2015
DOI: 10.1103/physreve.92.042143
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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 pha… Show more

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Cited by 168 publications
(189 citation statements)
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“…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.…”
Section: Introductionmentioning
confidence: 89%
See 1 more Smart Citation
“…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.…”
Section: Introductionmentioning
confidence: 89%
“…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.…”
Section: Observablementioning
confidence: 99%
“…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).…”
Section: Model Study: Bose-hubbard Dimermentioning
confidence: 99%
“…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.…”
mentioning
confidence: 92%