Spectral transitions and universal steady states in random Kraus maps and circuits

Lucas Sá (Avtor), Pedro Ribeiro (Avtor), Tankut Can (Avtor), Tomaž Prosen (Avtor)

Povzetek

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.

Ključne besede

neravnovesna statistična mehanika;odprti kvantni sistemi;nonequilibrium statistical mechanics;open quantum systems;

Podatki

Jezik:	Angleški jezik
Leto izida:	2020
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	536.93
COBISS:	42982147
ISSN:	2469-9950
Št. ogledov:	259
Št. prenosov:	261
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Slovenski jezik
Sekundarne ključne besede:	neravnovesna statistična mehanika;odprti kvantni sistemi;
Strani:	str. 134310-1-134310-13
Letnik:	ǂVol. ǂ102
Zvezek:	ǂiss. ǂ13
Čas izdaje:	2020
DOI:	10.1103/PhysRevB.102.134310
ID:	12345751