A-priori Estimates and Existence for Quantum Gibbs States

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dc.creatorAlbeverio, Sergio
dc.creatorKondratiev, Yuri G.
dc.creatorPasurek, Tatiana
dc.creatorRöckner, Michael
dc.date2005-12-20
dc.date.accessioned2026-07-07T06:55:33Z
dc.date.available2026-07-07T06:55:33Z
dc.descriptionWe prove a priori estimates and, as sequel, existence of Euclidean Gibbs states for quantum lattice systems. For this purpose we develop a new analytical approach, the main tools of which are: first, a characterization of the Gibbs states in terms of their Radon-Nikodym derivatives under shift transformations as well as in terms of their logarithmic derivatives through integration by parts formulae, and second, the choice of appropriate Lyapunov functionals describing stabilization effects in the system. The latter technique becomes applicable since on the basis of the integration by parts formulae the Gibbs states are characterized as solutions of an infinite system of partial differential equations. Our existence result generalize essentially all previous ones. In particular, superquadratic growth of the interaction potentials is allowed and $N$-particle interactions for $N\in \mathbb{N}\cup \{\infty \}$ are included. We also develop abstract frames both for the necessary single spin space analysis and for the lattice analysis apart from their applications to our concrete models. Both types of general results obtained in these two frames should be also of their own interest in infinite dimensional analysis.
dc.description101 pages; BiBoS-Preprint 02-06-089; to appear in Trans. Moscow Math. Soc
dc.identifierhttps://arxiv.org/abs/math/0512462
dc.identifierhttp://arxiv.org/abs/math/0512462
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106315
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectPrimary: 82B10; Secondary: 46G12, 60H30
dc.titleA-priori Estimates and Existence for Quantum Gibbs States
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