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

TL;DR

This paper defends previous findings that a light impurity in a Tonks-Girardeau gas does not exhibit Bloch oscillations and maintains a finite drift velocity as the external force approaches zero, challenging earlier claims of adiabaticity.

Contribution

It critically examines the assumptions behind earlier models, arguing that the truncated Hilbert space approach is unjustified for the many-body problem.

Findings

Absence of Bloch oscillations for light impurities in the thermodynamic limit.

Finite steady-state drift velocity as external force tends to zero.

Critique of the truncated Hilbert space approximation used in prior analytical arguments.

Abstract

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.