Recurrence times of the small-size Lieb-Liniger Bose gas in the weak- and strong-coupling regimes

Abstract

Quantum systems exhibit recurrence phenomena after equilibration, but it is a difficult task to evaluate the recurrence time of a quantum system because it drastically increases as the system size increases (usually double-exponential in the number of particles) and strongly depends on the initial state. Here, we analytically derive the recurrence times of the Lieb-Liniger model with relatively small particle numbers for the weak and strong coupling regimes. It turns out that these recurrence times are independent of the initial state and increases only polynomially in the system size.

Concentration of quantum equilibration and an estimate of the recurrence time

“…These bounds however scale as e Ω( L) and e Ω(L) respectively, which are exponential in the number of sites L. This is a fast scaling, but still exponentially slower than that from Corollaries 1 and 2. Even shorter recurrence times are also found in specific instances of Bose gases [40][41][42], which can even be experimentally tested [43] with cold atoms.…”