Time fluctuations in isolated quantum systems of interacting particles

Zangara, Pablo R.; Dente, Axel D.; Torres-Herrera, E. J.; Pastawski, Horacio M.; Iucci, Anı́bal; Santos, Lea F.

doi:10.1103/physreve.88.032913

Cited by 72 publications

(73 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In systems without an excessive number of degeneracies and for initial states away from the edges of the spectrum, in other words when |k 0 has a chaotic structure, the temporal fluctuations decrease exponentially with the system size [219]. It has been shown that this holds not only for models with a Wigner-Dyson level spacing distribution, but also for integrable models with interaction, such as Model 1.…”

Section: Relaxation Of Few-body Observablesmentioning

confidence: 94%

See 1 more Smart Citation

Quantum chaos and thermalization in isolated systems of interacting particles

et al. 2016

View full text Add to dashboard Cite

This review is devoted to the problem of thermalization in a small isolated conglomerate of interacting constituents. A variety of physically important systems of intensive current interest belong to this category: complex atoms, molecules (including biological molecules), nuclei, small devices of condensed matter and quantum optics on nano-and micro-scale, cold atoms in optical lattices, ion traps. Physical implementations of quantum computers, where there are many interacting qubits, also fall into this group. Statistical regularities come into play through inter-particle interactions, which have two fundamental components: mean field, that along with external conditions, forms the regular component of the dynamics, and residual interactions responsible for the complex structure of the actual stationary states. At sufficiently high level density, the stationary states become exceedingly complicated superpositions of simple quasiparticle excitations. At this stage, regularities typical of quantum chaos emerge and bring in signatures of thermalization. We describe all the stages and the results of the processes leading to thermalization, using analytical and massive numerical examples for realistic atomic, nuclear, and spin systems, as well as for models with random parameters. The structure of stationary states, strength functions of simple configurations, and concepts of entropy and temperature in application to isolated mesoscopic systems are discussed in detail. We conclude with a schematic discussion of the time evolution of such systems to equilibrium.

show abstract

Section: Relaxation Of Few-body Observablesmentioning

confidence: 94%

“…Systems that fall in this category are those without level clustering [219]. They include chaotic models and those with the Poisson level spacing distribution, known to be a fingerprint of integrable systems, but obviously exclude systems characterized by a picket fence spectrum.…”

mentioning

confidence: 99%

Quantum chaos and thermalization in isolated systems of interacting particles

et al. 2016

View full text Add to dashboard Cite

show abstract

“…In the absence of disorder, the envelope ρ n 0 (E) is particularly well filled for initial states with energy ε n 0 near the center of the spectrum of H [56,57]. Its Gaussian shape leads to the Gaussian decay F (t) ∼ exp(−σ 2 n 0 t 2 ).…”

Section: Survival Probabilitymentioning

confidence: 99%

Dynamics at the many-body localization transition

2015

Self Cite

View full text Add to dashboard Cite

The isolated one-dimensional Heisenberg model with static random magnetic fields has become paradigmatic for the analysis of many-body localization. Here, we study the dynamics of this system initially prepared in a highly-excited nonstationary state. Our focus is on the probability for finding the initial state later in time, the so-called survival probability. Two distinct behaviors are identified before equilibration. At short times, the decay is very fast and equivalent to that of clean systems. It subsequently slows down and develops a power-law behavior with an exponent that coincides with the multifractal dimension of the eigenstates.

show abstract

“…(iii) When the Ising interaction is present, we use = 0.48. This is sufficiently away from the midpoint = 1 2 , where the system develops additional nontrivial symmetries (see references in [55]), and it prevents conservation of total spin S 2 = ( L i=1 S i ) 2 , which happens at = 1. (iv) To avoid reflection symmetry, we add a small impurity of amplitude εJ on the first site of the chain.…”

Section: System Models and Quenchesmentioning

confidence: 99%

Local quenches with global effects in interacting quantum systems

2014

Self Cite

View full text Add to dashboard Cite

We study one-dimensional lattices of interacting spins-1/2 and show that the effects of quenching the amplitude of a local magnetic field applied to a single site of the lattice can be comparable to the effects of a global perturbation applied instantaneously to the entire system. Both quenches take the system to the chaotic domain, the energy distribution of the initial states approaches a Breit-Wigner shape, the fidelity (Loschmidt echo) decays exponentially, and thermalization becomes viable.

show abstract

Time fluctuations in isolated quantum systems of interacting particles

Cited by 72 publications

References 60 publications

Quantum chaos and thermalization in isolated systems of interacting particles

Quantum chaos and thermalization in isolated systems of interacting particles

Dynamics at the many-body localization transition

Local quenches with global effects in interacting quantum systems

Contact Info

Product

Resources

About