scholarly journals QUANTUM AND THERMAL CORRECTIONS TO A CLASSICALLY CHAOTIC DISSIPATIVE SYSTEM

2004 ◽  
Vol 04 (02) ◽  
pp. 185-200
Author(s):  
MANUEL RODRÍGUEZ-ACHACH ◽  
GABRIEL PÉREZ ◽  
HILDA A. CERDEIRA
Keyword(s):  
Density Matrix ◽  
Harmonic Oscillator ◽  
Chaotic Behavior ◽  
Classical Model ◽  
Cutoff Frequency ◽  
Dissipative System ◽  
System Change ◽  
Nonlinear Parameter ◽  
Quantum Langevin Equation ◽  
Moment Expansion

The effects of quantum and thermal corrections on the dynamics of a damped nonlinearly kicked harmonic oscillator are studied. This is done via the quantum Langevin equation formalism working on a truncated moment expansion of the density matrix of the system. We find that the type of bifurcations present in the system change upon quantization and that chaotic behavior appears for values of the nonlinear parameter that are far below the chaotic threshold for the classical model. Upon increase of temperature or Planck's constant, bifurcation points and chaotic thresholds are shifted towards lower values of the nonlinear parameter. There is also an anomalous reverse behavior for low values of the cutoff frequency.

scholarly journals Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sh. Saedi ◽  
F. Kheirandish
Keyword(s):  
Density Matrix ◽  
Equations Of Motion ◽  
Dissipative System ◽  
Characteristic Functions ◽  
Matrix Elements ◽  
Exact Density ◽  
Quadratic Hamiltonian ◽  
Heisenberg Equations ◽  
Reduced Density ◽  
Heisenberg Equations Of Motion

AbstractFor a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is based on the Heisenberg equations of motion and operator calculus. The special and limiting cases are discussed.

PATH INTEGRAL DERIVATION OF AN EXACT MASTER EQUATION

1995 ◽  
Vol 09 (02) ◽  
pp. 87-94 ◽  
Author(s):  
S. V. LAWANDE ◽  
Q. V. LAWANDE
Keyword(s):  
Density Matrix ◽  
Harmonic Oscillator ◽  
Master Equation ◽  
Path Integral ◽  
Open System ◽  
Coherent States ◽  
Reduced Density Matrix ◽  
Feynman Propagator ◽  
Reduced Density

The Feynman propagator in coherent states representation is obtained for a system of a single harmonic oscillator coupled to a reservoir of N oscillators. Using this propagator, an exact master equation is obtained for the evolution of the reduced density matrix for the open system of the oscillator.

The Real-Valued Maxwell–Bloch Equations with Controls: From a Hamilton–Poisson System to a Chaotic One

2017 ◽  
Vol 27 (09) ◽  
pp. 1750143 ◽  
Author(s):  
Cristian Lăzureanu
Keyword(s):  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Dissipative System ◽  
Homoclinic Orbits ◽  
Conservative System ◽  
Poisson System ◽  
Bloch Equations ◽  
The Stability ◽  
Transitional System ◽  
Maxwell Bloch Equations

Applying parametric controls to the 3D real-valued Maxwell–Bloch equations, we obtain a Hamilton–Poisson system, a dissipative system with chaotic behavior, and a transitional system between the aforementioned states, which is a conservative system that has only one constant of motion. In the Hamiltonian case, we present some connections of the energy-Casimir mapping with the equilibrium states and the existence of the homoclinic orbits. We study the stability of the equilibrium points of the transitional system and the dissipative system. Furthermore, we point out the chaotic behavior of the introduced system.

scholarly journals INVERSELY UNSTABLE SOLUTIONS OF TWO-DIMENSIONAL SYSTEMS ON GENUS-p SURFACES AND THE TOPOLOGY OF KNOTTED ATTRACTORS

2008 ◽  
Vol 18 (01) ◽  
pp. 109-119
Author(s):  
YI SONG ◽  
STEPHEN P. BANKS
Keyword(s):  
Chaotic Behavior ◽  
Dissipative System ◽  
Invariant Set ◽  
Invariant Sets ◽  
Time Varying ◽  
Two Dimensional ◽  
Unstable Solutions

In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins, 2004] and give conditions under which these invariant sets are not homeomorphic to a circle individually, which implies the existence of chaotic behavior. This is achieved by studying the appearance of inversely unstable solutions within each invariant set.

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