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Spectral transitions and universal steady states in random Kraus maps and circuits
Sá, Lucas (Avtor), Ribeiro, Pedro (Avtor), Can, Tankut (Avtor), Prosen, Tomaž (Avtor)

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Izvleček
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.

Jezik:Angleški jezik
Ključne besede:nonequilibrium statistical mechanics, open quantum systems
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:FMF - Fakulteta za matematiko in fiziko
Leto izida:2020
Št. strani:Str. 134310-1-134310-13
Številčenje:Vol. 102, iss. 13
UDK:536.93
ISSN pri članku:2469-9950
DOI:10.1103/PhysRevB.102.134310 Povezava se odpre v novem oknu
COBISS.SI-ID:42982147 Povezava se odpre v novem oknu
Število ogledov:103
Število prenosov:163
Metapodatki:XML RDF-CHPDL DC-XML DC-RDF
 
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Gradivo je del revije

Naslov:Physical review
Založnik:American Physical Society
ISSN:2469-9950
COBISS.SI-ID:2997348 Povezava se odpre v novem oknu

Gradivo je financirano iz projekta

Financer:EC - European Commission
Program financ.:H2020
Številka projekta:694544
Naslov:Open Many-body Non-Equilibrium Systems
Akronim:OMNES

Financer:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Številka projekta:P1-0402
Naslov:Matematična fizika

Sekundarni jezik

Jezik:Slovenski jezik
Ključne besede:neravnovesna statistična mehanika, odprti kvantni sistemi

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