dorsal/arxiv
View SchemaEntropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems
| Authors | V. V. Flambaum, F. M. Izrailev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103129 |
| URL | https://arxiv.org/abs/quant-ph/0103129 |
| DOI | 10.1103/PhysRevE.64.036220 |
| Journal | Phys.Rev.E64:036220,2001 |
Abstract
Highly excited many-particle states in quantum systems such as nuclei, atoms, quantum dots, spin systems, quantum computers etc., can be considered as ``chaotic'' superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is due to a very high level density of many-body states that are easily mixed by a residual interaction between particles (quasi-particles). For such systems, we have derived simple analytical expressions for the time dependence of energy width of wave packets, as well as for the entropy, number of principal basis components and inverse participation ratio, and tested them in numerical experiments. It is shown that the energy width $\Delta (t)$ increases linearly and very quickly saturates. The entropy of a system increases quadratically, $S(t) \sim t^2$ at small times, and after, can grow linearly, $S(t) \sim t$, before the saturation. Correspondingly, the number of principal components determined by the entropy, $N_{pc} \sim exp{(S(t))}$, or by the inverse participation ratio, increases exponentially fast before the saturation. These results are explained in terms of a cascade model which describes the flow of excitation in the Fock space of basis components. Finally, a striking phenomenon of damped oscillations in the Fock space at the transition to an equilibrium is discussed.
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"abstract": "Highly excited many-particle states in quantum systems such as nuclei, atoms,\nquantum dots, spin systems, quantum computers etc., can be considered as\n``chaotic\u0027\u0027 superpositions of mean-field basis states (Slater determinants,\nproducts of spin or qubit states). This is due to a very high level density of\nmany-body states that are easily mixed by a residual interaction between\nparticles (quasi-particles). For such systems, we have derived simple\nanalytical expressions for the time dependence of energy width of wave packets,\nas well as for the entropy, number of principal basis components and inverse\nparticipation ratio, and tested them in numerical experiments. It is shown that\nthe energy width $\\Delta (t)$ increases linearly and very quickly saturates.\nThe entropy of a system increases quadratically, $S(t) \\sim t^2$ at small\ntimes, and after, can grow linearly, $S(t) \\sim t$, before the saturation.\nCorrespondingly, the number of principal components determined by the entropy,\n$N_{pc} \\sim exp{(S(t))}$, or by the inverse participation ratio, increases\nexponentially fast before the saturation. These results are explained in terms\nof a cascade model which describes the flow of excitation in the Fock space of\nbasis components. Finally, a striking phenomenon of damped oscillations in the\nFock space at the transition to an equilibrium is discussed.",
"arxiv_id": "quant-ph/0103129",
"authors": [
"V. V. Flambaum",
"F. M. Izrailev"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"nlin.CD",
"nucl-th"
],
"doi": "10.1103/PhysRevE.64.036220",
"journal_ref": "Phys.Rev.E64:036220,2001",
"title": "Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems",
"url": "https://arxiv.org/abs/quant-ph/0103129"
},
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