A note on the non-commutative laplace-varadhan integral lemma

• Verfasst von: De Roeck, Wojciech [VerfasserIn]
• Verfasst von: Maes, Christian [VerfasserIn]
• Verfasst von: Netočný, Karel [VerfasserIn]
• Verfasst von: Rey-Bellet, Luc [VerfasserIn]
• Titel: A note on the non-commutative laplace-varadhan integral lemma
• Verf.angabe: W. De Roeck, Christian Maes, Karel Netočný, Luc Rey-Bellet
• Jahr: 2010
• Umfang: 20 S.
• Fussnoten: Gesehen am 15.09.2023
• Titel Quelle: Enthalten in: Reviews in mathematical physics
• Ort Quelle: [Singapore] : World Scientific, 1989
• Jahr Quelle: 2010
• Band/Heft Quelle: 22(2010), 7, Seite 839-858
• ISSN Quelle: 1793-6659
• DOI: doi:10.1142/S0129055X10004089
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Laplace-Varadhan lemma
• Sach-SW: Quantum large deviations
• Sach-SW: quantum lattice systems
• K10plus-PPN: 1859696848

Abstract

We continue the study of the free energy of quantum lattice spin systems where to the local Hamiltonian H an arbitrary mean field term is added, a polynomial function of the arithmetic mean of some local observables X and Y that do not necessarily commute. By slightly extending a recent paper by Hiai, Mosonyi, Ohno and Petz [10], we prove in general that the free energy is given by a variational principle over the range of the operators X and Y. As in [10], the result is a non-commutative extension of the Laplace-Varadhan asymptotic formula.