Return probability: Exponential versus Gaussian decay

Izrailev, F. M.; Castaneda-Mendoza, A.

doi:10.1016/j.physleta.2005.10.077

Cited by 40 publications

(50 citation statements)

References 32 publications

(70 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, as shown in Ref. [82], the change of the SF to the Gaussian corresponds to the predictions for Wigner BRM. Namely, the transition between the two different shapes, Breit-Wigner and Gaussian, occurs at Γ ∼ σ k , where Γ is the Breit-Wigner width (3.14) and σ 2 k is the variance of the strength function defined by Eq.…”

Section: Standard Model Of Strength Functionssupporting

confidence: 74%

“…The fit to the exponential dependence (6.9) determines Γ 0 ≈ 0.97 that can be compared with the rough estimate (see details in Ref. [82]), In the intermediate regime between Breit-Wigner and Gaussian, there are two time scales, see Fig. 21, middle panel.…”

Section: Survival Probability: Theoretical Backgroundmentioning

confidence: 63%

“…[213] for the strength function that depends on two key parameters, Γ 0 and σ k 0 , see also Ref. [82]. For the TBRI model with N p Fermi particles in N s active orbitals, one has [81], 10) where [−v 0 , v 0 ] is the range within which the two-body matrix elements are distributed randomly with a constant probability.…”

Section: Survival Probability: Theoretical Backgroundmentioning

confidence: 99%

See 2 more Smart Citations

Quantum chaos and thermalization in isolated systems of interacting particles

et al. 2016

Self Cite

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: Standard Model Of Strength Functionssupporting

confidence: 74%

Section: Survival Probability: Theoretical Backgroundmentioning

confidence: 63%

Section: Survival Probability: Theoretical Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

Quantum chaos and thermalization in isolated systems of interacting particles

et al. 2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…At an intermediate value, μ = λ = 0.4 (middle panels), the fidelity decays exponentially (after the short-time quadratic behavior) for both quenches. An eventual switch to an exponential decay was expected to occur even in the limit of strong perturbation [13,14,30,32]. However, we have shown that when the initial state fills the energy shell substantially (as in the bottom panels of Fig.…”

Section: Ldos Fidelitymentioning

confidence: 63%

Isolated many-body quantum systems far from equilibrium: Relaxation process and thermalization

Torres-Herrera

Santos

2014

AIP Conference Proceedings

View full text Add to dashboard Cite

Equilibration of an isolated quantum many-body system Phys. Today Abstract. We present an overview of our recent numerical and analytical results on the dynamics of isolated interacting quantum systems that are taken far from equilibrium by an abrupt perturbation. The studies are carried out on one-dimensional systems of spins-1/2, which are paradigmatic models of many-body quantum systems. Our results show the role of the interplay between the initial state and the post-perturbation Hamiltonian in the relaxation process, the size of the fluctuations after equilibration, and the viability of thermalization.

show abstract

“…Because of this, our studies concentrate on initial states that have energy E n 0 very close to the middle of the spectrum. The Fourier transform of a Gaussian LDOS results in the Gaussian decay of the survival probability, e −ω 2 n 0 t 2 , where ω n 0 is the width of the LDOS [1][2][3][4][5]27]. But when doing the Fourier transform, we should also take into account the unavoidable presence of energy bounds in the spectrum.…”

Section: Spin-1/2 Modelmentioning

confidence: 99%