We consider a non-interacting Fermi gas in d dimensions, both in the non-relativistic and relativistic case. The system of size Ld is initially prepared into two halves L and R, each of them thermalized at two different temperatures, TL and TR respectively. At time t = 0 the two halves are put in contact and the entire system is left to evolve unitarily. We show that, in the thermodynamic limit, the time evolution of the particle and energy densities is perfectly described by a semiclassical approach which permits to analytically evaluate the corresponding stationary currents. In particular, in the case of non-relativistic fermions, we find a low-temperature behavior for the particle and energy currents which is independent from the dimensionality d of the system, being proportional to the difference TL2-TR2 . Only in one spatial dimension (d = 1) do the results for the non-relativistic case agree with the massless relativistic ones.

Non-equilibrium transport in d-dimensional non-interacting Fermi gases / Collura, Mario; Martelloni, Gabriele. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2014:Aug(2014), pp. 1-19. [10.1088/1742-5468/2014/08/P08006]

Non-equilibrium transport in d-dimensional non-interacting Fermi gases

Collura, Mario;Martelloni, Gabriele
2014

Abstract

We consider a non-interacting Fermi gas in d dimensions, both in the non-relativistic and relativistic case. The system of size Ld is initially prepared into two halves L and R, each of them thermalized at two different temperatures, TL and TR respectively. At time t = 0 the two halves are put in contact and the entire system is left to evolve unitarily. We show that, in the thermodynamic limit, the time evolution of the particle and energy densities is perfectly described by a semiclassical approach which permits to analytically evaluate the corresponding stationary currents. In particular, in the case of non-relativistic fermions, we find a low-temperature behavior for the particle and energy currents which is independent from the dimensionality d of the system, being proportional to the difference TL2-TR2 . Only in one spatial dimension (d = 1) do the results for the non-relativistic case agree with the massless relativistic ones.
2014
Aug
1
19
P08006
https://arxiv.org/abs/1404.1319
Collura, Mario; Martelloni, Gabriele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/103464
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