The aim of this work is to derive logarithmic Sobolev inequalities, with respect to the Fock vacuum state and for the second quantized Hamiltonian dΓ(Hᴧ-μI) of an ideal Bose gas with Dirichlet boundary conditions in a finite volume ˄ from the free energy variation with respect to a Gibbs temperature state and from the monotonicity of the relative entropy. Hypercontractivity of the semigroup e-βdΓ(H˄) is also deduced.

Logarithmic Sobolev Inequalities for an Ideal Bose Gas

Cipriani, Fabio
2017-01-01

Abstract

The aim of this work is to derive logarithmic Sobolev inequalities, with respect to the Fock vacuum state and for the second quantized Hamiltonian dΓ(Hᴧ-μI) of an ideal Bose gas with Dirichlet boundary conditions in a finite volume ˄ from the free energy variation with respect to a Gibbs temperature state and from the monotonicity of the relative entropy. Hypercontractivity of the semigroup e-βdΓ(H˄) is also deduced.
2017
ADVANCES IN QUANTUM MECHANICS: CONTEMPORARY TRENDS AND OPEN PROBLEMS
978-3-319-58903-9
978-3-319-58904-6
Free energy; Gibbs state; Hypercontractivity; Ideal bose gas; Logarithmic sobolev inequality; Relative entropy; Mathematics (all)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1041001
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