini ) = SLat (T ≤ Tc )
What is the entropy of the Néel state in the lattice?
10
11. Mean-field theory in the lattice
• Mott insulator:
J X
H= S j · Sk
2
hjki
• Perform a mean-field analysis about the equilibrium value of the staggered
magnetisation hni :
J X½ ¾
H' (−1)i nSj + (−1)j nSi − J n2
2
hiji
∙ ¸
Jz 2 1 β|n|Jz 1
• Landau free energy: fL (n) = n − ln cosh( ) − ln(2).
2 β 2 β
Self-Consistency: Entropy:
¯
∂fL (n) ¯
¯
hni ∂fL (hni)
=0 S = −N
∂n ¯n=hni ∂T
11
12. Mean-field theory results
• Entropy in the lattice:
ln(2) Mott
Lattice depth
6ER ,
0.6
Tc = 0.036 TF
Cooling
0.4
S/NkB
l
Né e
0.2
Lattice Entropy
Trap Entropy
0.0
0.02 0.04 0.06 0.08
T/TF
Heating
kB Tc = 3J/2
12
13. Improved 2-site mean-field theory
• Improve on “single-site” mean-field theory by including the interaction between two
sites exactly:
ln(2)
• Incorporate correct Mott
0.6
low-temperature and
critical behaviour
Example: B 0.4
N éel
S/Nk
40
K atoms with
a lattice depth
of 8ER :
0.2 Lattice, MFT
Tc = 0.012 TF Lattice, fluc.
Trap
0.0
Tini = 0.059 TF 0.02 0.04 0.06 0.08
T/T
F
13
14. Heisenberg Model with imbalance
• Until now, N↑ = N↓ = N/2
• What happens if N↑ 6= N↓ — spin population imbalance?
• This gives rise to an overal magnetization m = (0, 0, mz )
N↑ − N↓ (fermions: S = 1 )
mz = S 2
N↑ + N↓
• Add a constraint to the Heisenberg model that enforces hSi = m
J X X
H= S j · Sk − B · (Si − m)
2
hjki i
Effective magnetic field (Lagrange multiplier): B
14
15. Mean field analysis
• J > 0 ⇒ ground state is antiferromagnetic (Néel state)
Two sublattices: A, B
A(B) A(B) A(B)
• Linearize the Hamiltonian Si = hSi i + δSi
B A B
hSA i + hSB i
• Magnetization: m= A B A
2
B A B
A B
hS i − hS i
• Néel order parameter: n=
2 A B A
• Obtain the on-site free energy f (n, m; B)
subject to the constraint ∇B f = 0 (eliminates B)
15
16. Phase Diagram in three dimensions
1.5
n=0
m
Canted:
1 n
kB T/J
0.5 n 6= 0 m
Ising:
n
0
0 0.1 0.2 0.3 0.4 0.5
mz
0.5
0.4
n
〈n〉
0.2
0.0
Add imbalance 0.0 0.2
0 mz
0.3
0.6 0.4
0 0.9
0 Tc kB T J 1.2
T
16
17. Spin waves (magnons)
dS i
• Spin dynamics can be found from: = [H, S]
dt ~
No imbalance: Doubly 0.5
degenerate antiferromagnetic
dispersion
0.4
• Imbalance splits the
¯ ω/J z
0.3
degeneracy:
0.2 Gap:
h
Ferromagnetic (Larmor
magnons: ω ∝ k2 0.1 precession
of n)
0 π π
Antiferromagnetic
− 0
magnons: ω ∝ |k| 2 kd 2
17
18. Long-wavelength dynamics: NLσM
• Dynamics are summarised a non-linear sigma model with an action
Z Z ½ µ ¶2
dx 1 ∂n(x, t)
S[n(x, t)] = dt ~ − 2Jzm × n(x, t)
dD 4Jzn2 ∂t
2
¾
Jd
− [∇n(x, t)]2
• lattice spacing: d = λ/2 2
• number of nearest neighbours: z = 2D
• local staggered magnetization: n(x, t)
• The equilibrium value of n(x, t) is found from the Landau free energy:
Z ½ 2 ¾
dx Jd 2
F [n(x), m] = [∇n(x)] + f [n(x), m]
dD 2
• NLσM admits spin waves but also topologically stable excitations in
the local staggered magnetisation n(x, t).
