Breit-Wigner Width and Inverse Participation Ratio in Finite Interacting Fermi Systems

Georgeot, Bertrand; Shepelyansky, Dima L.

doi:10.1103/physrevlett.79.4365

Cited by 71 publications

(93 citation statements)

References 25 publications

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“…The BW spreading also emerges in the well-known nuclear physics model of a state interacting with a large set of states with ρ = const by means of a constant or weakly fluctuating matrix element [5]. It has been verified numerically in our earlier calculations in Ce [8], the sd shell nuclear model [9][10][11][12] (for the interaction strengths which satisfied Γ < Db), and the two-body random interaction model [40]. Some of the deviations from the BW shape observed in [9][10][11][12] were attributed to the fact the ρ = const.…”

Section: Chaotic Eigenstatessupporting

confidence: 62%

Quantum chaos in many-body systems: what can we learn from the Ce atom?

Flambaum

Gribakina

Gribakin

et al. 1999

Physica D: Nonlinear Phenomena

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Results of an extensive study of a real quantum chaotic many-body system -the Ce atom -are presented. We discuss the origins of the quantum chaotic behaviour of the system, analyse statistical and dynamical properties of the multi-particle chaotic eigenstates and consider matrix elements or transition amplitudes between them. We show that based on the universal properties of the chaotic eigenstates a statistical theory of finite few-particle systems with strong interaction can be developed. We also discuss such important physical effects as enhancement of weak perturbations in many-body quantum chaotic systems, distribution of single-particle occupation numbers and its deviations from the standard Fermi-Dirac shape, and ways of introducing statistical temperature-based description in such systems.

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Section: Chaotic Eigenstatessupporting

confidence: 62%

Quantum chaos in many-body systems: what can we learn from the Ce atom?

Flambaum

Gribakina

Gribakin

et al. 1999

Physica D: Nonlinear Phenomena

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“…is the inverse participation ratio (IPR) [19]. Its inverse estimates the number of the NS eigenstates the IS one consists of.…”

mentioning

confidence: 99%

Memory of the Initial Conditions in an Incompletely Chaotic Quantum System: Universal Predictions with Application to Cold Atoms

Yurovsky

Olshanii

2011

Phys. Rev. Lett.

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Two zero-range-interacting atoms in a circular, transversely harmonic waveguide are used as a test-bench for a quantitative description of the crossover between integrability and chaos in a quantum system with no selection rules. For such systems we show that the expectation value after relaxation of a generic observable is given by a linear interpolation between its initial and thermal expectation values. The variable of this interpolation is universal; it governs this simple law to cover the whole spectrum of the chaotic behavior from integrable regime through the welldeveloped quantum chaos. The predictions are confirmed for the waveguide system, where the mode occupations and the trapping energy were used as the observables of interest; a variety of the initial states and a full range of the interaction strengths have been tested. Two distinct types of evolution of an isolated dynamical system are usually identified: a predictable evolution, strongly correlated with the initial state on one hand and a relaxation to the thermal equilibrium with no memory of the initial state on the other. An ideal gas of noninteracting atoms is a trivial example of a predictable evolution. In cold quantum gases, this type of behavior was observed for the single-mode excitations in BoseEinstein condensates [1, 2] and a one-dimensional gas of interacting atoms [3]. Such systems can be described by integrable models, i.e. models that have as many integrals of motion as there are degrees of freedom. Lifting of integrability leads to a chaotic motion. For ultracold atoms, notable examples of the quantum-chaotic motion include both a non-stationary δ-kicked rotor [4,5] and a stationary billiard [6].Interactions between the trapped atoms are the most common cause of integrability lifting (with the exception of the one-dimensional gas, see [7]). Even for the case of just two trapped atoms, interactions can already destroy integrability [8]. For ultracold atoms, the atomic de Brogle wavelength typically substantially exceeds the interaction range. In this case, the interaction couples every two eigenstates of non-interacting atoms with approximately the same strength, yielding no selection rules interaction can obey.In this Letter, we analyze the case of two interacting atoms in a circular, transversely harmonic waveguide in the multimode regime [8]. Similar models, thě Seba billiard [9] and a cylindrically-symmetric harmonic trap with a δ-scatterer [10], were considered by other authors as well. These models, as well as the waveguide model, are non-integrable and show some signatures of a quantum-chaotic behavior as a result. However, their behavior is only incompletely-chaotic, since the systems demonstrate some substantial deviations from quantumchaotic predictions as well (see [8,11] and the references therein). In these systems, the interaction strength can be used to tune the "chaoticity".Trajectories of a completely-chaotic classical system fill all the available phase space in a "mixing" motion. This leads to a relaxation to t...

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“…As mentioned in the introduction, the nature of NPC (which is the inverse of IPR) in wavefunctions in the λ c ≤ λ < λ F k domain where F k (E) is of BW form (i.e. in the BW domain) was studied in [9] while the present article is concerned with the λ > λ F k domain (i.e. the Gaussian domain) where F k (E) is of Gaussian form.…”

Section: Basic Results For (1+2)-body Random Matrix Ensemblesmentioning

confidence: 99%

Structure of wave functions in(1+2)-body random matrix ensembles

Kota

Sahu

2001

Phys. Rev. E

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Random matrix ensembles defined by a mean-field one-body plus a chaos generating random two-body interaction (called embedded ensembles of (1+2)-body interactions) predict for wavefunctions, in the chaotic domain, an essentially one parameter Gaussian forms for the energy dependence of the number of principal components NPC and the localization length l H (defined by information entropy), which are two important measures of chaos in finite interacting many particle systems. Numerical embedded ensemble calculations and nuclear shell model results, for NPC and l H , are compared with the theory. These analysis clearly point out that for realistic finite interacting many particle systems, in the chaotic domain, wavefunction structure is given by (1+2)-body embedded random matrix ensembles.

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Breit-Wigner Width and Inverse Participation Ratio in Finite Interacting Fermi Systems

Cited by 71 publications

References 25 publications

Quantum chaos in many-body systems: what can we learn from the Ce atom?

Quantum chaos in many-body systems: what can we learn from the Ce atom?

Memory of the Initial Conditions in an Incompletely Chaotic Quantum System: Universal Predictions with Application to Cold Atoms

Structure of wave functions in(1+2)-body random matrix ensembles

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