Semiclassical Husimi Distributions of Schur Vectors in Non-Hermitian Quantum Systems

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Semiclassical Husimi Distributions of Schur Vectors in Non-Hermitian Quantum Systems

Joseph Hall, Simon Malzard, and Eva-Maria Graefe

Phys. Rev. Lett. 131, 040402 – Published 27 July 2023

Abstract

We construct a semiclassical phase-space density of Schur vectors in non-Hermitian quantum systems. Each Schur vector is associated to a single Planck cell. The Schur states are organized according to a classical norm landscape on phase space—a classical manifestation of the lifetimes which are characteristic of non-Hermitian systems. To demonstrate the generality of this construction we apply it to a highly nontrivial example: a $P T$ -symmetric kicked rotor in the regimes of mixed and chaotic classical dynamics.

Received 28 November 2022
Accepted 23 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.040402

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society