dorsal/arxiv
View SchemaStrength functions, entropies and duality in weakly to strongly interacting fermionic systems
| Authors | D. Angom, S. Ghosh, V. K. B. Kota |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401103 |
| URL | https://arxiv.org/abs/quant-ph/0401103 |
| DOI | 10.1103/PhysRevE.70.016209 |
| Journal | Phys. Rev. E 70, 016209 (2004) |
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 $S^{\rm info}$ 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 $S^{\rm info}$ 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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"abstract": "We revisit statistical wavefunction properties of finite systems of\ninteracting fermions in the light of strength functions and their participation\nratio and information entropy. For weakly interacting fermions in a mean-field\nwith random two-body interactions of increasing strength $\\lambda$, the\nstrength functions $F_k(E)$ are well known to change, in the regime where level\nfluctuations follow Wigner\u0027s surmise, from Breit-Wigner to Gaussian form. We\npropose an ansatz for the function describing this transition which we use to\ninvestigate the participation ratio $\\xi_2$ and the information entropy $S^{\\rm\ninfo}$ during this crossover, thereby extending the known behavior valid in the\nGaussian domain into much of the Breit-Wigner domain. Our method also allows us\nto derive the scaling law for the duality point $\\lambda = \\lambda_d$, where\n$F_k(E)$, $\\xi_2$ and $S^{\\rm info}$ in both the weak ($\\lambda=0$) and strong\nmixing ($\\lambda = \\infty$) basis coincide as $\\lambda_d \\sim 1/\\sqrt{m}$,\nwhere $m$ is the number of fermions. As an application, the ansatz function for\nstrength functions is used in describing the Breit-Wigner to Gaussian\ntransition seen in neutral atoms CeI to SmI with valence electrons changing\nfrom 4 to 8.",
"arxiv_id": "quant-ph/0401103",
"authors": [
"D. Angom",
"S. Ghosh",
"V. K. B. Kota"
],
"categories": [
"quant-ph",
"nlin.CD",
"physics.atom-ph"
],
"doi": "10.1103/PhysRevE.70.016209",
"journal_ref": "Phys. Rev. E 70, 016209 (2004)",
"title": "Strength functions, entropies and duality in weakly to strongly interacting fermionic systems",
"url": "https://arxiv.org/abs/quant-ph/0401103"
},
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