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arXiv 0912.4493cond-mat.quant-gascond-mat.stat-mechquant-ph
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准一维超冷玻色气体的热化

Thermalization in a quasi-1D ultracold bosonic gas

I. E. Mazets, J. Schmiedmayer

摘要:

我们研究了一维系统中导致热化的碰撞过程。对于两体碰撞,横模的激发是能量交换和热化的先决条件。在非常低的温度下,横模的激发被指数抑制,两体碰撞的热化停止,系统应该变得可积。在量子力学中,更高径向模的虚激发是可能的。这些虚拟激发的径向模式引起有效的三体速度变化碰撞,导致热化。我们发现,这些三体弹性相互作用被抑制成对的量子关联时,接近强关联制度。如果相对动量$k$与两体耦合常数$c$相比较小,则三粒子散射态会被因子$(k/c)^{12}$抑制,该因子与$γ^{12}$成正比,即与Lieb-Liniger参数$γ\gg 1$极限中零距离处三体关联函数的平方成正比。这表明,在一维量子系统中,它不是两体碰撞的冻结,而是强量子关联,这确保了在实验相关的时间尺度上没有热化。

英文摘要:

We study the collisional processes that can lead to thermalization in one-dimensional systems. For two body collisions excitations of transverse modes are the prerequisite for energy exchange and thermalzation. At very low temperatures excitations of transverse modes are exponentially suppressed, thermalization by two body collisions stops and the system should become integrable. In quantum mechanics virtual excitations of higher radial modes are possible. These virtually excited radial modes give rise to effective three-body velocity-changing collisions which lead to thermalization. We show that these three-body elastic interactions are suppressed by pairwise quantum correlations when approaching the strongly correlated regime. If the relative momentum $k$ is small compared to the two-body coupling constant $c$ the three-particle scattering state is suppressed by a factor of $(k/c)^{12}$, which is proportional to $γ^{12}$, that is to the square of the three-body correlation function at zero distance in the limit of the Lieb-Liniger parameter $γ\gg 1$. This demonstrates that in one dimensional quantum systems it is not the freeze-out of two body collisions but the strong quantum correlations which ensures absence of thermalization on experimentally relevant time scales.

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