In this Letter we study how fast the energy density of a quantum gas can increase in time, when the interatomic interaction characterized by the $s$-wave scattering length $a_s$ is increased from zero with arbitrary time dependence. We show that, at short time, the energy density can at most increase as $\sqrt{t}$, which can be achieved when the time dependence of $a_s$ is also proportional to $\sqrt{t}$, and especially, a universal maximum energy growth rate can be reached when $a_s$ varies as $2\sqrt{\hslash t/(\pi m)}$. If $a_s$ varies faster or slower than $\sqrt{t}$, it is, respectively, proximate to the quench process and the adiabatic process, and both result in a slower energy growth rate. These results are obtained by analyzing the short time dynamics of the short-range behavior of the many-body wave function characterized by the contact, and are also confirmed by numerically solving an example of interacting bosons with time-dependent Bogoliubov theory. These results can also be verified experimentally in ultracold atomic gases.

中文翻译：

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稀释量子气体中的最大能量增长率

在这封信中，我们研究了当原子间相互作用以 $秒$-波散射长度 ${\mathrm{一种}}_{秒}$随任意时间依赖性从零增加。我们表明，在短时间内，能量密度最多可以增加为$\sqrt{吨}$，当时间依赖性为 ${\mathrm{一种}}_{秒}$ 也成正比 $\sqrt{吨}$，特别是，当达到普遍最大能量增长率时 ${\mathrm{一种}}_{秒}$ 变化为 $2\sqrt{\hslash 吨/(\pi 米)}$. 如果${\mathrm{一种}}_{秒}$ 变化快于或慢于 $\sqrt{吨}$，分别接近淬火过程和绝热过程，两者都导致较慢的能量增长速度。这些结果是通过分析以接触为特征的多体波函数的短程行为的短时动力学而获得的，并且还通过使用时间相关的 Bogoliubov 理论数值求解相互作用玻色子的例子得到了证实。这些结果也可以在超冷原子气体中进行实验验证。