18
19. Topological excitations
• The topological excitaitons are vortices; Néel vector has an out-of-
easy-plane component in the core
• In two dimensions, these are merons:
• Spin texture of a meron:
⎛ p ⎞
n 2 − [n (r)]2 cos φ
p z
n = ⎝nv n2 − [nz (r)]2 sin φ⎠
nz (r) nv = 1
n
• Ansatz: nz (r) =
[(r/λ)2 + 1]2
• Merons characterised by:
Pontryagin index ±½
Vorticity nv = ±1
Core size λ nv = −1
19
20. Meron size
• Core size λ of meron found by plugging the spin texture into F [n(x), m]
and minimizing (below Tc):
1.5 Meron core size
6
1 Λ
kB T/J
Merons 4
d 2
0.5 present 1.5
1.2
0 0.9
0 0 kB T J
0 0.1 0.2 0.3 0.4 0.5 0.1 0.6
mz 0.2
0.3 0.3
mz 0.4
• At low temperatures, the energy of a single meron diverges
logarithmically with the system area A as
Jn2 π A
ln 2
2 πλ
merons must be created in pairs.
20
21. Meron pairs
Low temperatures:
A pair of merons with opposite vorticity, has a finite energy since
the deformation of the spin texture cancels at infinity:
Higher temperatures:
Entropy contributions overcome the divergent energy of a single
meron
The system can lower its free energy through the proliferation of
single merons
21
22. Kosterlitz-Thouless transition
• The unbinding of meron pairs in 2D signals a KT transition. This
drives down Tc compared with MFT:
1 MFT in 2D
0.8 0.06
0.6
kB T/J
kB T/J
0.04
n 6= 0
0.4
KT transition 0.02
0.2
0 0
0 0.05 0.1
0 0.2 0.4
mz
mz
• New Tc obtained by analogy to an anisotropic O(3) model (Monte
Carlo results: [Klomfass et al, Nucl. Phys. B360, 264 (1991)] )
22
23. Experimental feasibility
• Experimental realisation:
Néel state in optical lattice: adiabatic cooling
Imbalance: drive spin transitions with RF field
• Observation of Néel state
Correlations in atom shot noise
Bragg reflection (also probes spin waves)
• Observation of KT transition
Interference experiment [Hadzibabic et al. Nature 441, 1118 (2006)]
In situ imaging [Gericke et al. Nat. Phys. 4, 949 (2008); Würtz et al.
arXiv:0903.4837]
23
24. Conclusion
• Néel state appears to be is experimentally achievable (just) by adiabatically
ramping up the optical lattice – accurate determination of initial T is crucial.
• The imbalanced antiferrromagnet is a rich system
spin-canting below Tc
ferro- and antiferromagnetic properties, topological excitations
in 2D, KT transition significantly lowers Tc compared to MFT results
models quantum magnetism, bilayers, etc.
possible application to topological quantum computation and information:
merons possess an internal Ising degree of freedom associated to
Pontryagin index
• Future work:
incorporate equilibrium in the NLσM action
gradient of n gives rise to a magnetization (can possibly be used to
manipulate topological excitations)
effect of imbalance on initial temperature needed to achieving the canted
Néel state by adiabatic cooling
24
25. Free energy and Tc for imbalanced AFM
• On-site free energy:
Jz 2
f (n, m; B) = (n − m2 ) + m · B
2 ∙ µ ¶ µ ¶¸
1 |BA | |BB |
− kB T ln 4 cosh cosh
2 2kB T 2kB T
where BA (B) = B − Jzm ± Jzn
• Constraint equation:
∙ µ ¶ µ ¶¸
1 BA |BA | BB |BB |
m= tanh + tanh
4 |BA | 2kB T |BB | 2kB T
• Critical temperature: Jzmz
Tc =
2kB arctanh(2mz )
• Effective magnetic field below the critical temperature: B = 2Jzm
25
26. Finding KT transition: Anisotropic O(3) model
• Dimensionless free energy of the anisotropic O(3) model [Klomfass et al, Nucl.
