scholarly journals Macrostates Thermodynamics and Its Stable Classical Limit in Global One-Dimensional Quantum General Relativity

2009 ◽  
Vol 6 (1) ◽  
pp. 19-42
Author(s):  
L. A. Glinka
Keyword(s):  
General Relativity ◽  
Classical Limit ◽  
One Dimensional

A NONLINEAR-OSCILLATOR MODEL FOR STRONG INTERACTION IN MOLECULAR SOLIDS

2006 ◽  
Vol 20 (30) ◽  
pp. 1953-1955 ◽  
Author(s):  
M. A. GRADO-CAFFARO ◽  
M. GRADO-CAFFARO
Keyword(s):  
Classical Limit ◽  
Vibrational Energy ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
Potential Interaction ◽  
Strong Interactions ◽  
Molecular Solids ◽  
One Dimensional ◽  
Vibrational Energy Levels ◽  
Type Potential

A theoretical model based upon a one-dimensional anharmonic oscillator is proposed in order to describe strong interactions in molecular solids. Vibrational energy levels are studied in terms of the associated vibrational quantum number; in particular, classical limit is discussed. Kinetic energy corresponding to a typical collision process is calculated. In addition, Morse-type potential interaction is found to be an approximation to our model.

scholarly journals The Damped Harmonic Oscillator at the Classical Limit of the Snyder-de Sitter Space

2021 ◽  
Vol 13 (2) ◽  
pp. 1
Author(s):  
Lat´evi M. Lawson ◽  
Ibrahim Nonkan´e ◽  
Komi Sodoga
Keyword(s):  
Harmonic Oscillator ◽  
Classical Limit ◽  
Minimal Length ◽  
Poisson Brackets ◽  
Canonical Transformations ◽  
Trigonometric Functions ◽  
De Sitter ◽  
One Dimensional ◽  
Damped Harmonic Oscillator ◽  
Math Phys

Valtancoli in his paper entitled (P. Valtancoli, Canonical transformations and minimal length, J. Math. Phys. 56, 122107 2015) has shown how the deformation of the canonical transformations can be made compatible with the deformed Poisson brackets. Based on this work and through an appropriate canonical transformation, we solve the problem of one dimensional (1D) damped harmonic oscillator at the classical limit of the Snyder-de Sitter (SdS) space. We show that the equations of the motion can be described by trigonometric functions with frequency and period depending on the deformed and the damped parameters. We eventually discuss the influences of these parameters on the motion of the system.

QUANTUM HAMILTONIANS AND SELF-ORGANISED CRITICALITY

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3463-3471 ◽  
Author(s):  
JOHN CARDY
Keyword(s):  
Master Equation ◽  
Quantum System ◽  
Critical Behavior ◽  
Classical Limit ◽  
Particle Model ◽  
Hydrodynamic Behavior ◽  
One Dimensional ◽  
Self Organised Criticality ◽  
Stochastic Particle

We consider a stochastic particle model which has been proposed to exhibit the essential features of self-organised criticality. The master equation is reformulated as a one-dimensional quantum system of interacting bosons. The hydrodynamic behavior of the system is recovered as the classical limit of the quantum system, and the problem of fluctuations, important for the critical behavior, is discussed.

THE ONE-DIMENSIONAL PERIODIC BLOCH-POISSON EQUATION

1991 ◽  
Vol 01 (01) ◽  
pp. 83-112 ◽  
Author(s):  
ANTON ARNOLD ◽  
PETER A. MARKOWICH ◽  
NORBERT MAUSER
Keyword(s):  
Numerical Simulation ◽  
Classical Limit ◽  
Smooth Solution ◽  
Iterative Procedure ◽  
Poisson Model ◽  
Positive Temperature ◽  
Thermodynamical Equilibrium ◽  
One Dimensional ◽  
The One ◽  
Unique Smooth Solution

We analyze the Bloch-Poisson model describing quantum steady states of electrons in thermodynamical equilibrium. The problem is set in a one-dimensional periodic geometry. The existence of a unique smooth solution for every positive temperature is proved, a convergent iterative procedure useful for the numerical simulation is obtained, and the classical limit is analyzed.

