dorsal/arxiv
View SchemaDissipation in finite Fermi systems
| Authors | Sudhir R. Jain |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9912062 |
| URL | https://arxiv.org/abs/nucl-th/9912062 |
| DOI | 10.1016/S0375-9474(00)00151-2 |
| Journal | Nucl.Phys. A673 (2000) 423-451 |
Abstract
We present a systematic theory of dissipation in finite Fermi systems like nuclei and metallic clusters. This theory is based on the application of semiclassical methods and random matrix theory to linear response of many-body systems. The theory is developed in the approximation wherein the many-body system can be treated as a single particle in an effective, time-dependent mean-field. We find semiclassical expressions for energy dissipation relevant in one-body dissipation in heavy nuclei. We also show that this energy dissipation, related to damping of collective excitations, is irreversible. The irreversibility is proved by our development of a quantum diffusion equation. It may be noted that the quantum diffusion equation is derived from the von Neumann equation and makes no assumption about the initial form of the density operator. It is shown that, in the semiclassical limit, the quantum diffusion equation reduces to the classical Smoluchowski equation. Further, we show that the dissipation is a purely quantal phenomenon as it is related to the geometric phase acquired by a single-particle wavefunction as the system evolves in a slow-varying mean-field. It is explicitly shown that the dissipation rate is related to the nature of dynamics and the spectrum of the classical Liouvillian operator. Finally, we present an expression for the viscosity tensor encountered in nuclear fission in terms of periodic orbits of the single particle in an adiabatically deforming nucleus.
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"abstract": "We present a systematic theory of dissipation in finite Fermi systems like\nnuclei and metallic clusters. This theory is based on the application of\nsemiclassical methods and random matrix theory to linear response of many-body\nsystems. The theory is developed in the approximation wherein the many-body\nsystem can be treated as a single particle in an effective, time-dependent\nmean-field. We find semiclassical expressions for energy dissipation relevant\nin one-body dissipation in heavy nuclei. We also show that this energy\ndissipation, related to damping of collective excitations, is irreversible. The\nirreversibility is proved by our development of a quantum diffusion equation.\nIt may be noted that the quantum diffusion equation is derived from the von\nNeumann equation and makes no assumption about the initial form of the density\noperator. It is shown that, in the semiclassical limit, the quantum diffusion\nequation reduces to the classical Smoluchowski equation. Further, we show that\nthe dissipation is a purely quantal phenomenon as it is related to the\ngeometric phase acquired by a single-particle wavefunction as the system\nevolves in a slow-varying mean-field. It is explicitly shown that the\ndissipation rate is related to the nature of dynamics and the spectrum of the\nclassical Liouvillian operator. Finally, we present an expression for the\nviscosity tensor encountered in nuclear fission in terms of periodic orbits of\nthe single particle in an adiabatically deforming nucleus.",
"arxiv_id": "nucl-th/9912062",
"authors": [
"Sudhir R. Jain"
],
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"doi": "10.1016/S0375-9474(00)00151-2",
"journal_ref": "Nucl.Phys. A673 (2000) 423-451",
"title": "Dissipation in finite Fermi systems",
"url": "https://arxiv.org/abs/nucl-th/9912062"
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