Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums

Žnidarič, Marko (author)

Phantom relaxation is relaxation with a rate that is not given by a finite spectral gap. Studying the average purity dynamics in a staircase random Haar circuit and the spectral decomposition of a nonsymmetric matrix describing the underlying Markovian evolution, we explain how that can arise out of an ordinary-looking spectrum. Crucial are alternating expansion coefficients that diverge in the thermodynamic limit due to the non-Hermitian skin effect in the matrix describing the average purity dynamics under an overall unitary evolution. The mysterious phantom relaxation emerges out of localized generalized eigenvectors describing the Jordan normal form kernel, and, independently, also out of interesting trigonometric sums due to localized true eigenvectors. All this shows that when dealing with non-Hermitian matrices it can happen that the spectrum is not the relevant object; rather, it is the pseudospectrum or, equivalently, a delicate cancellation enabled by localized eigenvectors.

• Language: English
• Keywords: quantum mechanics
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication version: Version of Record
• Publication date: 01.09.2023
• Year: 2023
• Number of pages: Str. 033145-1-033145-17
• Numbering: Vol. 5, iss. 3
• PID: 20.500.12556/RUL-155002
• UDC: 530.145
• ISSN on article: 2643-1564
• DOI: 10.1103/PhysRevResearch.5.033145
• COBISS.SI-ID: 188725251
• Publication date in RUL: 13.03.2024

Record is a part of a journal

• Title: Physical review research
• Publisher: American Phyisical Society
• ISSN: 2643-1564
• COBISS.SI-ID: 32822823

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: kvantna mehanika

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: J1-4385
• Name: Kvantna večdelčna fizika in nehermitskost

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika