Microcanonical Distributions, Gibbs States, and the Equivalence of Ensembles

1991 ◽  
pp. 399-424 ◽  
Author(s):  
Daniel W. Stroock ◽  
Ofer Zeitouni
Keyword(s):  
Gibbs States ◽  
Equivalence Of Ensembles

scholarly journals Improved Thermal Area Law and Quasilinear Time Algorithm for Quantum Gibbs States

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tomotaka Kuwahara ◽  
Álvaro M. Alhambra ◽  
Anurag Anshu
Keyword(s):  
Time Algorithm ◽  
Gibbs States ◽  
Area Law

scholarly journals PHASE TRANSITIONS AND QUANTUM STABILIZATION IN QUANTUM ANHARMONIC CRYSTALS

2008 ◽  
Vol 20 (05) ◽  
pp. 529-595 ◽  
Author(s):  
ALINA KARGOL ◽  
YURI KONDRATIEV ◽  
YURI KOZITSKY
Keyword(s):  
Phase Transitions ◽  
Gibbs Measures ◽  
Quantum Effects ◽  
Gibbs States ◽  
Translation Invariance ◽  
Unified Theory ◽  
The Relationship ◽  
Anharmonic Crystals

A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs states in terms of path measures (Euclidean Gibbs measures). It covers the case of crystals without translation invariance, as well as the case of asymmetric anharmonic potentials. The results obtained are compared with those known in the literature.

scholarly journals R-positivity of nearest neighbor matrices and applications to Gibbs states

2010 ◽  
Vol 120 (12) ◽  
pp. 2432-2446 ◽  
Author(s):  
Jorge Littin ◽  
Servet Martínez
Keyword(s):  
Nearest Neighbor ◽  
Gibbs States

scholarly journals Gibbs states on random configurations

2014 ◽  
Vol 55 (8) ◽  
pp. 083513 ◽  
Author(s):  
Alexei Daletskii ◽  
Yuri Kondratiev ◽  
Yuri Kozitsky ◽  
Tanja Pasurek
Keyword(s):  
Gibbs States

Mental Retardation in Infants and Children

PEDIATRICS ◽  
1961 ◽  
Vol 27 (5) ◽  
pp. 739-739
Author(s):  
ROBERT B. KUGEL
Keyword(s):  
Mental Retardation ◽  
Gibbs States ◽  
Infants And Children ◽  
Brain Disorder ◽  
Area Of Concern ◽  
Present Text ◽  
In Infants And Children

In the forward Frederic A. Gibbs states "Changed attitudes toward feeblemindedness allow the present text to start from a simple, logical, and completely realistic premise, viz., that mental retardation is due to brain disorder." Hopefully, many more physicians accept this statement as correct, but it is unfortunately clear that there are still many physicians who have not yet accepted the fact that mental retardation is a reasonable and profitable area of concern and investigation. The authors carefully and persistently present the mass of information now available to support Gibbs' statement.

Gibbs states on the symbolic space over an infinite alphabet

2001 ◽  
Vol 125 (1) ◽  
pp. 93-130 ◽  
Author(s):  
R. Daniel Mauldin ◽  
Mariusz Urbański
Keyword(s):  
Gibbs States ◽  
Symbolic Space

scholarly journals Gibbs' States for Moser-Calogero Potentials

1997 ◽  
Vol 11 (01n02) ◽  
pp. 203-211 ◽  
Author(s):  
K. L. Vaninsky
Keyword(s):  
Phase Space ◽  
Equation Of State ◽  
Gibbs States ◽  
Symplectic Structures ◽  
Classical Particles

We present two independent approaches for computing the thermodynamics for classical particles interacting via the Moser-Calogero potential Combining the results we conjecture the form of equation of state or, what is equivalent, the asymptotics of the Jacobian between volume elements corresponding to two symplectic structures on the phase space.

scholarly journals Free transport for convex potentials

10.53733/102 ◽  
2021 ◽  
Vol 52 ◽  
pp. 259-359
Author(s):  
Yoann Dabrowski ◽  
Alice Guionnet ◽  
Dima Shlyakhtenko
Keyword(s):  
Tensor Product ◽  
Stochastic Analysis ◽  
Gibbs State ◽  
Gibbs States ◽  
Convexity Condition ◽  
Semicircle Law ◽  
Free Transport ◽  
Transport Maps

We construct non-commutative analogs of transport maps among free Gibbs state satisfying a certain convexity condition. Unlike previous constructions, our approach is non-perturbative in nature and thus can be used to construct transport maps between free Gibbs states associated to potentials which are far from quadratic, i.e., states which are far from the semicircle law. An essential technical ingredient in our approach is the extension of free stochastic analysis to non-commutative spaces of functions based on the Haagerup tensor product.

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