scholarly journals Emptiness formation in polytropic quantum liquids

2022 ◽  
Author(s):  
Hsiu-Chung Yeh ◽  
Dimitri M Gangardt ◽  
A Kamenev
Keyword(s):  
Equation Of State ◽  
Large Deviations ◽  
Infinite Sequence ◽  
Analytic Solutions ◽  
Hydrodynamic Equations ◽  
Imaginary Time ◽  
Instanton Solution ◽  
Instanton Action ◽  
Quantum Liquids ◽  
Polytropic Equation

Abstract We study large deviations in interacting quantum liquids with the polytropic equation of state P (ρ) ∼ ργ, where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ≥ 1. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.

The motion of the particles volume corresponding to invariant solution of rank 2 submodel of hydrodynamic type

2016 ◽  
Vol 11 (2) ◽  
pp. 205-209
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Invariant Solution ◽  
Hydrodynamic Type ◽  
Lagrangian Coordinates ◽  
Hydrodynamic Equations ◽  
Rank 2 ◽  
Invariant Submodel ◽  
Entropy Functions

Invariant submodel of rank 2 on the subalgebra consisting of the sum of transfers for hydrodynamic equations with the equation of state in the form of pressure as the sum of density and entropy functions, is presented. In terms of the Lagrangian coordinates from condition of nonhyperbolic submodel solutions depending on the four essential constants are obtained. For simplicity, we consider the solution depending on two constants. The trajectory of particles motion, the motion of parallelepiped of the same particles are studied using the Maple.

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

OF CHARGED STARS AND CHARGED BLACK HOLES

2004 ◽  
Vol 13 (07) ◽  
pp. 1375-1379 ◽  
Author(s):  
MANUEL MALHEIRO ◽  
RODRIGO PICANÇO ◽  
SUBHARTHI RAY ◽  
JOSÉ P. S. LEMOS ◽  
VILSON T. ZANCHIN
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Charged Particle ◽  
Equation Of State ◽  
Mass Density ◽  
Compact Star ◽  
Maximum Amount ◽  
Stellar Structure ◽  
Charged Black Holes ◽  
Polytropic Equation

Effect of maximum amount of charge a compact star can hold, is studied here. We analyze the different features in the renewed stellar structure and discuss the reasons why such huge charge is possible inside a compact star. We studied a particular case of a polytropic equation of state (EOS) assuming the charge density is proportional to the mass density. Although the global balance of force allows a huge charge, the electric repulsion faced by each charged particle forces it to leave the star, resulting in the secondary collapse of the system to form a charged black hole.

scholarly journals New classes of anisotropic models with generalized polytropic equation of state

2018 ◽  
Vol 78 (6) ◽  
Author(s):  
S. A. Mardan ◽  
I. Noureen ◽  
M. Azam ◽  
M. A. Rehman ◽  
M. Hussan
Keyword(s):  
Equation Of State ◽  
Anisotropic Models ◽  
Polytropic Equation

scholarly journals A Magnetized Dark Energy Type R/W Model with Polytropic Equation of State in Brans-Dicke Theory

2020 ◽  
Vol 12 (3) ◽  
pp. 251-257
Author(s):  
M. Dewri
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Variable Cosmological Constant ◽  
Volumetric Expansion ◽  
Dynamical Behaviors ◽  
Tensor Theory ◽  
Polytropic Equation ◽  
Theory Of Gravitation ◽  
Energy Type ◽  
Physical Quantities

In this paper, we study the spatially homogeneous Robertson-Walker cosmological models with magnetized isotropic dark energy like fluid in the scalar-tensor theory of gravitation proposed by Brans-Dicke. Variable cosmological constant ᴧ and Polytropic equation of state have been used to find exact solutions of the models with volumetric expansion and power-law relation. The Physical and dynamical behaviors of the models have been discussed using some physical quantities like energy density, pressure, and coefficient of bulk viscosity.

