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E' possibile controllare la corrente di calore?
 

E' possibile controllare la corrente di calore?

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Seminario del Prof. Giulio Casati

Seminario del Prof. Giulio Casati
25 marzo 2010 in occasione del primo MicroEnergy Day

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  • Discuss the possibility to derive macroscopic eqs. of heat transport from dynamical eqs of motion And in particular the possibility to control heat current as we do with electric current
  • The possibilit to derive Fourier law from QM. calls directly in question the issue of quantum chaos. In this connection QM has no exp instability, a property at the heart of classical chaos. This make questionable the possibility To derive fourier law from QM.
  • The possibilit to derive Fourier law from QM. calls directly in question the issue of quantum chaos. In this connection QM has no exp instability, a property at the heart of classical chaos. This make questionable the possibility To derive fourier law from QM.
  • The possibilit to derive Fourier law from QM. calls directly in question the issue of quantum chaos. In this connection QM has no exp instability, a property at the heart of classical chaos. This make questionable the possibility To derive fourier law from QM.
  • Consider a Ising chain of L spins with coupling constant Q subject to a uniform magnetic field, with open boundaries. If hz = 0, the Hamiltonian (1) corresponds to the Ising chain in a transversal magnetic field. In this case the system is integrable as (1) can be mapped into a model of free fermions through standard Wigner-Jordan transformations.
  • In the harmonic limit, the eqs. of motion, without thermostats, have plane wave solutions with dispersion relations.. So that allowed solutions are in the phonon bands.. Consider the harmonic, inhomogeneous chain: in order to propagate through the system, a wave must satisfy both dispersion relations. If D1 different from D only a fraction of waves can propagate.. If the difference is large enough then waves from thermostats are reflected back from the central part of the chain..
  • THE TEMPERATURE PROFILE CHANGES AS D1-D IS INCREASED UNTIL THE CENTRAL REGION BEHAVES AS AN INSULATOR, THE LEFT AND RIGHT REGIONS ARE THERMALIZED AT T1 AND T2. The change of D1 can induce a conductor insulator transition.
  • A strongly nonlinear region is sandwiched between two weakly anharmonic left and right domains. In the central part, due to thermal gradient, the effective phonons frequencies change in space in a way that depends on the orientation of the gradient.
  • Trimethyl cyclopentadienyl platinum is deposited to achieve non uniform mass distribution
  • Scanning electron microscope image (SEM) Transmission electron microscope (TEM)
  • Born in Tallin, he graduated in medicine in 1802 at Gottingen university 1°legge: il contatto tra due metalli diversi alla stessa temperatura fa sì che si stabilisca una differenza di potenziale caratteristica della natura dei metalli che non dipende dall'estensione del contatto (effetto Volta) Fellow citizien-the Volta effect does correspond to a weak electric potential difference developed by the contact of different metals. Nowadays, this is often known as a contact potential difference. This effect was first discovered by Alessandro Volta
  • Amerigon estimates about a 2% reduction in fuel consumption (Bell 2008) because 1) in cooler mode the cabin air conditioner is used less and 2) in heater mode it is more efficient than the cabin heater.
  • The challenge lies in the fact that S , σ, and k are interdependent—changing one alters the others, making optimization extremely difficult. The only way to reduce k without affecting S and σ
  • The challenge lies in the fact that S , σ, and k are interdependent—changing one alters the others, making optimization extremely difficult. The only way to reduce k without affecting S and σ
  • The challenge lies in the fact that S , σ, and k are interdependent—changing one alters the others, making optimization extremely difficult. The only way to reduce k without affecting S and σ
  • due to the equivalence between electric and chemical potentials [6], it is sufficient to study non-equilibrium effects due to the chemical potential difference only.
  • Second law does not impose upper bound to ZT
  • This model is not suitable for the engine. In spite of the abstract nature of the model, the above open the possibility for a theoretical understanding of the basic microscopic requirements that a classical dynamical system must fulfil in order to lead to a high figure of merit and therefore to thermoelectric efficiency which, in principle, is arbitrarily close to Carnot’s. a heuristic hint taken from [10] might suggest that inter-particle interaction may led to higher ZT. Therefore we consider a 1D hard-point gas
  • The model is composed of two thermochemical reservoirs of ideal gas of equal point particles connected by two one-dimensional wires indexed by i1,2. In the middle of each wire we place a deterministic and energy conserving scatterer, which either reflects or transmits the particle depending on its kinetic energy . This behavior is completely described by the transmission function i0,1 of the ith scatterer.

