Gibbs states of interacting systems of quantum anharmonic oscillators

DOI10.1007/s11005-006-0114-2zbMath1104.82011OpenAlexW2158439486MaRDI QIDQ861726

Yuri V. Kozitskij, T. V. Tsykalenko

Publication date: 30 January 2007

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-006-0114-2

zbMATH Keywords

phase transitionsquantum anharmonic crystalquantum effectsDobrushin-Lanford-Ruelle equation: DLR equationGibbs specificationtemperature loopstempered configurations

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Phase transitions (general) in equilibrium statistical mechanics (82B26) Quantum equilibrium statistical mechanics (general) (82B10)

Related Items (2)

PHASE TRANSITIONS AND QUANTUM STABILIZATION IN QUANTUM ANHARMONIC CRYSTALS ⋮ Dobrushin's compactness criterion for Euclidean Gibbs measures

Cites Work

• Unnamed Item
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• Ground state for point particles interacting through a massless scalar Bose field
• On a theorem of Høegh-Krohn
• Euclidean Gibbs measures of interacting quantum anharmonic oscillators
• Periodic Gaussian Osterwalder-Schrader positive processes and the two- sided Markov property on the circle
• Compactness and the maximal Gibbs state for random Gibbs fields on a lattice
• Stochastic processes associated with KMS states
• Gibbs measures and phase transitions
• Homogeneous random fields and statistical mechanics
• Suppression of critical fluctuations by strong quantum effects in quantum lattice systems
• The quasiclassical limit for the Schrödinger operator and phase transitions in quantum statistical physics
• Uniqueness of Gibbs states for quantum lattice systems
• Dobrushin's uniqueness for quantum lattice systems with nonlocal interaction
• Laguerre entire functions and the Lee-Yang property.
• Small mass implies uniqueness of Gibbs states of a quantum crystal
• Quantum stabilization and decay of correlations in anharmonic crystals
• Gibbs measures relative to Brownian motion
• Gap estimates for double-well Schrödinger operators and quantum stabilization of anharmonic crystals
• Euclidean Gibbs measures on loop lattices: existence and a priori estimates.
• A priori estimates for symmetrizing measures and their applications to Gibbs states
• KMS, ETC.
• EUCLIDEAN GIBBS STATES OF QUANTUM LATTICE SYSTEMS
• Prescribing a System of Random Variables by Conditional Distributions

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