Eigenstate thermalization and ensemble equivalence in few-body fermionic systems

Physical Review. E
Ph Jacquod

Abstract

We investigate eigenstate thermalization from the point of view of vanishing particle and heat currents between a few-body fermionic Hamiltonian prepared in one of its eigenstates and an external, weakly coupled Fermi-Dirac gas. The latter acts as a thermometric probe, with its temperature and chemical potential set so that there is neither particle nor heat current between the two subsystems. We argue that the probe temperature can be attributed to the few-fermion eigenstate in the sense that (i) it varies smoothly with energy from eigenstate to eigenstate, (ii) it is equal to the temperature obtained from a thermodynamic relation in a wide energy range, (iii) it is independent of details of the coupling between the two systems in a finite parameter range, (iv) it satisfies the transitivity condition underlying the zeroth law of thermodynamics, and (v) it is consistent with Carnot's theorem. For the spinless fermion model considered here, these conditions are essentially independent of the interaction strength. When the latter is weak, however, orbital occupancies in the few-fermion system differ from the Fermi-Dirac distribution so that partial currents from or to the probe will eventually change its state. We find that (vi) ...Continue Reading

References

Feb 15, 1991·Physical Review. a·J M Deutsch
Mar 1, 1986·Physical Review. B, Condensed Matter·M Büttiker
Aug 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M Srednicki
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Feb 21, 2006·Physical Review Letters·Sheldon GoldsteinNino Zanghì
Apr 19, 2008·Nature·Marcos RigolMaxim Olshanii
Dec 17, 2008·Nano Letters·Yonatan Dubi, Massimiliano Di Ventra
Jun 24, 2010·Nanotechnology·Ph Jacquod
Jun 5, 2018·Reports on Progress in Physics·Joshua M Deutsch

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