dorsal/arxiv
View SchemaMonte Carlo evaluation of path integrals for the nuclear shell model
| Authors | G. H. Lang, C. W. Johnson, S. E. Koonin, W. E. Ormand |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9305009 |
| URL | https://arxiv.org/abs/nucl-th/9305009 |
| DOI | 10.1103/PhysRevC.48.1518 |
| Journal | Phys.Rev.C48:1518-1545,1993 |
Abstract
We present in detail a formulation of the shell model as a path integral and Monte Carlo techniques for its evaluation. The formulation, which linearizes the two-body interaction by an auxiliary field, is quite general, both in the form of the effective `one-body' Hamiltonian and in the choice of ensemble. In particular, we derive formulas for the use of general (beyond monopole) pairing operators, as well as a novel extraction of the canonical (fixed-particle number) ensemble via an activity expansion. We discuss the advantages and disadvantages of the various formulations and ensembles and give several illustrative examples. We also discuss and illustrate calculation of the imaginary-time response function and the extraction, by maximum entropy methods, of the corresponding strength function. Finally, we discuss the "sign-problem" generic to fermion Monte Carlo calculations, and prove that a wide class of interactions are free of this limitation.
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"abstract": "We present in detail a formulation of the shell model as a path integral and\nMonte Carlo techniques for its evaluation. The formulation, which linearizes\nthe two-body interaction by an auxiliary field, is quite general, both in the\nform of the effective `one-body\u0027 Hamiltonian and in the choice of ensemble. In\nparticular, we derive formulas for the use of general (beyond monopole) pairing\noperators, as well as a novel extraction of the canonical (fixed-particle\nnumber) ensemble via an activity expansion. We discuss the advantages and\ndisadvantages of the various formulations and ensembles and give several\nillustrative examples. We also discuss and illustrate calculation of the\nimaginary-time response function and the extraction, by maximum entropy\nmethods, of the corresponding strength function. Finally, we discuss the\n\"sign-problem\" generic to fermion Monte Carlo calculations, and prove that a\nwide class of interactions are free of this limitation.",
"arxiv_id": "nucl-th/9305009",
"authors": [
"G. H. Lang",
"C. W. Johnson",
"S. E. Koonin",
"W. E. Ormand"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.48.1518",
"journal_ref": "Phys.Rev.C48:1518-1545,1993",
"title": "Monte Carlo evaluation of path integrals for the nuclear shell model",
"url": "https://arxiv.org/abs/nucl-th/9305009"
},
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