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Logarithmic Sobolev Inequalities for an Ideal Bose Gas

  • Fabio CiprianiEmail author
Chapter
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Part of the Springer INdAM Series book series (SINDAMS, volume 18)

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.

Keywords

Free energy Gibbs state Hypercontractivity Ideal bose gas Logarithmic sobolev inequality Relative entropy 

Notes

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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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