scholarly journals Equilibrium States, Phase Transitions and Dynamics in Quantum Anharmonic Crystals

2018 ◽  
pp. 529-538
Author(s):  
Yuri Kozitsky
Keyword(s):  
Phase Transitions ◽  
Equilibrium States ◽  
Anharmonic Crystals

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 Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Alexis Larrañaga ◽  
Natalia Herrera ◽  
Juliana Garcia
Keyword(s):  
Heat Capacity ◽  
Black Hole ◽  
Phase Transitions ◽  
Equilibrium States ◽  
Geometric Description ◽  
Curvature Scalar ◽  
Schwarzschild Black Hole ◽  
Thermodynamic Interaction

The thermodynamics of the noncommutative Schwarzschild black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD). Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.

scholarly journals Legendre Invariance and Geometrothermodynamics Description of the 3D Charged-Dilaton Black Hole

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yiwen Han ◽  
XiaoXiong Zeng
Keyword(s):  
Black Hole ◽  
Phase Transitions ◽  
Information Geometry ◽  
Heat Capacities ◽  
Equilibrium States ◽  
Dilaton Black Hole

We first review Weinhold information geometry and Ruppeiner information geometry of 3D charged-dilaton black hole. Then, we use the Legendre invariant to introduce a 2-dimensional thermodynamic metric in the space of equilibrium states, which becomes singular at those points. According to the analysis of the heat capacities, these points are the places where phase transitions occur. This result is valid for the black hole, therefore, provides a geometrothermodynamics description of black hole phase transitions in terms of curvature singularities.

scholarly journals PHASE TRANSITIONS AND QUANTUM EFFECTS IN ANHARMONIC CRYSTALS

2012 ◽  
Vol 26 (11) ◽  
pp. 1250063 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
YURI KONDRATIEV ◽  
YURI KOZITSKY ◽  
MICHAEL RÖCKNER
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Sufficient Conditions ◽  
Interaction Strength ◽  
Quantum Effects ◽  
Free Energy Density ◽  
Single Oscillator ◽  
Necessary And Sufficient ◽  
Anharmonic Crystals ◽  
Main Characteristic Feature

The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some temperature are given in the form of simple inequalities involving the interaction strength and the parameters describing a single oscillator. The main characteristic feature of the theory is that both mentioned phenomena are described in one and the same setting, in which thermodynamic phases of the model appear as probability measures on path spaces. Then the possibility of a phase transition to occur is related to the existence of multiple phases at the same values of the relevant parameters. Other definitions of phase transitions, based on the nondifferentiability of the free energy density and on the appearance of ordering, are also discussed.

Equilibrium states and phase transitions in epitaxial ferroelectric thin films

1999 ◽  
Vol 223 (1) ◽  
pp. 79-90 ◽  
Author(s):  
N. A. Pertsev ◽  
A. G. Zembilgotov ◽  
A. K. Tagantsev
Keyword(s):  
Thin Films ◽  
Phase Transitions ◽  
Equilibrium States ◽  
Ferroelectric Thin Films

Equilibrium dynamics and phase transitions in quantum anharmonic crystals

2009 ◽  
Author(s):  
Yuri Kozitsky ◽  
Yurij Holovatch ◽  
Bertrand Berche ◽  
Nikolai Bogolyubov ◽  
Reinhard Folk
Keyword(s):  
Phase Transitions ◽  
Equilibrium Dynamics ◽  
Anharmonic Crystals

scholarly journals Thermodynamic stability of the stationary Lifshitz black hole of new massive gravity

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
K. Kolev ◽  
K. Staykov ◽  
T. Vetsov
Keyword(s):  
Black Hole ◽  
Phase Transitions ◽  
Thermodynamic Stability ◽  
Black Hole Solution ◽  
Information Geometry ◽  
Massive Gravity ◽  
Equilibrium States ◽  
Point Of View ◽  
Curvature Invariants ◽  
Lifshitz Black Hole

AbstractIn this paper we investigate the thermodynamic properties of the stationary Lifshitz black hole solution of New Massive Gravity. We study the thermodynamic stability from local and global point of view. We also consider the space of equilibrium states for the solution within the framework of thermodynamic information geometry. By investigating the proper thermodynamic metrics and their curvature invariants we find a set of restrictions on the parameter space and the critical points indicating phase transitions of the system. We confirm our findings by analytical analysis of the geodesics on the space of equilibrium states.

Thermodynamic Formalism and Phase Transitions of Generalized Mean-Field Quantum Lattice Models

1998 ◽  
Vol 53 (5) ◽  
pp. 179-207
Author(s):  
T. Gerisch ◽  
A. Rieckers ◽  
H.-J. Volkert
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
Energy Density ◽  
Landau Theory ◽  
Thermodynamic Formalism ◽  
Free Energy Density ◽  
Equilibrium States ◽  
Minimal Free Energy ◽  
Symmetry Properties ◽  
Quantum Statistical

The general structure of thermodynamic equilibrium states for a class of quantum mechanical (multi-lattice) systems is elaborated, combining quantum statistical and thermodynamical methods. The quantum statistical formulation is performed in terms of recent operator algebraic concepts emphasizing the role of the permutation symmetry due to homogeneous coarse graining and employing the internal symmetries. The variational principle of the free energy functional is derived, which determines together with the symmetries the general form of the limiting Gibbs states in terms of their central decomposition. The limiting minimal free energy density and its possible equilibrium states are analyzed on various levels of the description by means of convex analysis, where the Fenchel transforms of the free energies provide entropy like potentials. On the thermodynamic level a modified entropy surface is obtained, which specifies only in combination with its concave envelope the regions of pure and mixed phase states. The symmetry properties of a certain model allow to specify the (non-) differentiability of the minimal free energy density. A characterization and classification of phase transitions in terms of quantum statistical equilibrium states is proposed, and the connection to the Landau theory is established demonstrating that the latter implies a (continuous) deformation of the sets of equilibrium states along a canonically given curve.

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