dorsal/arxiv
View SchemaExact and approximate many-body dynamics with stochastic one-body density matrix evolution
| Authors | Denis Lacroix |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407042 |
| URL | https://arxiv.org/abs/quant-ph/0407042 |
| DOI | 10.1103/PhysRevC.71.064322 |
| Journal | Physical Review C71, (2005) 064322 |
Abstract
We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, $D_{ab}=| \Phi_a > < \Phi_b |$, where each state evolves according to the Stochastic Schr\"odinger Equation (SSE) given in ref. \cite{Jul02}. A stochastic Liouville-von Neumann equation is derived as well as the associated Bogolyubov-Born-Green-Kirwood-Yvon (BBGKY) hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended Time-Dependent Hartree-Fock (Extended TDHF) scheme. In this stochastic mean field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.
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"abstract": "We show that the dynamics of interacting fermions can be exactly replaced by\na quantum jump theory in the many-body density matrix space. In this theory,\njumps occur between densities formed of pairs of Slater determinants, $D_{ab}=|\n\\Phi_a \u003e \u003c \\Phi_b |$, where each state evolves according to the Stochastic\nSchr\\\"odinger Equation (SSE) given in ref. \\cite{Jul02}. A stochastic\nLiouville-von Neumann equation is derived as well as the associated\nBogolyubov-Born-Green-Kirwood-Yvon (BBGKY) hierarchy. Due to the specific form\nof the many-body density along the path, the presented theory is equivalent to\na stochastic theory in one-body density matrix space, in which each density\nmatrix evolves according to its own mean field augmented by a one-body noise.\nGuided by the exact reformulation, a stochastic mean field dynamics valid in\nthe weak coupling approximation is proposed. This theory leads to an\napproximate treatment of two-body effects similar to the extended\nTime-Dependent Hartree-Fock (Extended TDHF) scheme. In this stochastic mean\nfield dynamics, statistical mixing can be directly considered and jumps occur\non a coarse-grained time scale. Accordingly, numerical effort is expected to be\nsignificantly reduced for applications.",
"arxiv_id": "quant-ph/0407042",
"authors": [
"Denis Lacroix"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"nucl-th"
],
"doi": "10.1103/PhysRevC.71.064322",
"journal_ref": "Physical Review C71, (2005) 064322",
"title": "Exact and approximate many-body dynamics with stochastic one-body density matrix evolution",
"url": "https://arxiv.org/abs/quant-ph/0407042"
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