dorsal/arxiv
View SchemaExtended BCS Theories
| Authors | R. Balian, H. Flocard, M. Vénéroni |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9706041 |
| URL | https://arxiv.org/abs/nucl-th/9706041 |
Abstract
Extensions of the Hartree-Fock-Bogoliubov theory are worked out which are tailored for, (i) the consistent evaluation of fluctuations and correlations and (ii) the restoration through projection of broken symmetries. For both purposes we rely on a single variational principle which optimizes the characteristic function. The Bloch equation is used as a constraint to define the equilibrium state, and the trial quantities are a density operator and a Lagrangian multiplier matrix which is akin to an observable. The conditions of stationarity are respectively a Schr\"odinger-like equation and a Heisenberg-- like equation with an imaginary time running backwards. General conditions for the trial spaces are stated that warrant the preservation of thermodynamic relations. When the trial spaces are chosen to be of the independent-quasi-particle type, the ensuing coupled equations provide an extension of the Hartree-Fock-Bogoliubov approximation, which optimizes the characteristic function. Variational expressions for thermodynamic quantities or characteristic functions are also obtained with projected trial states, whether an invariance symmetry is broken or not. In particular, the projection on even or odd particle number is worked out for a pairing Hamiltonian, which leads to new equations replacing the BCS ones. Qualitative differences between even and odd systems, depending on the temperature $T$, the level density and the strength of the pairing force, are investigated analytically and numerically.
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"abstract": "Extensions of the Hartree-Fock-Bogoliubov theory are worked out which are\ntailored for, (i) the consistent evaluation of fluctuations and correlations\nand (ii) the restoration through projection of broken symmetries. For both\npurposes we rely on a single variational principle which optimizes the\ncharacteristic function. The Bloch equation is used as a constraint to define\nthe equilibrium state, and the trial quantities are a density operator and a\nLagrangian multiplier matrix which is akin to an observable. The conditions of\nstationarity are respectively a Schr\\\"odinger-like equation and a Heisenberg--\nlike equation with an imaginary time running backwards. General conditions for\nthe trial spaces are stated that warrant the preservation of thermodynamic\nrelations. When the trial spaces are chosen to be of the\nindependent-quasi-particle type, the ensuing coupled equations provide an\nextension of the Hartree-Fock-Bogoliubov approximation, which optimizes the\ncharacteristic function. Variational expressions for thermodynamic quantities\nor characteristic functions are also obtained with projected trial states,\nwhether an invariance symmetry is broken or not. In particular, the projection\non even or odd particle number is worked out for a pairing Hamiltonian, which\nleads to new equations replacing the BCS ones. Qualitative differences between\neven and odd systems, depending on the temperature $T$, the level density and\nthe strength of the pairing force, are investigated analytically and\nnumerically.",
"arxiv_id": "nucl-th/9706041",
"authors": [
"R. Balian",
"H. Flocard",
"M. V\u00e9n\u00e9roni"
],
"categories": [
"nucl-th",
"cond-mat"
],
"title": "Extended BCS Theories",
"url": "https://arxiv.org/abs/nucl-th/9706041"
},
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