Phys. B360, 264 (1991)] :
X X
βf3 = −β3 Si · Sj + γ3 (Si )2
z
hi,ji i
• KT transition:
1.0
0.8
g3êH1+g3L
0.6
0.4
0.2
0.0
1.0 1.2 1.4 1.6 1.8 2.0
b3
β3
• Numerical fit: γ3 (β3 ) = exp[−5.6(β3 − 1.085)].
β3 − 1.06
26
27. Finding KT transition: Analogy with the anisotropic O(3) model
• Landau free energy:
βJ X X
βF = − ni · nj + β f (m, ni , β)
2 i
hI,ji
βJn2 X 2
X
'− Si · Sj + βn γ(m, β) (Si )2
z
2 i
hI,ji
3.0 Numerical fit parameter
2.5 2
Mapping of our model to 0.0
Anisotropic O(3) model: 2.0 β =
1/J 0.2
g Hm, bLêJ
1.5
Jβn2 0.4
β3 =
2 1.0 0.6
2β3 0.8
γ3 = γ(m, β) 0.5
Tc
J
0.0
0.0 0.1 0.2 0.3 0.4 0.5
m
27
28. 2-Site Mean-Field Theory
• Improve on standard mean-field approach by including 2 sites exactly:
H = JS1 · S2 + J(z − 1)|n|(Sz − Sz ) + J(z − 1)n2
1 2
• First Term: Treats interactions
between two neighboring sites
exactly,
1 2
• Second Term: Treats interactions
between other neighbors within
mean-field theory
28
29. 2-site mean-field theory: Néel order parameter
0.5
Comparison with 1-site mean-
field theory:
0.4
• Depletion at zero temperature
due to quantum fluctuations 0.3
〈 n〉
0.2
0.1
2-site
1-site
0
0 0.5 1 1.5
k BT/J
• Lowering of Tc:
kB
Tc ' 1.44
J
29
30. Entropy in the lattice: Three temperature regimes
• High T: 2-site mean field theory result
∙ 2
¸
3J
S(T À Tc ) = N kB ln(2) − 2
64kB T 2
• Low T: entropy of magnon gas
µ ¶3
4π 2 k T
S(T ¿ Tc ) = N kB √B
45 2 3Jhni
• Intermediate T: non-analytic critical behaviour
T − Tc
S(T = Tc ) = S(Tc ) ± A ± |t|dν−1 t= → 0±
Tc
Where, from renormalization group theory [Zinn-Justin]
d = 3, ν = 0.63, A+/A− ' 0.54
•Tc: from quantum Monte-Carlo [Staudt et al. ’00]: Tc = 0.957J/kB
30
31. Entropy in the lattice, T>Tc
•Function with the correct properties above Tc:
∙µ ¶κ ¸
S(T ≥ Tc ) T − Tc κTc
' α1 −1+ + ln(2)
NkB T T
First term: Critical behavior
Other terms: To retrieve correct high-T limit of 2-site theory.
→ Found by expanding critical term and subtracting all terms of lower order
than in T than high-T expression, which is ∼ 1/T 2 .
•Result: 3J 2
κ = 3ν − 1 ' 0.89 α1 = 2 2
(32κ(κ − 1)kB Tc )
31
32. Entropy in the lattice, T<Tc
• Function for with the correct properties below Tc:
∙µ ¶κ ¸
S(T ≤ Tc ) Tc − T T κ(κ − 1) T 2 T3 T4
= −α2 −1+κ − 2
+ β0 3 + β1 4
N kB Tc Tc 2 Tc Tc Tc
First term and last term: Critical behavior and continuous
interpolation with T>Tc result.
Other terms: Retrieve low-T behavior of magons, again found by
expanding critical term and subtracting all terms of lower order than T 3.
32
34. Maximum number of particles in the trap
For smooth traps, tunneling is not site-dependent, overfilling leads to
double occupancy:
Destroys Mott-
insulator state in
the centre!
The trap limits the number of particles to avoid double occupancy:
µ ¶3/2
4π 8U
N ≤ Nmax = Example:
3 mω2 λ2
40 K
atoms
with a lattice
depth of 8ER
and λ = 755 nm
⇒ Nmax ' 3 × 106
34