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Title: Interferometric geometric phases of PT -symmetric quantum mechanics
We present a generalization of the geometric phase to pure and thermal states in $$\mathcal{PT}$$-symmetric quantum mechanics (PTQM) based on the approach of the interferometric geometric phase (IGP). The formalism first introduces the parallel-transport conditions of quantum states and reveals two geometric phases, $$\theta^1$$ and $$\theta^2$$, for pure states in PTQM according to the states under parallel-transport. Due to the non-Hermitian Hamiltonian in PTQM, $$\theta^1$$ is complex and $$\theta^2$$ is its real part. The imaginary part of $$\theta^1$$ plays an important role when we generalize the IGP to thermal states in PTQM. The generalized IGP modifies the thermal distribution of a thermal state, thereby introducing effective temperatures. \textcolor{red}{At certain critical points, the generalized IGP may exhibit discrete jumps at finite temperatures, signaling a geometric phase transition. We illustrate the IGP of PTQM through two examples and compare their differences}.  more » « less
Award ID(s):
2310656
PAR ID:
10517996
Author(s) / Creator(s):
; ; ; ; ;
Publisher / Repository:
American Physical Society
Date Published:
Journal Name:
Physical Review B
Volume:
109
Issue:
24
ISSN:
2469-9950
Page Range / eLocation ID:
245411
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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