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 .
Highlights
Over the past few decades, there has been a major push to understand statistical physics by applying tools from quantum information
We open the partition at t = 0, and the observable we focus on is M, which counts the particles in the left half of the box
Finding the timescale involved in equilibration is an important problem in physics, especially in light of recent advances in experiments with mesoscopic quantum systems [1, 2]
Summary
Over the past few decades, there has been a major push to understand statistical physics by applying tools from quantum information. The best general upper bounds on the timescale [6,7,8] are far too large for even mesoscopic systems This is a consequence of the generality of the results. We will look at N particle systems in the regime of negligible interactions to see when equilibration occurs. Such situations appear often: Luttinger liquids [19] are one example. First we will look at some examples and we will show that equilibration of N particle systems in this setting occurs quite generally and appears to be much faster than what general timescale bounds suggest
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