Multiple Quantum Mpemba Effect: Exceptional Points and Oscillations: Appendix B: Eigenvectors by@oscillation
Multiple Quantum Mpemba Effect: Exceptional Points and Oscillations: Appendix B: Eigenvectors
by The Oscillation PublicationMarch 5th, 2024
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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.
Table of Links
- Introduction
- Model and Protocol
- Different Regimes in d˜− Γ˜ Plain and Multiple QMPE
- QMPE in Region (d): Second-order Ep
- QMPE in Region (a1): Oscillations
- Summary
- Appendix A: Eigenvectors of L in region (d)
- Appendix B: Eigenvectors of L in region (a1)
- Appendix C: QMPE in region (b): purely exponential relaxation
- Appendix D: QMPE in region (e): 3rd order EP
- References
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
L O A D I N G
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