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 Dynamical system analysis of quintessence models with exponential potential — Revisited

2019 ◽  
Vol 34 (09) ◽  
pp. 1950069
Author(s):  
A. Savaş Arapoğlu ◽  
A. Emrah Yükselci
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Equation Of State ◽  
System Analysis ◽  
Three Dimensional ◽  
State Parameter ◽  
Late Time ◽  
Exponential Potential ◽  
Effective Equation ◽  
Equation Of State Parameter

Dynamical system analysis of a universe model which contains matter, radiation and quintessence with exponential potential, [Formula: see text], is studied in the light of recent observations and the tensions between different datasets. The three-dimensional phase space is constructed by the energy density parameters and all the critical points of the model with their physical meanings are investigated. This approach provides an easy way of comparing the model directly with the observations. We consider a solution that is compatible with observations and is continuous in the phase space in both directions of time, past and future. Although in many studies of late-time acceleration, the radiation is neglected, here we consider all components together and this makes the calculated effective equation of state parameter more realistic. Additionally, a relation between potential parameter, [Formula: see text], and the value of quintessence equation of state parameter, [Formula: see text], today is found by using numerical analysis. We conclude that [Formula: see text] has to be small in order to explain the current accelerated phase of the universe and this result can be seen directly from the relation we obtain. Finally, we compare the usual dynamical system approach with the approach that we follow in this paper.

Extended phase-space thermodynamics of black holes in massive gravity

2019 ◽  
Vol 34 (09) ◽  
pp. 1950063
Author(s):  
Parthapratim Pradhan
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Black Hole ◽  
Phase Space ◽  
Equation Of State ◽  
Critical Point ◽  
Massive Gravity ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Thermodynamics Of Black Holes

We study the extended phase-space thermodynamics of black holes in massive gravity. Particularly, we examine the critical behavior of this black hole using the extended phase-space formalism. Extended phase-space can be defined as one in which the cosmological constant should be treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. In this phase-space, we derive the black hole equation of state, the critical pressure, the critical volume and the critical temperature at the critical point. We also derive the critical ratio of this black hole. Moreover, we derive the black hole reduced equation of state in terms of the reduced pressure, the reduced volume and the reduced temperature. Furthermore, we examine the Ehrenfest equations of black holes in massive gravity in the extended phase-space at the critical point. We show that the Ehrenfest equations are satisfied on this black hole and the black hole encounters a second-order phase transition at the critical point in the said phase-space. This is re-examined by evaluating the Pregogine–Defay ratio [Formula: see text]. We determine the value of this ratio is [Formula: see text]. The outcome of this study is completely analogous to the nature of liquid–gas phase transition at the critical point. This investigation also further gives us the profound understanding between the black hole of massive gravity with the liquid–gas system.

scholarly journals Poly-symplectic geometry and the AKSZ formalism

2021 ◽  
pp. 2150030
Author(s):  
Ivan Contreras ◽  
Nicolás Martínez Alba
Keyword(s):  
Phase Space ◽  
General Theory ◽  
Symplectic Geometry ◽  
Symplectic Structure ◽  
Sigma Model ◽  
Type Theorem ◽  
Poisson Structures ◽  
Action Functional ◽  
Symplectic Structures ◽  
Poisson Sigma Model

In this paper, we extend the AKSZ formulation of the Poisson sigma model to more general target spaces, and we develop the general theory of graded geometry for poly-symplectic and poly-Poisson structures. In particular, we prove a Schwarz-type theorem and transgression for graded poly-symplectic structures, recovering the action functional and the poly-symplectic structure of the reduced phase space of the poly-Poisson sigma model, from the AKSZ construction.

