scholarly journals A Dynamical System with q-Deformed Phase Space Represented in Ordinary Variable Spaces

2010 ◽  
Vol 124 (6) ◽  
pp. 1019-1035
Author(s):  
S. Naka ◽  
H. Toyoda ◽  
T. Takanashi
Keyword(s):  
Dynamical System ◽  
Phase Space

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

scholarly journals ON BARYON NUMBER NONCONSERVATION IN TWO-DIMENSIONAL O(2N+1) QCD

2010 ◽  
Vol 25 (06) ◽  
pp. 1253-1266
Author(s):  
TAMAR FRIEDMANN
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Matrix Models ◽  
Gauge Group ◽  
Baryon Number ◽  
Two Dimensional ◽  
Infinite Dimensional ◽  
Field Approach ◽  
Large N ◽  
Classical Dynamical System

We construct a classical dynamical system whose phase space is a certain infinite-dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O (2N+1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.

A DYNAMICAL SYSTEM APPROACH TO THE GBIG COSMOLOGY

2011 ◽  
Vol 08 (06) ◽  
pp. 1179-1188 ◽  
Author(s):  
KOUROSH NOZARI ◽  
F. KIANI
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Cosmological Constant ◽  
System Approach ◽  
Stable Solution ◽  
Late Time ◽  
Curvature Effect ◽  
De Sitter ◽  
Dynamical System Approach ◽  
Bonnet Term

We study the phase space of an extension of the normal DGP cosmology with a cosmological constant on the brane and curvature effect that is incorporated via the Gauss–Bonnet term in the bulk action. We study late-time cosmological dynamics of this scenario within a dynamical system approach. We show that the stable solution of the cosmological dynamics in this model is a de Sitter phase.

scholarly journals Bifurcation and anomalous spectral accumulation in an oval billiard

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
Hironori Makino
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Limited Region ◽  
Classical Dynamical System ◽  
Classical Trajectories ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Spectral Statistics ◽  
Math Phys ◽  
Good Agreement

Abstract The spectral statistics of a quantum oval billiard whose classical dynamical system shows bifurcations is numerically investigated in terms of the two-point correlation function (TPCF), which is defined as the probability density of finding two levels at a specific energy interval. The eigenenergy levels at the bifurcation point are found to show anomalous accumulation, which is observed as a periodic spike oscillation of the TPCF. We analyzed the eigenfunctions localizing onto the various classical trajectories in the phase space and found that the oscillation is supplied from a limited region in the phase space that contains the bifurcating orbit. We also show that the period of the oscillation is in good agreement with the period of a contribution from the bifurcating orbit to the semiclassical TPCF obtained by Gutzwiller’s trace formula [J. Math. Phys. 12, 343 (1971)].

scholarly journals When is a dynamical system mean sensitive?

2017 ◽  
Vol 39 (06) ◽  
pp. 1608-1636 ◽  
Author(s):  
FELIPE GARCÍA-RAMOS ◽  
JIE LI ◽  
RUIFENG ZHANG
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
The Other ◽  
Positive Entropy ◽  
Topological Dynamical System ◽  
Other Hand ◽  
Open Question ◽  
Uniquely Ergodic ◽  
Mean Sensitivity ◽  
Transitive System

This article is devoted to studying which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things, we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive. On the other hand, we provide an example of a transitive system which is cofinitely sensitive or Devaney chaotic with positive entropy but fails to be mean sensitive. As applications of our theory and examples, we negatively answer an open question regarding equicontinuity/sensitivity dichotomies raised by Tu, we introduce and present results of locally mean equicontinuous systems and we show that mean sensitivity of the induced hyperspace does not imply that of the phase space.

Catastrophes with indeterminate outcome

1991 ◽  
Vol 432 (1884) ◽  
pp. 113-123 ◽  
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Invariant Manifolds ◽  
Space Geometry ◽  
Dissipative Dynamical System ◽  
Forced Oscillators ◽  
Phase Space Geometry

A catastrophe in a dissipative dynamical system which causes an attractor to completely lose stability will result in a transient trajectory making a rapid jump in phase space to some other attractor. In systems where more than one other attractor is available, the attractor chosen may depend very sensitively on how the catastrophe is realized. Two examples in forced oscillators of Duffing type illustrate how the probabilities of different outcomes can be estimated using the phase space geometry of invariant manifolds.

scholarly journals Cosmological Dynamics of a Hybrid Chameleon Scenario

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Kourosh Nozari ◽  
Narges Rashidi
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Scalar Field ◽  
Fixed Points ◽  
Effective Potential ◽  
Matter Density ◽  
Phantom Divide ◽  
Stable Attractor ◽  
System Technique ◽  
The Universe

We consider a hybrid scalar field which is nonminimally coupled to the matter and models a chameleon cosmology. By introducing an effective potential, we study the dependence of the effective potential's minimum and hybrid chameleon field's masses on the local matter density. In a dynamical system technique, we analyze the phase space of this two-field chameleon model, find its fixed points and study their stability. We show that the hybrid chameleon domination solution is a stable attractor and the universe in this setup experiences a phantom divide crossing.

Phase Space Reconstruction

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Dynamical Systems ◽  
Statistical Mechanics ◽  
State Space ◽  
Phase Plane ◽  
Material Point ◽  
The Other ◽  
Straight Line ◽  
Mathematical Construction

In this chapter we introduce an important concept concerning the study of both discrete and continuous dynamical systems, the concept of phase space or “state space”. It is an abstract mathematical construction with important applications in statistical mechanics, to represent the time evolution of a dynamical system in geometric shape. This space has as many dimensions as the number of variables needed to define the instantaneous state of the system. For instance, the state of a material point moving on a straight line is defined by its position and velocity at each instant, so that the phase space for this system is a plane in which one axis is the position and the other one the velocity. In this case, the phase space is also called “phase plane”. It is later applied in many chapters of the book.

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