Strength functions, entropies and duality in weakly to strongly interacting fermionic systems

Abstract

We revisit statistical wavefunction properties of finite systems of interacting fermions in the light of strength functions and their participation ratio and information entropy. For weakly interacting fermions in a mean-field with random two-body interactions of increasing strength $\lambda$, the strength functions $F_k(E)$ are well known to change, in the regime where level fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We propose an ansatz for the function describing this transition which we use to investigate the participation ratio ${\xi }_2$ and the information entropy $S^{\mathrm{info}}$ during this crossover, thereby extending the known behavior valid in the Gaussian domain into much of the Breit-Wigner domain. Our method also allows us to derive the scaling law for the duality point $\lambda ={\lambda }_d$, where $F_k(E)$, ${\xi }_2$ and $S^{\mathrm{info}}$ in both the weak ($\lambda =0$) and strong mixing ($\lambda =\infty$) basis coincide as ${\lambda }_d\sim 1/\sqrt{m}$, where $m$ is the number of fermions. As an application, the ansatz function for strength functions is used in describing the Breit-Wigner to Gaussian transition seen in neutral atoms CeI to SmI with valence electrons changing from 4 to 8.

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• Spectroscopy with random and displaced random ensembles
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Cited by in corpus (15)

• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Nonexponential fidelity decay in isolated interacting quantum systems
• Quantum spectrum as a time series : Fluctuation measures
• Thermalization in the Two-Body Random Ensemble
• Thermalization in one- plus two-body ensembles for dense interacting boson systems
• Chaos and localization in the wavefunctions of complex atoms NdI, PmI and SmI
• Self-averaging in many-body quantum systems out of equilibrium: Time dependence of distributions
• Localization-Delocalization Transitions in Bosonic Random Matrix Ensembles
• Bivariate $t$-distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems
• Structure of wavefunction for interacting bosons in mean-field with random $k$-body interactions
• Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model
• Generalized Survival Probability
• Wavefunction structure in quantum many-fermion systems with $k$-body interactions: conditional $q$-normal form of strength functions
• Eigenstate thermalization and disappearance of quantum many-body scar states in interacting fermion systems
• Thermalization in many-fermion quantum systems with one- plus random $k$-body interactions