Stability of generalized polytropic models

2019 ◽  
Vol 16 (04) ◽  
pp. 1950056
Author(s):  
I. Nazir ◽  
M. Azam
Keyword(s):  
Equation Of State ◽  
Local Density ◽  
Hydrostatic Equilibrium ◽  
Physical Parameters ◽  
Spherically Symmetric ◽  
Anisotropic Matter ◽  
Polytropic Equation ◽  
Density Perturbations ◽  
Radial Forces ◽  
The Stability

In this paper, we have investigated the stability of a spherically symmetric object with charged anisotropic matter by using the concept of cracking. The cracking is a very intuitive technique to check the stability which is based on the analysis of the radial forces that appear on the system due to perturbations taking it out of its equilibrium state. For this, we have applied and studied the effect of local density perturbations to the hydrostatic equilibrium equation and on all the physical parameters with generalized polytropic equation of state. It is found that some of the generalized polytropic models exhibit cracking.

scholarly journals Modeling Tidal Effects in Accretion Discs

1997 ◽  
Vol 163 ◽  
pp. 335-338
Author(s):  
Patrick Godon
Keyword(s):  
Equation Of State ◽  
White Dwarf ◽  
Accretion Discs ◽  
Time Dependent ◽  
Two Dimensional ◽  
Mass Ratio ◽  
Tidal Effects ◽  
Azimuthal Mode ◽  
Polytropic Equation

AbstractA two-dimensional time-dependent spectral code is used for the study of tidal effects in accretion discs. A cool disc around a white dwarf (characteristic of CV systems) is modeled under the assumption of a polytropic equation of state and a standard alpha viscosity prescription. For a mass ratio q < 0.1 (considered here) and under the assumption of a reflective inner boundary, tidal effects induce an eccentric (m=l azimuthal) mode in the disc together with an elliptic (m=2 azimuthal) mode in the inner disc.

scholarly journals Framework for generalized polytropes with complexity factor

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Shiraz Khan ◽  
S. A. Mardan ◽  
M. A. Rehman
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Differential Equations ◽  
Spherical Symmetry ◽  
Mass Density ◽  
Fluid Distribution ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Polytropic Equation

AbstractA framework is developed for generalized polytropes with the help of complexity factor introduced by Herrera (Phy Rev D 97:044010, 2018), by using the spherical symmetry with anisotropic inner fluid distribution. For this purpose generalized polytropic equation of state will be used, having two cases (i) for mass density $$(\mu _{o})$$(μo), (ii) for energy density $$(\mu )$$(μ), each case leads to a system of differential equations. These systems of differential equations involve two equations with three unknowns and they will be made consistent by using the complexity factor. The analysis of the solutions of these systems will be carried out graphically by using different parametric values involved in the systems.

Study of conformally flat polytropes with tilted congruence

2018 ◽  
Vol 27 (07) ◽  
pp. 1850063 ◽  
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Equation Of State ◽  
Matter Content ◽  
Energy Conditions ◽  
Spherically Symmetric ◽  
Conformally Flat ◽  
Flat Condition ◽  
Polytropic Equation ◽  
Dissipative Fluid ◽  
Symmetric Spacetime ◽  
Fluid Configuration

This paper is aimed to study the modeling of spherically symmetric spacetime in the presence of anisotropic dissipative fluid configuration. This is accomplished for an observer moving relative to matter content using two cases of polytropic equation-of-state under conformally flat condition. We formulate the corresponding generalized Tolman–Oppenheimer–Volkoff equation, mass equation, as well as energy conditions for both cases. The conformally flat condition is imposed to find an expression for anisotropy which helps to study spherically symmetric polytropes. Finally, Tolman mass is used to analyze stability of the resulting models.

scholarly journals Impact of generalized polytropic equation of state on charged anisotropic polytropes

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
S. A. Mardan ◽  
M. Rehman ◽  
I. Noureen ◽  
R. N. Jamil
Keyword(s):  
Equation Of State ◽  
Speed Of Sound ◽  
Graphical Analysis ◽  
Maxwell Field ◽  
Anisotropic Fluid ◽  
Polytropic Index ◽  
Model Parameters ◽  
Field Equations ◽  
Polytropic Equation ◽  
Fluid Configuration

Abstract In this paper, generalized polytropic equation of state is used to get new classes of polytropic models from the solution of Einstein-Maxwell field equations for charged anisotropic fluid configuration. The models are developed for different values of polytropic index $$n=1,~\frac{1}{2},~2$$n=1,12,2. Masses and radii of eight different stars have been regained with the help of developed models. The speed of sound technique and graphical analysis of model parameters is used for the viability of developed models. The analysis of models indicates they are well behaved and physically viable.

Sign in / Sign up

Export Citation Format

Share Document