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arXiv 1407.4433cond-mat.quant-gas
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对“简并Tonks-Girardeau气体中可动杂质的动力学理论”一文的答复

Reply to "Comment on 'Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas'"

O. Gamayun, O. Lychkovskiy, V. Cheianov

发表信息：
Phys. Rev. E 92, 016102 (2015)
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摘要：

在我们最近的论文[Phys. Rev. E 90，032132（2014）]中，我们研究了移动杂质粒子与Tonks-Girardeau气体弱相互作用并被小外力$F$拉动的动力学。在热力学极限先于小力极限的情况下，我们发现在轻杂质的情况下不存在杂质速度的布洛赫振荡。此外，我们认为，对于轻杂质的稳态漂移速度，$V_D$，仍然有限的限制$F\rightarrow 0$。这些结果与Gangardt，Kamenev和Schecter的早期作品相矛盾[Phys. Rev. Lett. 102，070402（2009），Annals of Physics 327，639（2012）]。我们中的一位（OL）已经证实[Phys. Rev. A 91，040101（2015）]，这些工作的中心假设-动力学的绝热性-可以在热力学极限中崩溃。在前面的评论[Phys. Rev. E 92，016101（2015）]中，Schecter、Gangardt和Kamenev反对这一猜想，并支持$V_D(F)$存在布洛赫振荡和线性。他们认为，杂质-流体系统的基态是准束缚态，这足以确保热力学极限中的绝热性。他们的分析论点是基于系统的希尔伯特空间的某种截断。我们认为，扩展的结果和直觉的基础上截断模型的原始多体问题缺乏理由。

英文摘要：

In our recent paper [Phys. Rev. E 90, 032132 (2014)] we have studied the dynamics of a mobile impurity particle weakly interacting with the Tonks-Girardeau gas and pulled by a small external force, $F$. Working in the regime when the thermodynamic limit is taken prior to the small force limit, we have found that the Bloch oscillations of the impurity velocity are absent in the case of a light impurity. Further, we have argued that for a light impurity the steady state drift velocity, $V_D$, remains finite in the limit $F\rightarrow 0$. These results are in contradiction with earlier works by Gangardt, Kamenev and Schecter [Phys. Rev. Lett. 102, 070402 (2009), Annals of Physics 327, 639 (2012)]. One of us (OL) has conjectured [Phys. Rev. A 91, 040101 (2015)] that the central assumption of these works - the adiabaticity of the dynamics - can break down in the thermodynamic limit. In the preceding Comment [Phys. Rev. E 92, 016101 (2015)] Schecter, Gangardt and Kamenev have argued against this conjecture and in support of the existence of Bloch oscillations and linearity of $V_D(F)$. They have suggested that the ground state of the impurity-fluid system is a quasi-bound state and that this is sufficient to ensure adiabaticity in the thermodynamic limit. Their analytical argument is based on a certain truncation of the Hilbert space of the system. We argue that extending the results and intuition based on their truncated model on the original many-body problem lacks justification.

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