Generalization of von Neumann’s Approach to Thermalization

Reimann, Peter

doi:10.1103/physrevlett.115.010403

Cited by 74 publications

(110 citation statements)

References 43 publications

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“…As an aside we note that the preparation of an initial condition ρ(0) with a distinct non-equilibrium expectation value of A at time t=0 must actually amount to a quite special selection of the terms ρ mn (0)A nm (in particular of their complex phases) on the right hand side of (5) [23]. This issue is in fact also quite closely related to a variety of so-called typicality concepts and results, see [25][26][27].…”

Section: Equilibration and Thermalizationmentioning

confidence: 95%

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: 95%

Transportless equilibration in isolated many-body quantum systems

Reimann

2019

New J. Phys.

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“…This statement has many aspects, it may imply that a reduced density matrix of a part of some system approaches a thermal state [3,4,7,42], it may imply that expectation values of specific observables evolve more or less against constant values [1,43], or it may additionally even imply that these constant values do not depend on the initial state [1,17,44]. It is this latter initial state independence (ISI) which is in the focus of the paper at hand.…”

Section: Introductionmentioning

confidence: 99%

“…However, while the three features are sufficient for ISI, they are not necessary in a mathematical sense: classes of initial states exist that exhibit ISI even though the ETH may not apply. Some papers put much more emphasis on the extremely high relative frequency with which ISI may be expected if initial state are drawn essentially at random from some prescribed sets, rather than on the ETH [5,7,43,46]. However, it may be the case that the relative frequency of initial states from the above sets, that exhibit a significant deviation of the respective expectation value from its equilibrium value at all, even at t = 0, is very low.…”

Section: Introductionmentioning

confidence: 99%

Initial-state-independent equilibration at the breakdown of the eigenstate thermalization hypothesis

2016

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This work aims at understanding the interplay between the Eigenstate Thermalization Hypothesis (ETH), initial state independent equilibration and quantum chaos in systems that do not have a direct classical counterpart. It is based on numerical investigations of asymmetric Heisenberg spin ladders with varied interaction strengths between the legs, i.e., along the rungs. The relaxation of the energy difference between the legs is investigated. Two different parameters, both intended to quantify the degree of accordance with the ETH, are computed. Both indicate violation of the ETH at large interaction strengths but at different thresholds. Indeed the energy difference is found not to relax independently of its initial value above some critical interaction strength which coincides with one of the thresholds. At the same point the level statistics shift from Poisson-type to Wigner-type. Hence the system may be considered to become integrable again in the strong interaction limit.

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“…In fact, it was shown that any such subsystem of the total system is described by the canonical thermal ensemble for the overwhelming majority of pure states of the total system. [15,16] Thus, according to the second law of thermodynamics and in spite of the unitary time evolution of the total system, the subsystem will evolve for long times to the density matrix of a (grand) canonical ensemble in thermodynamic equilibrium. The blue dots represent atoms in the condensate, while the red dots depict incoherent excitations (quasiparticles) out of the condensate.…”

Section: Introductionmentioning

confidence: 99%

Thermalization of Isolated Bose‐Einstein Condensates by Dynamical Heat Bath Generation

2017

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If and how an isolated quantum system thermalizes despite its unitary time evolution is a long-standing, open problem of many-body physics. The eigenstate thermalization hypothesis (ETH) postulates that thermalization happens at the level of individual eigenstates of a system's Hamiltonian. However, the ETH requires stringent conditions to be validated, and it does not address how the thermal state is reached dynamically from an initial non-equilibrium state. We consider a Bose-Einstein condensate (BEC) trapped in a double-well potential with an initial population imbalance. We find that the system thermalizes although the initial conditions violate the ETH requirements. We identify three dynamical regimes. After an initial regime of undamped Josephson oscillations, the subsystem of incoherent excitations or quasiparticles (QP) becomes strongly coupled to the BEC subsystem by means of a dynamically generated, parametric resonance. When the energy stored in the QP system reaches its maximum, the number of QPs becomes effectively constant, and the system enters a quasi-hydrodynamic regime where the two subsystems are weakly coupled. In this final regime the BEC acts as a grand-canonical heat reservoir for the QP system (and vice versa), resulting in thermalization. We term this mechanism dynamical bath generation (DBG).

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Generalization of von Neumann’s Approach to Thermalization

Cited by 74 publications

References 43 publications

Transportless equilibration in isolated many-body quantum systems

Transportless equilibration in isolated many-body quantum systems

Initial-state-independent equilibration at the breakdown of the eigenstate thermalization hypothesis

Thermalization of Isolated Bose‐Einstein Condensates by Dynamical Heat Bath Generation

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