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- W2293413 abstract "In many exactly solvable models of quantum statistical mechanics, an interaction Hamiltonian is equal to an integral of a product of operators of annihilation and creation and a potential divided by a volume of a system raised to a certain power. For example, the interaction Hamiltonian of the BCS model of superconductivity has the form $$ {H_{I,M}} = frac{g}{{2V}}iint {iint {Phi ({x_1} - {x_2},{{x'}_1} - {{x'}_2}){psi ^ + }({x_2})psi ({{x'}_1})psi ({{x'}_2}})d{x_1}d{x_2}d{{x'}_1}d{{x'}_2},} $$ (1) where integration is carried out over the whole three-dimensional Euclidean space ℝ3, V is the volume of ℝ3, ψ+ and ψ- are operators of creation and annihilation of Fermi particles, and Φ is a potential that satisfies the conditions $$ Phi ({x_1} - {x_2},{x'_1} - {x'_2}) = Phi (overline {{x_1} - {x_2},{{x'}_1} - {{x'}_2}} ) = Phi ({x'_2} - {x'_1},{x_2} - {x_2}),Phi ({x_2} - {x_1},{x'_1} - {x'_2}) = Phi ({x_2} - {x_1},{x'_2} - {x'_1}) $$ (2) and is a test function with respect to x 1-x 2 and ( {x'_1} - {x'_2} ). The dependence on spin is omitted here." @default.
- W2293413 created "2016-06-24" @default.
- W2293413 creator A5069345081 @default.
- W2293413 date "1994-01-01" @default.
- W2293413 modified "2023-09-23" @default.
- W2293413 title "General Hamiltonians and Model Hamiltonians of the Theory of Superconductivity and Superfluidity in the Hilbert Space of Translation-Invariant Functions" @default.
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- W2293413 doi "https://doi.org/10.1007/978-3-0348-8545-4_26" @default.
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