2020
DOI: 10.1103/physrevb.102.134310
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Spectral transitions and universal steady states in random Kraus maps and circuits

Abstract: The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those properties are. Here, we address these issues by considering a different description of dissipative quantum systems, namely, the discrete-time Kraus map representation of completely positive quantum dynamics. Through random matrix theory (RMT) techniques and numerical exact … Show more

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Cited by 37 publications
(21 citation statements)
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“…Non-Hermitian physics has advanced significantly in recent years in the study of optics [15][16][17], acoustics [18,19], parity-time-symmetric systems [20,21], mesoscopic physics [22][23][24][25], cold atoms [26,27], driven dissipative systems [28][29][30][31][32], biological systems [33], disordered systems [5]. Recent studies on spectral properties have focused on the shape of eigenvalue density, the spectral gap, and the spacing between nearest-neighbour eigenvalues [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. The goal of this letter is to introduce and analyze a simple indicator that characterizes the level statistics of non-Hermitian matrices up to an arbitrary energy (and, equivalently, time) scale, and show that it captures universal signatures of dissipative quantum chaos.…”
mentioning
confidence: 99%
“…Non-Hermitian physics has advanced significantly in recent years in the study of optics [15][16][17], acoustics [18,19], parity-time-symmetric systems [20,21], mesoscopic physics [22][23][24][25], cold atoms [26,27], driven dissipative systems [28][29][30][31][32], biological systems [33], disordered systems [5]. Recent studies on spectral properties have focused on the shape of eigenvalue density, the spectral gap, and the spacing between nearest-neighbour eigenvalues [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. The goal of this letter is to introduce and analyze a simple indicator that characterizes the level statistics of non-Hermitian matrices up to an arbitrary energy (and, equivalently, time) scale, and show that it captures universal signatures of dissipative quantum chaos.…”
mentioning
confidence: 99%
“…We then discuss in more detail the Keldysh rotation performed in the Main Text and derive Eqs. (21) and (22) (the Schwinger-Dyson equations for ρ ± and σ ± ). Then, we elaborate on the numerical method used to solve these equations.…”
Section: Numerical Solution Of the Schwinger-dyson Equationsmentioning
confidence: 99%
“…Along similar lines, the past couple of years have seen the development of the (non-Hermitian) random matrix theory of Lindbladian dynamics [12][13][14][15][16][17][18][19][20]. By randomly sampling the Hamiltonian and jump operators, many statistical properties, including the spectral support [12] and distribution [19], the spectral gap [13][14][15], and the steady state [15,21] have been computed. However, physical systems have few-body interactions, rendering them very different from dense random matrices.…”
mentioning
confidence: 97%
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