Equilibration time scales in closed many-body quantum systems

Oliveira, Thiago R. de; Charalambous, Christos; Jonathan, Daniel; Lewenstein, Maciej; Riera, Arnau

doi:10.1088/1367-2630/aab03b

Cited by 61 publications

(65 citation statements)

References 38 publications

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“…Intuitively, the essential mechanism is expected to be a 'dephasing' [9,23,24] of the oscillating summands on the right hand side of (5): there must be sufficiently many different 'frequencies' E E n m  -[ ] which notably contribute to the sum, resulting in an approximate cancellation for most sufficiently large t, provided H, ρ(0), and A satisfy certain 'minimal' conditions:…”

Section: Equilibration and Thermalizationmentioning

confidence: 99%

“…Moreover, all the remaining non-negligible p n ʼs are usually still far from being approximately equally large, hence it is not obvious why the larger ones should not play in some sense a more important role than the smaller ones. The main objective of this section is to amend the approach from section 3 (see (24) and main text). Solid: convolution of the dotted line with a Gaussian of standard deviation 5.5 fs, accounting for the finite widths of the pump and probe laser pulses.…”

Section: Amended Theory Of Transportless Relaxationmentioning

confidence: 99%

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Transportless equilibration in isolated many-body quantum systems

Reimann

2019

New J. Phys.

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A general analytical theory of temporal relaxation processes in isolated quantum systems with many degrees of freedom is elaborated, which unifies and substantially amends several previous approximations. Specifically, the Fourier transform of the initial energy distribution is found to play a key role, which is furthermore equivalent to the so-called survival probability in case of a pure initial state. The main prerequisite is the absence of any notable transport currents, caused for instance by some initially unbalanced local densities of particles, energy, and so on. In particular, such a transportless relaxation scenario naturally arises when both the system Hamiltonian and the initial non-equilibrium state do not exhibit any spatial inhomogeneities on macroscopic scales. A further requirement is that the relaxation must not be notably influenced by any approximate (but not exact) constant of motion or metastable state. The theoretical predictions are compared with various experimental and numerical results from the literature.

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Section: Equilibration and Thermalizationmentioning

confidence: 99%

Section: Amended Theory Of Transportless Relaxationmentioning

confidence: 99%

Transportless equilibration in isolated many-body quantum systems

Reimann

2019

New J. Phys.

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“…In this picture, an important open question is how long it takes for isolated quantum systems to reach equilibrium. Despite the increasing number of recent works addressing this issue [6,[11][12][13][14][15][16][17][18][19][20][21][22], there is no agreement regarding how the relaxation timescale should depend on system size, range of interactions, observables, and initial states.…”

Section: Introductionmentioning

confidence: 99%

Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system

et al. 2019

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Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations comes in the form of the so-called correlation hole, which is a dip below the saturation point of the survival probability's time evolution. In this work, we study the correlation hole in the spin-boson (Dicke) model, which presents a chaotic regime and can be realized in experiments with ultracold atoms and ion traps. We derive an analytical expression that describes the entire evolution of the survival probability and allows us to determine the timescales of its relaxation to equilibrium. This expression shows remarkable agreement with our numerical results. While the initial decay and the time to reach the minimum of the correlation hole depend on the initial state, the dynamics beyond the hole up to equilibration is universal. We find that the relaxation time of the survival probability for the Dicke model increases linearly with system size. arXiv:1905.03253v2 [cond-mat.stat-mech]

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“…In this work we show that the equilibration dynamics [12][13][14][15][16][17] of a quantum system can be used to extract information on the dimension of the Hilbert space. Indeed, advancements in quantum technologies described above have inspired a bounty of theoretical work in the field of quantum thermalization [18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Ergodicity probes: using time-fluctuations to measure the Hilbert space dimension

Nation

Porras

2019

Quantum

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Quantum devices, such as quantum simulators, quantum annealers, and quantum computers, may be exploited to solve problems beyond what is tractable with classical computers. This may be achieved as the Hilbert space available to perform such 'calculations' is far larger than that which may be classically simulated. In practice, however, quantum devices have imperfections, which may limit the accessibility to the whole Hilbert space. Actually, the dimension of the space of quantum states that are available to a quantum device is a meaningful measure of its functionality, but unfortunately this quantity cannot be directly experimentally determined. Here we outline an experimentally realisable approach to obtaining the scaling of the required Hilbert space of such a device to compute such evolution, by exploiting the thermalization dynamics of a probe qubit. This is achieved by obtaining a fluctuation-dissipation theorem for high-temperature chaotic quantum systems, which facilitates the extraction of information on the Hilbert space dimension via measurements of the decay rate, and time-fluctuations. arXiv:1906.06206v1 [quant-ph]

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Equilibration time scales in closed many-body quantum systems

Cited by 61 publications

References 38 publications

Transportless equilibration in isolated many-body quantum systems

Transportless equilibration in isolated many-body quantum systems

Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system

Ergodicity probes: using time-fluctuations to measure the Hilbert space dimension

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