Information scrambling of the dilute Bose gas at low temperature

TL;DR

This paper investigates quantum chaos in a dilute Bose gas at low temperatures, calculating Lyapunov exponents and butterfly velocities using a generalized Boltzmann approach, revealing temperature-dependent behaviors and differences from energy diffusion.

Contribution

It provides the first detailed calculation of quantum Lyapunov exponent and butterfly velocity in a dilute Bose gas across temperature regimes using out-of-time ordered correlators.

Findings

At very low T, λ_L ∝ T^5 and v_B ≈ c.

At higher T, λ_L ∝ T and v_B scales with T.

Chaos diffusion constant differs from energy diffusion constant.

Abstract

We calculate the quantum Lyapunov exponent $\lambda_L$ and butterfly velocity $v_B$ in the dilute Bose gas at temperature $T$ deep in the Bose-Einstein condensation phase. The generalized Boltzmann equation approach is used for calculating out-of-time ordered correlators, from which $\lambda_L$ and $v_B$ are extracted. At very low temperature where elementary excitations are phonon-like, we find $\lambda_L\propto T^5$ and $v_B\sim c$, the sound velocity. At relatively high temperature, we have $\lambda_L\propto T$ and $v_B\sim c(T/T_*)^{0.23}$. We find $\lambda_L$ is always comparable to the damping rate of a quasiparticle, whose energy depends suitably on $T$. The chaos diffusion constant $D_L=v_B^2/\lambda_L$, on the other hand, differs from the energy diffusion constant $D_E$. We find $D_E\ll D_L$ at very low temperature and $D_E\gg D_L$ otherwise.