Lindbladian dynamics of the Sachdev-Ye-Kitaev model

We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Here, the linear jump operators are non-random while the quadratic jump operators...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Kulkarni, Anish, Numasawa, Tokiro, Ryu, Shinsei
Format: Article
Language:English
Subjects:
Decay rate
Eigenvalues
Fermions
Green's functions
Normal distribution
Operators
Online Access:Get full text
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Summary:We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Here, the linear jump operators are non-random while the quadratic jump operators are sampled from a Gaussian distribution. In the limit of large \(N\), where \(N\) is the number of Majorana fermion operators, and also in the limit of large \(N\) and \(M\), where \(M\) is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green's functions, from which we can read off the decay rate. For finite \(N\), we also study the distribution of the eigenvalues of the SYK Lindbladians.
ISSN:2331-8422
DOI:10.48550/arxiv.2112.13489