scholarly journals Classical Limit for Dirac Fermions with Modified Action in the Presence of a Black Hole

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1294
Author(s):  
Meir Lewkowicz ◽  
Mikhail Zubkov
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Fermi Surface ◽  
Gravitational Collapse ◽  
Classical Limit ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Einstein Equations ◽  
Covariant Formulation ◽  
Dirac Fermions

We consider the model of Dirac fermions coupled to gravity as proposed, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates from Planck physics. Due to this term, a closed Fermi surface is formed in equilibrium inside the black hole. In this paper we propose the covariant formulation of this model and analyse its classical limit. We consider the dynamics of gravitational collapse. It appears that the Einstein equations admit a solution identical to that of ordinary general relativity. Next, we consider the motion of particles in the presence of a black hole. Numerical solutions of the equations of motion are found which demonstrate that the particles are able to escape from the black hole.

CLASSICAL LIMIT PROBLEM OF QUANTUM MECHANICAL ENERGY EIGENFUNCTIONS — EXTENSION TO TWO- AND THREE-DIMENSIONAL CASES

2005 ◽  
Vol 20 (32) ◽  
pp. 7515-7524 ◽  
Author(s):  
D. SEN ◽  
S. SENGUPTA
Keyword(s):  
Classical Limit ◽  
Bound States ◽  
Mechanical Energy ◽  
Three Dimensional ◽  
Limit Problem ◽  
Quantum Mechanical ◽  
One Dimensional ◽  
Special Cases ◽  
Objective Description ◽  
Quantum Mechanical Energy

In an earlier paper appropriate limiting procedure is discussed in a general way for quantum mechanical energy eigenfunctions (one-dimensional bound states) — a single interpretational postulate leading smoothly to entire compatible classical objective description without facing any contradiction. The method is consistently extended to two- and three-dimensional cases and it is interesting to note that results of earlier study on the classical limit of the radial distribution function of hydrogen atom are easily obtained as special cases of our analysis.

scholarly journals Bulk viscous quintessential inflation

2018 ◽  
Vol 27 (05) ◽  
pp. 1850052 ◽  
Author(s):  
Jaume Haro ◽  
Supriya Pan
Keyword(s):  
General Relativity ◽  
Particle Production ◽  
Cosmic Acceleration ◽  
Inflationary Universe ◽  
De Sitter ◽  
Thermodynamical Equilibrium ◽  
One Dimensional ◽  
Inflationary Phase ◽  
Bulk Viscous ◽  
The Universe

In a spatially-flat Friedmann–Lemaître–Robertson–Walker universe, the incorporation of bulk viscous process in general relativity leads to an appearance of a nonsingular background of the universe that both at early and late times depicts an accelerated universe. These early and late scenarios of the universe can be analytically calculated and mimicked, in the context of general relativity, by a single scalar field whose potential could also be obtained analytically where the early inflationary phase is described by a one-dimensional Higgs potential and the current acceleration is realized by an exponential potential. We show that the early inflationary universe leads to a power spectrum of the cosmological perturbations which match with current observational data, and after leaving the inflationary phase, the universe suffers a phase transition needed to explain the reheating of the universe via gravitational particle production. Furthermore, we find that at late times, the universe enters into the de Sitter phase that can explain the current cosmic acceleration. Finally, we also find that such bulk viscous-dominated universe attains the thermodynamical equilibrium, but in an asymptotic manner.

PERELOMOV AND BARUT–GIRARDELLO SU(1, 1) COHERENT STATES FOR HARMONIC OSCILLATOR IN ONE-DIMENSIONAL HALF SPACE

2006 ◽  
Vol 21 (12) ◽  
pp. 2635-2644 ◽  
Author(s):  
Q. H. LIU ◽  
H. ZHUO
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Half Space ◽  
Ground State ◽  
Classical Limit ◽  
Coherent States ◽  
Mean Values ◽  
One Dimensional ◽  
The Mean

The Perelomov and the Barut–Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below [Formula: see text] that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut–Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

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