Thermal conductivity of the degenerate one-dimensional Fermi gas

Abstract

We study heat transport in a gas of one-dimensional fermions in the presence of a small temperature gradient. At temperatures well below the Fermi energy there are two types of relaxation processes in this system, with dramatically different relaxation rates. As a result, in addition to the usual thermal conductivity, one can introduce the thermal conductivity of the gas of elementary excitations, which quantifies the dissipation in the system in the broad range of frequencies between the two relaxation rates. We develop a microscopic theory of these transport coefficients in the limit of weak interactions between the fermions. arXiv:1901.08136v2 [cond-mat.mes-hall]

Thermal Transport in One-Dimensional Electronic Fluids

“…Results of Ref. 55 for σ(ω) match ours in what concerns the "plateaus" II and V in Fig. 2 but do not capture other regions, where σ(ω) is controlled by a slow relaxation of bosonic modes.…”

Superdiffusive transport of energy in one-dimensional metals

“…The results presented here show that even simple, well-studied problems in quantum condensed-matter physics lead to long-time scaling that is distinct from these three standard possibilities. Note that the superdiffusion described in the present work is distinct from that known to exist in momentum-conserving many-body systems (13)(14)(15)(16), in which linear-response coefficients are not finite in the thermodynamic limit but rather diverge as a power law in system size.…”

Relaxation of the degenerate one-dimensional Fermi gas

“…The thermal conductivity of one-dimensional systems of spinless fermions has been recently studied in Refs. [5,9]. The dc thermal conductivity κ of these systems is controlled by the processes involving exponentially weak backscattering of particles near the bottom of the band.…”

“…[7]. The result, τ −1 ∝ T , is much greater than the decay rate τ −1 ∝ T 7 [2][3][4][5] for spin-polarized fermions, because the scattering amplitude, instead of being suppressed due to the Pauli principle, diverges at small momentum transfer as |p 1 − p 1 | −1 . The processes shown in Fig.…”

“…Most importantly, the scattering processes involving only two fermions do not lead to relaxation, and thus the dominant processes involve three particles. The relaxation rate for spin-polarized one-dimensional fermions scales as τ −1 ∝ T 7 [2][3][4][5]. Such a weak relaxation at T → 0 is due to the small density of states for threeparticle scattering and a strong suppression of the scattering amplitude for spin-polarized fermions, which is a manifestation of the Pauli principle [6].…”