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Multiple Quantum Mpemba Effect: Exceptional Points and Oscillations: Appendix B: Eigenvectors

Written by @oscillation | Published on 2024/3/5

TL;DR
In this paper, we explore the role of exceptional points and complex eigenvalues on the occurrence of the quantum Mpemba effect.

This paper is available on arxiv under CC 4.0 license.

Authors:

(1) Amit Kumar Chatterjee, Yukawa Institute for Theoretical Physics, Kyoto University & Department of Physics, Ramakrishna Mission Vidyamandira;

(2) Satoshi Takada, Department of Mechanical Systems Engineering and Institute of Engineering;

(3) Hisao Hayakawa, Yukawa Institute for Theoretical Physics, Kyoto University.

Appendix B: Eigenvectors of L in region (a1)

(a1) In this Appendix, we give the explicit expressions for the right eigenvectors |rki and left eigenvectors hℓk| of the Lindbladian [Eq. (2)] in region (a1) [Sec. V], where k = 2, 3, 4. The right and left eigenvectors corresponding to the zero eigenvalue i.e. steady state. have already been provided in Eq. (3). Below are the expressions for the right eigenvectors

The left eigenvectors are given by

where

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Written by
@oscillation
#1 Publication focused exclusively on Oscillation, ie regular variation in magnitude or position around a central point.

Topics and
tags
multiple-quantum-mpemba|points-and-oscillations|complex-eigenvalues|quantum-mpemba-effect|dissipative-coupling|mpemba-effect|quantum-master-equation|exponential-relaxation
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