The Laser Phase Transition Analogy and the Partition Function for Bose Condensation of N Atoms in a Trap

2000 ◽  
pp. 23-30
Author(s):  
Marlan O. Scully
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Bose Condensation

THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

Partition-function zeros and the SU(3) deconfining phase transition

1990 ◽  
Vol 64 (26) ◽  
pp. 3107-3110 ◽  
Author(s):  
Nelson A. Alves ◽  
Bernd A. Berg ◽  
Sergiu Sanielevici
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Partition Function Zeros ◽  
Function Zeros

Error catastrophe for viruses infecting cells: analysis of the phase transition in terms of error classes

2010 ◽  
Vol 368 (1933) ◽  
pp. 5569-5582 ◽  
Author(s):  
Julia Alonso ◽  
Hugo Fort
Keyword(s):  
Phase Transition ◽  
Rna Viruses ◽  
Rna Virus ◽  
Bose Condensation ◽  
Viral Dynamics ◽  
Replication Rate ◽  
Genetic Sequence ◽  
Coupled Equations ◽  
Error Catastrophe ◽  
Common Framework

RNA viruses offer a very exciting arena in which to study evolution in ‘real time’ owing to both their high replication rate—many generations per day are possible—and their high mutation rate, leading to a large phenotypic variety. They can be regarded as a swarm of genetically related mutants around a dominant or master genetic sequence. This system is called a ‘viral quasi-species’. Thus, a common framework to describe RNA viral dynamics is by means of the quasi-species equation (QSE). The QSE is in fact a system of a very large number of nonlinear coupled equations. Here, we consider a simpler formulation in terms of ‘error classes’, which groups all the sequences differing from the master sequence by the same number of genomic differences into one population class. From this, based on the analogies with Bose condensation, we use thermodynamic inspired observables to analyse and characterize the ‘phase transition’ through the so-called ‘RNA virus error catastrophe’.

SIGNATURES OF AN EMERGENT GRAVITY FROM BLACK HOLE ENTROPY

2009 ◽  
Vol 18 (14) ◽  
pp. 2323-2327
Author(s):  
CENALO VAZ
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Mass Spectrum ◽  
Partition Function ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Thermodynamic Description ◽  
Black Hole Entropy ◽  
Fundamental Particle ◽  
Horizon Radius

The existence of a thermodynamic description of horizons indicates that space–time has a microstructure. While the "fundamental" degrees of freedom remain elusive, quantizing Einstein's gravity provides some clues about their properties. A quantum AdS black hole possesses an equispaced mass spectrum, independent of Newton's constant, G, when its horizon radius is large compared to the AdS length. Moreover, the black hole's thermodynamics in this limit is inextricably connected with its thermodynamics in the opposite (Schwarzschild) limit by a duality of the Bose partition function. G, absent in the mass spectrum, re-emerges in the thermodynamic description through the Schwarzschild limit, which should be viewed as a natural "ground state." It seems that the Hawking–Page phase transition separates fundamental, "particle-like" degrees of freedom from effective, "geometric" ones.

scholarly journals Deformations of JT gravity via topological gravity and applications

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Stefan Förste ◽  
Hans Jockers ◽  
Joshua Kames-King ◽  
Alexandros Kanargias
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Form Factors ◽  
Temperature Limit ◽  
Partition Functions ◽  
De Sitter ◽  
Spectral Form ◽  
Kdv Hierarchy ◽  
Topological Gravity ◽  
Perturbative Corrections

Abstract We study the duality between JT gravity and the double-scaled matrix model including their respective deformations. For these deformed theories we relate the thermal partition function to the generating function of topological gravity correlators that are determined as solutions to the KdV hierarchy. We specialise to those deformations of JT gravity coupled to a gas of defects, which conforms with known results in the literature. We express the (asymptotic) thermal partition functions in a low temperature limit, in which non-perturbative corrections are suppressed and the thermal partition function becomes exact. In this limit we demonstrate that there is a Hawking-Page phase transition between connected and disconnected surfaces for this instance of JT gravity with a transition temperature affected by the presence of defects. Furthermore, the calculated spectral form factors show the qualitative behaviour expected for a Hawking-Page phase transition. The considered deformations cause the ramp to be shifted along the real time axis. Finally, we comment on recent results related to conical Weil-Petersson volumes and the analytic continuation to two-dimensional de Sitter space.

Phase transition to blob-hole coherent structure in the Hasegawa–Mima model for plasmas

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
Chjan C. Lim
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Critical Temperature ◽  
Partition Function ◽  
Open System ◽  
Ground State ◽  
Spherical Model ◽  
Toroidal Plasmas ◽  
Fixed Energy ◽  
System A

An equilibrium statistical mechanics theory for the Hasegawa–Mima equations of toroidal plasmas, with canonical constraint on energy and microcanonical constraint on potential enstrophy, is solved exactly as a spherical model. The use of a canonical energy constraint instead of a fixed-energy microcanonical approach is justified by the preference for viewing real plasmas as an open system. A significant consequence of the results obtained from the partition function, free energy and critical temperature, is the condensation into a ground state exhibiting a blob-hole-like structure observed in real plasmas.

INTEGRAL REPRESENTATION FOR THE GR AND PARTITION FUNCTION IN QUANTUM STATISTICAL MECHANICS OF EXCLUSION STATISTICS

2000 ◽  
Vol 14 (05) ◽  
pp. 485-506 ◽  
Author(s):  
KAZUMOTO IGUCHI ◽  
KAZUHIKO AOMOTO
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Integral Representation ◽  
Quantum Statistical Mechanics ◽  
Ideal Gas ◽  
Alternative Proof ◽  
Quantum Statistical

We derive an exact integral representation for the gr and partition function for an ideal gas with exclusion statistics. Using this we show how the Wu's equation for the exclusion statistics appears in the problem. This can be an alternative proof for the Wu's equation. We also discuss that singularities are related to the existence of a phase transition of the system.

scholarly journals Exact Solution of a One-dimensional Spin System

1970 ◽  
Vol 23 (5) ◽  
pp. 927 ◽  
Author(s):  
RW Gibberd
Keyword(s):  
Phase Transition ◽  
Exact Solution ◽  
Free Energy ◽  
Partition Function ◽  
Thermodynamic Limit ◽  
Spin System ◽  
Spin Systems ◽  
One Dimensional ◽  
Gibb’S Free Energy ◽  
Theory Of Superconductivity

The partition function and the Gibb's free energy are calculated exactly in the thermodynamic limit, using techniques which are well known in the theory of superconductivity. This calculation illustrates explicitly the similarity between the phase transition in superconductivity and the molecular field transitions in spin systems.

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