论文标题
信息在低温下稀释的bose气体争夺
Information scrambling of the dilute Bose gas at low temperature
论文作者
论文摘要
我们计算量子lyapunov指数$λ_l$和蝴蝶速度$ v_b $在稀释的bose气体中，在Bose-Einstein冷凝阶段深处$ t $。通用的玻尔兹曼方程方法用于计算超时有序的相关器，从中提取$λ_l$和$ v_b $。在非常低的温度下，基本激发像声子一样，我们发现$λ_l\ propto t^5 $和$ v_b \ sim c $，声音速度。在相对较高的温度下，我们有$λ_l\ propto t $和$ v_b \ sim c（t/t _*）^{0.23} $。我们发现$λ_l$始终与准粒子的阻尼率相提并论，后者的能量适当地取决于$ t $。另一方面，混乱扩散常数$ d_l = v_b^2/λ_l$与能量扩散常数$ d_e $不同。我们在非常低的温度下找到$ d_e \ ll d_l $，$ d_e \ gg d_l $否则。
We calculate the quantum Lyapunov exponent $λ_L$ 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 $λ_L$ and $v_B$ are extracted. At very low temperature where elementary excitations are phonon-like, we find $λ_L\propto T^5$ and $v_B\sim c$, the sound velocity. At relatively high temperature, we have $λ_L\propto T$ and $v_B\sim c(T/T_*)^{0.23}$. We find $λ_L$ is always comparable to the damping rate of a quasiparticle, whose energy depends suitably on $T$. The chaos diffusion constant $D_L=v_B^2/λ_L$, 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.