E' possibile controllare la corrente di calore? E' possibile controllare la corrente di calore? Presentation Transcript

  • CENTER FOR NONLINEAR AND COMPLEX SYSTEMS Como - Italy The purpose of this talk is to understand the properties of the heat Transport from the microscopic dynamical eqs. of motion In particular if we can control the hear current as we do for example With the electric current
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  • Providing a sustainable supply of energy to the world’s population will become a major societal problem for the 21 st century as fossil fuel supplies decrease and world demand increases. Thermoelectric phenomena are expected to play an increasingly important role in meeting the energy challenge of the future. … a newly emerging field of low-dimensional thermoelectricity, enabled by materials nanoscience and nanotechnology. Dresselhaus et al: Adv. Mater. 2007
  • ‘ It seems there is no problem in modern physics for which there are one record as many false starts and as many theories which overlook some essential features as in the problem of the thermal conductivity of non conducting crystals’ R. E. PEIERLS
  • J. B. FOURIER 1808 - Attempt to explain the thermal gradient inside the earth
  • QUESTION: Can one derive the Fourier law of heat conduction from dynamical equations of motion without any statistical assumptions? Normal transport
  • REMARK: Randonmnes is an essential ingredient of thermal conductivity deterministically random systems are tacitly required by the transport theory
  • THE DING-A -LING MODEL
  • THE DING-A -LING MODEL
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  • J. B. FOURIER 1808 - Attempt to explain the thermal gradient inside the earth
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  • Nature, 7 june 1984
  • FOURIER LAW IN QUANTUM MECHANICS?
  • FOURIER LAW IN QUANTUM MECHANICS? Deterministic chaos appear to be an important ingredient for Fourier law. No exponential instability in Quantum Mechanics
  • FOURIER LAW IN QUANTUM MECHANICS? Deterministic chaos appear to be an important ingredient for Fourier law. No exponential instability in Quantum Mechanics Terra Incognita
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  • SIGNATURES OF QUANTUM CHAOS The distribution of energy levels spacings obeys the Wigner-Dyson surmise RANDOM MATRIX THEORY
  • Lettere al Nuovo Cimento 28 (1980) 279
  • G. Monasterio, T. Prosen, G.C. EPL (2005)
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  • Plane waves solutions Dispersion relations Phonon band
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  • INTERNAL TEMPERATURE PROFILE
  • In nonlinear systems the position of the band depends on the temperature
  • p.r.l. 88, (2002)
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  • For uniform mass distribution, thermal conduction is symmetric
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  • All measurements showed that a higher thermal conductance was observed when heat flowed from the high-mass region to the low -mass region
  • NEGATIVE DIFFERENTIAL THERMAL CONDUCTIVITY
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  • Volta effect: an electric potential difference is developed by the contact of two different metals at the same temperature. A.Volta (Como)
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  • Powerful heat . In 1822, the Estonian–German physicist Thomas Johann Seebeck discovered that if heat is applied across the junction of two wires, a current is generated.
  • Abram Ioffe, 1950s : doped semiconductors have large thermoelectric effect The initial excitement about semiconductors in 1950 was due to their promise, not in electronics but in refrigeration . The discovery that semiconductors can act as efficient heat pumps led to expectations of environmentally benign solid state home refrigerators and power generators
  • Here comes another talk on fundamental limits
  • Thermoelectricity concerns the conversion of temperatures differencies into electrical potential or viceversa It can be used to perform useful electrical work or to pump heat from cold to hot place, thus performing refrigeration
  • The field of thermoelectric advanced rapidly in the 1950s when the basic science of thermoelectric materials became well established, the thermoelectric material Bi 2 Te 3 was developed for commercialization, thus launching the thermoelectric industry Thermoelectric (Peltier) refrigerators have poor efficiency compared to compressor-based refrigerators.
  • During this 1960–1995 period , the thermoelectric field received little attention from the worldwide scientific research community. Nevertheless, the thermoelectric industry grew slowly and steadily, by finding niche applications: space missions laboratory equipment medical applications where cost and energy efficiency were not as important as energy availability, reliability, predictability, and the quiet operation of equipment.
  • devices used for cooling, and for power generation Voyager mission to Jupiter and Saturn, here at its launch in 1977.
  • Thermoelectric devices provide on board power to operate radio signal trasmitters, on board computers, gyros and navigational systems, spectrometers and many other scientific instruments. These power generating systems can operate unattended, maintenance free, for many years NASA uses thermoelectric because key advantages include high reliability, small size and no noise.
    • Radioisotope Thermoelectric Generators (RTGs) is the only
