Relaxation times of dissipative many-body quantum systems

Abstract

We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap can not be larger than ∼ 1/L. In integrable systems with boundary dissipation one typically observes scaling ∼ 1/L 3 , while in chaotic ones one can have faster relaxation with the gap scaling as ∼ 1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.

Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: Phenomenological description and its microscopic foundation

“…In the case of low-temperature baths, we observe three characteristic decay time scales. The emergence of different timescales has also been observed in various other systems due to relaxation or thermalization processes [37][38][39][40][41][42][43][44] . Here, one of the three time scales is associated with an intricate decay mechanism that emerges due to an interplay of coherent evolution and bath-induced relaxation.…”

“…Definition Decay (e λt ) particle asymmetry ∆N λ = −2Γ particle current IN λ = −2Γ total energy H S λ = λ0, −2Γ interaction HU λ = λ2 hopping HJ λ = λ2 spin asymmetry ∆Sz λ = λ1 spin current IS z λ = λ1 antisymmetric exchange n · (S1 × S2) λ = λ1 symmetric exchange 4 S1 · S2 λ = λ0, λ2 total spin squared (S1 + S2) 2 λ = λ0, λ2 parity P λ = λ0, λ2 isospin I λ = λ2 Table I: Further observables with their definitions and decay rates, where λ 0 = 0 indicates the approach to a constant value, while λ 1 and λ 2 are given by Eqs. (40) and (42), respectively.…”

Asymptotic Floquet states of open quantum systems: the role of interaction

“…where l 2 is the second largest eigenvalue by absolute value, can be used to estimate the inverse relaxation time from a randomly chosen initial state [48][49][50]. The spectral gap also exhibits a strong dependence on the interaction strength; see figure 1(b).…”

Universal Dynamics of Stochastically Driven Quantum Impurities

“…Note that at very long-times we generally expect to see decay of the Loschmidt echo in any finite system as it heats up under the action of the incoherent drive, h b (t) [33,34]. However, this occurs on time scales of at least t * ∝ L [35,36], while in our simulations we keep t < L/2 to reduce finite-size effects, ensuring t t * . Fig.…”