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arXiv:1401.2012

Reply to the Comment on "General Non-Markovian Dynamics of Open Quantum System"

Wei-Min Zhang, Ping‐Yuan Lo, Heng-Na Xiong, Matisse Wei-Yuan Tu, Franco Nori

Published Jan 9, 2014• 0 citations
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Abstract

This is the reply to the 2nd version of the comment, [arXiv.1312.5286v2], by McCutcheon {\it et al.} on our paper [PRL 109, 170402 (2012)]. Our letter presents three examples. For the steady-state solution of the first example, i.e., the dissipationless part of Eq.(12) in the PRL, the 2nd version of the Comment claimed that "this [dissipationless] regime exists if and only if the total Hamiltonian is unbounded from below, casting serious doubts on the usefulness of this result." In this reply, we show again that the 2nd version of the Comment is also incorrect.

DOI
10.48550/arxiv.1401.2012

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This is the reply to the 2nd version of the comment, [arXiv.1312.5286v2], by McCutcheon {\it et al.} on our paper [PRL 109, 170402 (2012)]. Our letter presents three examples. For the steady-state solution of the first example, i.e., the dissipationless part of Eq.(12) in the PRL, the 2nd version of the Comment claimed that "this [dissipationless] regime exists if and only if the total Hamiltonian is unbounded from below, casting serious doubts on the usefulness of this result." In this reply, we show again that the 2nd version of the Comment is also incorrect.
I point out that if one defines the operator UR(t)U_R(t)UR​(t) as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of UR(t)U_R(t)UR​(t) as given in his paper [arXiv:0710.5653v1], one finds that the time-evolution of the associated quantum system is not governed by the Schrödinger equation for the Hamiltonian operator HHH but an operator H′H'H′ which differs from HHH if the metric operator is time-dependent. In the latter case this effective Hamiltonian H′H'H′ is not observable. This is consistent with the conclusions of my paper [Phys. Lett. B 650, 208 (2007), arXiv:0706.1872v2] which allow for unitary time-evolution generated by unobservable Hamiltonians.