dorsal/arxiv
View SchemaSelf-consistent theory of large amplitude collective motion: Applications to approximate quantization of non-separable systems and to nuclear physics
| Authors | G. Do Dang, A. Klein, N. R. Walet |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9911081 |
| URL | https://arxiv.org/abs/nucl-th/9911081 |
Abstract
The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of $^{28}$Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other topics included are a nuclear Born-Oppenheimer approximation for an {\em ab initio} quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included.
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"abstract": "The goal of the present account is to review our efforts to obtain and apply\na ``collective\u0027\u0027 Hamiltonian for a few, approximately decoupled, adiabatic\ndegrees of freedom, starting from a Hamiltonian system with more or many more\ndegrees of freedom. The approach is based on an analysis of the classical limit\nof quantum-mechanical problems. Initially, we study the classical problem\nwithin the framework of Hamiltonian dynamics and derive a fully self-consistent\ntheory of large amplitude collective motion with small velocities. We derive a\nmeasure for the quality of decoupling of the collective degree of freedom. We\nshow for several simple examples, where the classical limit is obvious, that\nwhen decoupling is good, a quantization of the collective Hamiltonian leads to\naccurate descriptions of the low energy properties of the systems studied. In\nnuclear physics problems we construct the classical Hamiltonian by means of\ntime-dependent mean-field theory, and we transcribe our formalism to this case.\nWe report studies of a model for monopole vibrations, of $^{28}$Si with a\nrealistic interaction, several qualitative models of heavier nuclei, and\npreliminary results for a more realistic approach to heavy nuclei. Other topics\nincluded are a nuclear Born-Oppenheimer approximation for an {\\em ab initio}\nquantum theory and a theory of the transfer of energy between collective and\nnon-collective degrees of freedom when the decoupling is not exact. The\nexplicit account is based on the work of the authors, but a thorough survey of\nother work is included.",
"arxiv_id": "nucl-th/9911081",
"authors": [
"G. Do Dang",
"A. Klein",
"N. R. Walet"
],
"categories": [
"nucl-th"
],
"title": "Self-consistent theory of large amplitude collective motion: Applications to approximate quantization of non-separable systems and to nuclear physics",
"url": "https://arxiv.org/abs/nucl-th/9911081"
},
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