Scale-free relaxation of a wave packet in a quantum well with power-law tails

Abstract

We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: a quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ∼x −2 and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.

Effects of resonance states in barrier region on non-exponential decay of wave-packets scattered by rounded-rectangular potentials

“…In the period of the t −3 decay of the pre-exponential decay, the wave-packet over the potential top behaves as a free wave-packet involving momentum components of small values, namely a continuous part of energy spectrum just above the flat top of the potential induces a temporal power-law decay. The work by Miccichè et al seems to be related with this fact [32]. That is, they treated a class of double barrier potentials forming a well with power-law tails, and theoretically and numerically showed that a continuous part of the spectrum attached to the ground or equilibrium state induces a non-exponential decay, whose power-law exponent changes depending on the potential parameters; the author guesses that this is due to the unlocalized potential tails.…”

“…Non-exponential decays can be observed and explained in slightly different contexts. According to Miccichè et al [32], for a class of double barrier potentials forming a well with power-law tails, a continuous part of the spectrum attached to the ground or equilibrium state induces a non-exponential decay. Non-exponential decays are also observed for classically non-integrable systems.…”

Mean-Field Transport of a Bose-Einstein Condensate

“…Yet, this possibility of controlling the dynamics of a Bose-Einstein condensate is quite interesting. We refer to similar situations where the effect of the interaction was approximately cancelled by applying appropriate external potentials in theory [18] and an actual experiment at Innsbruck [19]. Fig.…”

Mean-field transport of a Bose-Einstein condensate

“…Yet, this possibility of controlling the dynamics of a Bose-Einstein condensate is quite interesting. We refer to similar situations where the effect of the interaction was approximately cancelled by applying appropriate external potentials in theory [18] and an actual experiment at Innsbruck [19].…”