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Spectral transitions and universal steady states in random Kraus maps and circuits
ID
Sá, Lucas
(
Author
),
ID
Ribeiro, Pedro
(
Author
),
ID
Can, Tankut
(
Author
),
ID
Prosen, Tomaž
(
Author
)
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https://journals.aps.org/prb/abstract/10.1103/PhysRevB.102.134310
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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 diagonalization, we study random Kraus maps, allowing for a varying dissipation strength, and their local circuit counterpart. We find the spectrum of the random Kraus map to be either an annulus or a disk inside the unit circle in the complex plane, with a transition between the two cases taking place at a critical value of dissipation strength. The eigenvalue distribution and the spectral transition are well described by a simplified RMT model that we can solve exactly in the thermodynamic limit, by means of non-Hermitian RMT and quaternionic free probability. The steady state, on the contrary, is not affected by the spectral transition. It has, however, a perturbative crossover regime at small dissipation, inside which the steady state is characterized by uncorrelated eigenvalues. At large dissipation (or for any dissipation for a large-enough system), the steady state is well described by a random Wishart matrix. The steady-state properties thus coincide with those already observed for random Lindbladian dynamics, indicating their universality. Quite remarkably, the statistical properties of the local Kraus circuit are qualitatively the same as those of the nonlocal Kraus map, indicating that the latter, which is more tractable, already captures the realistic and universal physical properties of generic open quantum systems.
Language:
English
Keywords:
nonequilibrium statistical mechanics
,
open quantum systems
Typology:
1.01 - Original Scientific Article
Organization:
FMF - Faculty of Mathematics and Physics
Publication status:
Published
Publication version:
Author Accepted Manuscript
Year:
2020
Number of pages:
Str. 134310-1-134310-13
Numbering:
Vol. 102, iss. 13
PID:
20.500.12556/RUL-124026
UDC:
536.93
ISSN on article:
2469-9950
DOI:
10.1103/PhysRevB.102.134310
COBISS.SI-ID:
42982147
Publication date in RUL:
21.12.2020
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803
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427
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Record is a part of a journal
Title:
Physical review
Publisher:
American Physical Society
ISSN:
2469-9950
COBISS.SI-ID:
2997348
Secondary language
Language:
Slovenian
Keywords:
neravnovesna statistična mehanika
,
odprti kvantni sistemi
Projects
Funder:
EC - European Commission
Funding programme:
H2020
Project number:
694544
Name:
Open Many-body Non-Equilibrium Systems
Acronym:
OMNES
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0402
Name:
Matematična fizika
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