Absence of thermalisation in a Fermi liquid

Abstract

We study a weak interaction quench in a three-dimensional Fermi gas. We first show that, under some general assumptions on time-dependent perturbation theory, the perturbative expansion of the long-wavelength structure factor $S(\bq)$ is not compatible with the hypothesis that steady-state averages correspond to thermal ones. In particular, $S(\bq)$ does develop an analytical component $\sim const.+O(q^2)$ at $\bq\to\bnot$, as implied by thermalization, but, in contrast, it maintains a non-analytic part $\sim |\bq|$ characteristic of a Fermi-liquid at zero-temperature. In real space, this non-analyticity corresponds to persisting power-law decaying density-density correlations, whereas thermalization would predict only an exponential decay. We next consider the case of a dilute gas, where one can obtain non-perturbative results in the interaction strength but at lowest order in the density. We find that in the steady-state the momentum distribution jump at the Fermi surface remains finite, though smaller than in equilibrium, up to second order in $k_F{f}_0$, where $f_0$ is the scattering length of two particles in the vacuum. Both results question the emergence of a finite length scale in the quench-dynamics as expected by thermalization.

18 pages, 6 figures

References in corpus (6)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Dynamical Transition in Interaction Quenches of the One-Dimensional Hubbard Model

Cited by in corpus (3)

• Quantum quenches in 1+1 dimensional conformal field theories
• Equilibration and GGE in interacting-to-free Quantum Quenches in dimensions d>1
• Dynamical instabilities and transient short-range order in the fermionic Hubbard model