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Register a new userThermalization with detailed-balanced two-site Lindblad dissipators
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The use of two-site Lindblad dissipator to generate thermal states and study heat transport raised to prominence since [J. Stat. Mech. (2009) P02035] by Prosen and v{Z}nidariv{c}. Here we propose a variant of this method based on detailed balance of internal levels of the two site Hamiltonian and characterize its performance. We study the thermalization profile in the chain, the effective temperatures achieved by different single and two-site observables, and we also investigate the decay of two-time correlations. We find that at a large enough temperature the steady state approaches closely a thermal state, with a relative error below 1% for the inverse temperature estimated from different observables.
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The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal system to study the nonequilibrium dynamics in isolated quantum systems, triggering intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation in relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.
By calculating correlation functions for the Lieb-Liniger model based on the algebraic Bethe ansatz method, we conduct a finite-size scaling analysis of the eigenstate thermalization hypothesis (ETH) which is considered to be a possible mechanism of thermalization in isolated quantum systems. We find that the ETH in the weak sense holds in the thermodynamic limit even for an integrable system although it does not hold in the strong sense. Based on the result of the finite-size scaling analysis, we compare the contribution of the weak ETH to thermalization with that of yet another thermalization mechanism, the typicality, and show that the former gives only a logarithmic correction to the latter.
We investigate experimentally a two-dimensional rocking ratchet for cold atoms, realized by using a driven three-beam dissipative optical lattice. AC forces are applied in perpendicular directions by phase-modulating two of the lattice beams. As predicted by the general theory [S. Denisov et al., Phys. Rev. Lett. 100, 224102 (2008)], we observe a rectification phenomenon unique to high-dimensional rocking ratchets, as determined by two single-harmonic drivings applied in orthogonal directions. Also, by applying two bi-harmonic forces in perpendicular directions, we demonstrate the possibility of generating a current in an arbitrary direction within the optical lattice plane.
Complexity of dynamics is at the core of quantum many-body chaos and exhibits a hierarchical feature: higher-order complexity implies more chaotic dynamics. Conventional ergodicity in thermalization processes is a manifestation of the lowest order complexity, which is represented by the eigenstate thermalization hypothesis (ETH) stating that individual energy eigenstates are thermal. Here, we propose a higher-order generalization of the ETH, named the $ k $-ETH ($ k=1,2,dots $), to quantify higher-order complexity of quantum many-body dynamics at the level of individual energy eigenstates, where the lowest order ETH (1-ETH) is the conventional ETH. As a non-trivial contribution of the higher-order ETH, we show that the $ k $-ETH with $ kgeq 2 $ implies a universal behavior of the $ k $th Renyi entanglement entropy of individual energy eigenstates. In particular, the Page correction of the entanglement entropy originates from the higher-order ETH, while as is well known, the volume law can be accounted for by the 1-ETH. We numerically verify that the 2-ETH approximately holds for a nonintegrable system, but does not hold in the integrable case. To further investigate the information-theoretic feature behind the $ k $-ETH, we introduce a concept named a partial unitary $ k $-design (PU $ k $-design), which is an approximation of the Haar random unitary up to the $ k $th moment, where partial means that only a limited number of observables are accessible. The $ k $-ETH is a special case of a PU $ k $-design for the ensemble of Hamiltonian dynamics with random-time sampling. In addition, we discuss the relationship between the higher-order ETH and information scrambling quantified by out-of-time-ordered correlators. Our framework provides a unified view on thermalization, entanglement entropy, and unitary $ k $-designs, leading to deeper characterization of higher-order quantum complexity.
By exploring a phase space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the Fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle, observable in experiments in an one dimensional free Fermi gas or Tonks gas (Bose gas with infinite repulsion).
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