Equilibration of quantum gases

authored by: Terry Farrelly
Abstract: Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators. We show that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N, which is much faster than previous general upper bounds, which were exponential in N. For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one-dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists of N fermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time .
Type: Article
Journal: New journal of physics
Volume: 18
ISSN: 1367-2630
Publication date: 07.2016
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Physics and Astronomy(all)
Electronic version(s): https://doi.org/10.1088/1367-2630/18/7/073014 (Access: Open)

BibTeX

@article{1c0f3187a8bc467cabdc9c7c8985425d,
title = "Equilibration of quantum gases",
abstract = "Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators. We show that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N, which is much faster than previous general upper bounds, which were exponential in N. For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one-dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists of N fermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time .",
keywords = "quantum information, quantum mechanics, quantum statistical physics",
author = "Terry Farrelly",
note = "Publisher Copyright: {\textcopyright} 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.",
year = "2016",
month = jul,
doi = "10.1088/1367-2630/18/7/073014",
language = "English",
volume = "18",
journal = "New journal of physics",
issn = "1367-2630",
publisher = "IOP Publishing Ltd.",
number = "7",
}