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arXiv:cond-mat/9707231 · Physical Review Letters

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

Bertrand Georgeot, Dima L. Shepelyansky

Published Dec 1, 1997• 73 citations
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Abstract

For many-body Fermi systems we determine the dependence of the Breit-Wigner width $\ensuremath{\gamma}$ and inverse participation ratio $\ensuremath{\xi}$ on interaction strength $U\ensuremath{\ge}{U}_{c}$ and energy excitation $\ensuremath{\delta}E\ensuremath{\ge}\ensuremath{\delta}{E}_{\mathrm{ch}}$ when a crossover from Poisson to Wigner-Dyson $P(s)$ statistics takes place. At $U\ensuremath{\ge}{U}_{c}$ the eigenstates are composed of a large number of noninteracting states and even for $U<{U}_{c}$ there is a regime where $P(s)$ is close to the Poisson distribution but $\ensuremath{\xi}\ensuremath{\gg}1$.

DOI
10.1103/physrevlett.79.4365

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The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution P(s)P(s)P(s) as a function of interaction strength U and the excitation energy $\ensuremath{\epsilon}$ above the Fermi level. As U increases, P(s)P(s)P(s) undergoes a transition from Poissonian (nonchaotic) to Wigner-Dyson (chaotic) statistics and the transition is described by a single scaling parameter given by $Z=(U{\ensuremath{\epsilon}}^{\ensuremath{\alpha}}\ensuremath{-}{u}_{0}){\ensuremath{\epsilon}}^{1/(2\ensuremath{\nu})},$ where u0{u}_{0}u0​ is a constant. While the exponent $\ensuremath{\alpha},$ which determines the global change of the chaos border, is indecisive within a broad range of $0.9\ensuremath{\sim}2.0,$ the finiteness of $\ensuremath{\nu},$ which comes from the increase of the Fock space size with $\ensuremath{\epsilon},$ suggests that the transition becomes sharp as $\ensuremath{\epsilon}$ increases.
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