Classical approximations to Gibbs states

1979 ◽  
Vol 86 (3) ◽  
pp. 521-527
Author(s):  
E. B. Davies
Keyword(s):  
Phase Space ◽  
Coherent States ◽  
Gibbs State ◽  
Gibbs States ◽  
Microcanonical Ensemble ◽  
Trace Norm ◽  
Classical Approximation

AbstractWe obtain two approximate representations of a one-particle Gibbs state, both of which become asymptotically exact in trace norm as m → ∞. The second representation is an integral of pure coherent states over phase space, and can therefore be regarded as a classical approximation to the Gibbs state. We also obtain a version of the second representation applicable to the microcanonical ensemble.

scholarly journals HAMILTONIAN AND LAGRANGIAN DYNAMICS IN A NONCOMMUTATIVE SPACE

2003 ◽  
Vol 18 (39) ◽  
pp. 2795-2806 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Phase Space ◽  
Quantum Groups ◽  
Physical System ◽  
Hamiltonian Formulation ◽  
Noncommutative Space ◽  
Two Dimensional ◽  
Lagrangian Dynamics ◽  
Symplectic Structures ◽  
First Order ◽  
Tangent Manifold

We discuss the dynamics of a particular two-dimensional (2D) physical system in the four-dimensional (4D) (non-)commutative phase space by exploiting the consistent Hamiltonian and Lagrangian formalisms based on the symplectic structures defined on the 4D (non-)commutative cotangent manifolds. The noncommutativity exists equivalently in the coordinate or the momentum planes embedded in the 4D cotangent manifolds. The signature of this noncommutativity is reflected in the derivation of the first-order Lagrangians where we exploit the most general form of the Legendre transformation defined on the (non-)commutative (co-)tangent manifolds. The second-order Lagrangian, defined on the 4D tangent manifold, turns out to be the same irrespective of the noncommutativity present in the 4D cotangent manifolds for the discussion of the Hamiltonian formulation. A connection with the noncommutativity of the dynamics, associated with the quantum groups on the q-deformed 4D cotangent manifolds, is also pointed out.

Thomas–Fermi approximation for the equation of state of nuclear matter: A semi-classical approach from the Landau Fermi-Liquid theory

2017 ◽  
Vol 26 (06) ◽  
pp. 1750038 ◽  
Author(s):  
M. Ghazanfari Mojarrad ◽  
S. K. Mousavi Khoroshtomi
Keyword(s):  
Phase Space ◽  
Equation Of State ◽  
Nuclear Matter ◽  
Fermi Liquid ◽  
Occupation Number ◽  
Nucl Phys ◽  
Classical Approach ◽  
Fermi Liquid Theory ◽  
Thomas Fermi ◽  
Liquid Theory

The equation of state (EOS) of nuclear matter is investigated in a semi-classical mean-field (MF) approach. Starting from the phase-space NN-interaction of Myers and Swiatecki [Nucl. Phys. A 601 (1996) 141], the EOS of nuclear matter by the Thomas–Fermi approximation is derived. A self-consistent semi-classical approach is presented by employing the Landau Fermi-Liquid theory (LFT). In our statistical approach, the phase-space occupation number can be expressed in terms of an extended effective mass which is affected by both temperature and nucleonic density. Accordingly, an explicit expression of the nucleonic chemical potential inside the nucleonic occupation number can be obtained. Special attention is also devoted to the density dependence of the nuclear symmetry free energy at different temperatures. The results of this model are compared with other theoretical predictions.

Hyperon-rich matter in a two-solar-mass neutron star within the Thomas-Fermi approximation

2016 ◽  
Vol 25 (12) ◽  
pp. 1650102 ◽  
Author(s):  
M. Ghazanfari Mojarrad ◽  
R. Arabsaeidi
Keyword(s):  
Neutron Star ◽  
Phase Space ◽  
Equation Of State ◽  
Statistical Model ◽  
Mean Field ◽  
Maximum Mass ◽  
Structure And Properties ◽  
Solar Mass ◽  
Baryon Interaction ◽  
Thomas Fermi

The equation of state (EOS) of hyperon-rich matter for neutron stars (NSs) is investigated in a semi-classical mean-field (MF) model. We present a new generalized baryon–baryon interaction in phase space to derive the EOS by the Thomas–Fermi approximation. Our findings have profound consequences for the structure and properties of NSs. Within this statistical model, the EOS of NS matter with hyperons is stiff enough. Consequently, the results for the maximum mass of NSs are consistent with [Formula: see text] and [Formula: see text]. It is also revealed that the hyperon–hyperon interactions slightly soften the EOS.

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