    • technology (so far) capable of providing electrical power for
    • deep-space missions including:
    • - Voyagers I and II,
    • Galileo, Cassini, and the New Horizons mission to Pluto .
    (The RTG is the black, cylindrical finned object at lower left). New Horizon spacecraft to Pluto
  • This RTG consists of hundreds of individual silicongermanium (SiGe) thermocouples arranged around graphite-encased plutonium. One such RTG weighs about 55 kg and produces about 240 Watts of electricity at about 7% conversion efficiency the radioisotope heat source half-life is 87 years. Even in the harsh environment of space these thermocouples have accumulated more than a trillion device-hours without a single failure.
  • - Key step 1990 : first significant consumer product, picnic basket cooler - Thermoelectric industry stable and growing
  • Thermoelectric coolers/heaters by “Amerigon“(USA)
  • -2 milion climate control seats in 2006 Estimate 2% reduction in fuel consumption -World market in 2010 up to 1 billion US$
  • The suitability of a thermoelectric material for energy conversion or electronic refrigeration is evaluated by
  • The ZT figure of merit The suitability of a thermoelectric material for energy conversion or electronic refrigeration is evaluated by
  • The conversion efficiency is given by
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  • In five decades the ZT of semiconductors has increased only marginally, from about 0.6 to 1 A. Majumdar Science 303, 777(2004)
  • A ZT value > 3 would make solid –state home refrigerators economically competitive with compressor-based refrigerators
  • Metals are poor thermoelectric materials because of low Seebeck coefficient and large electronic contribution to thermal conductivity. A ZT value > 3 would make solid –state home refrigerators economically competitive with compressor-based refrigerators
  • Metals are poor thermoelectric materials because of low Seebeck coefficient and large electronic contribution to thermal conductivity. Insulators have large Seebeck coefficient but have too few carriers which result in large electrical resistivity A ZT value > 3 would make solid –state home refrigerators economically competitive with compressor-based refrigerators
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  • ZT =1.5
  • Mass ratio
  • R radius of scatterers
  • Heterogeneous channel
  • If If and
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  • When the number d int of internal degrees of freedoms of moving particles become large
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  • G.C , C.Monasterio, T. Prosen, Phys. Rev. Lett. 101 , 016601(2008) ZT increases with geometrical and internal degrees of freedom D of gas particles.
  • An efficient engine M. Horvat, T. Prosen, G.C., Phys Rev. E 80 , 010102 (2009)
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  • Two things appeared almost simultaneously in the 1990s: new ideas and new funding . New ideas: indicate that large improvements in ZT might be possible by making an artificial material modified on a nanometer length scale. This idea, known as a ‘quantum well superlattice’, has been important for inspiring nano-scale engineering to improve ZT.
  • -Environmental concern about chlorofluorocarbons used in most compression-based refrigeration technologies. -Home heating, automotive exhaust, etc. generate an enormous amount of unused waste heat - Generation of electric power from waste heat using thermoelectrics is becoming more and more attractive (e.g. automobile exhaust and engine heat)
  • Modern semiconductor manufacturing techniques are under development at two recent startups : - Nextreme (US) , a spin-off from the Research Triangle Institute utilizing a superlattice technology - Micropelt (Germany), a spin-off from an Infineon/ Fraunhofer Institute collaboration utilizing a wafer-scale device fabrication method . Both companies offer evaluation kits but are not yet in general production.
  • Efforts are underway to replace alternator in cars with a thermoelectric generator mounted on the exhaust stream
  • to produce electricity rather than using drive train power and an alternator. More drive train power is available to move the vehicle and electricity is still available. Plan is to improve overall fuel economy by 10% and aims to reach production in the 2011-2014 Vehicle waste heat is redirected to a thermoelectric generator
  • New funding. In the early 1990s DARPA and the Office of Naval Research initiated support for basic thermoelectric materials research: thermoelectric coolers are used for night vision, sensors, guidance systems, etc . and even modest efficiency gains might make TE air conditioning practical in submarines (TE cooling is quiet) and enhance the existing DoD applications. USS DOLPHIN AGSS 555 – Test for Silent Running
    • A large number of complex materials are now
    • available
    At issue are some fundamental scientific challenges, which could be overcome by deeper understanding of heat and charge transport .
  • Uno si innamora di una idea scientifica come con una donna: all’inizio la conosce poco e non vede i difetti. Quando la conosce bene per vedere i difetti oramai ne e’ innamorato R. Feynman
  • HOW FUTURE MAY LOOK LIKE……..
  • Thermal diodes and transistors Phys Rev Lett 88 094302 (2002) Phys Rev Lett. 93 184301 (2004) Chaos 15 015120 (2005) Phys Lev Lett 98 104302 (2007) Thermoelectric Phys Rev Lett 101 01601 (2008) J Stat Mech L03004 (2009) Phys Rev E 80 010102 (2009) Phys Rev E 80 031136 (2009)