The aim of this work is to derive logarithmic Sobolev inequalities, with respect to the Fock vacuum state and for the second quantized Hamiltonian dÎ(Há´§-μI) of an ideal Bose gas with Dirichlet boundary conditions in a finite volume Ë 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-βdÎ(HË) 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 dÎ(Há´§-μI) of an ideal Bose gas with Dirichlet boundary conditions in a finite volume Ë 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-βdÎ(HË) is also deduced.File in questo prodotto:
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