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 \(d\varGamma (H^{\varLambda } -\mu \mathbb{I})\) of an ideal Bose gas with Dirichlet boundary conditions in a finite volume Λ, from the free energy variation with respect to a Gibbs temperature state and from the monotonicity of the relative entropy. Hypercontractivity of the semigroup \(e^{-\beta d\varGamma (H^{\varLambda }) }\) is also deduced.
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Acknowledgements
This work has been supported by GREFI-GENCO INDAM Italy-CNRS France and MIUR PRIN 2012 Project No 2012TC7588-003.
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Cipriani, F. (2017). Logarithmic Sobolev Inequalities for an Ideal Bose Gas. In: Michelangeli, A., Dell'Antonio, G. (eds) Advances in Quantum Mechanics. Springer INdAM Series, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-58904-6_7
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DOI: https://doi.org/10.1007/978-3-319-58904-6_7
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