On the constant of motion of dissipative systems

2002 ◽  
Vol 80 (1) ◽  
pp. 1-5 ◽  
Author(s):  
A Patiño ◽  
H Rago
Keyword(s):  
Harmonic Oscillator ◽  
Equations Of Motion ◽  
Viscous Medium ◽  
Dissipative Systems ◽  
Damped Harmonic Oscillator ◽  
Constant Of Motion

We apply results on symmetries of equations of motion and equivalent Lagrangians to obtain a constant of motion for a particle travelling through a viscous medium and for the damped harmonic oscillator. PACS No.: 45.20Jj

scholarly journals RADIATION REACTION AND QUANTUM DAMPED HARMONIC OSCILLATOR

2005 ◽  
Vol 20 (39) ◽  
pp. 3025-3034 ◽  
Author(s):  
F. KHEIRANDISH ◽  
M. AMOOSHAHI
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Dynamics ◽  
Transition Probabilities ◽  
Quantum Dissipative Systems ◽  
Radiation Reaction ◽  
Dissipative Systems ◽  
Minimal Coupling ◽  
Damped Harmonic Oscillator ◽  
Energy Flows ◽  
Klein Gordon

By taking a Klein–Gordon field as the environment of a harmonic oscillator and using a new method for dealing with quantum dissipative systems (minimal coupling method), we find out the quantum dynamics and radiation reaction for a quantum damped harmonic oscillator. Applying perturbation method, we obtain some transition probabilities indicating the way energy flows between oscillator, reservoir and quantum vacuum.

NEW METHOD FOR TREATING RELAXATION PROCESSES: DAMPED HARMONIC OSCILLATOR AND THE JAYNES-CUMMINGS MODEL WITH CAVITY LOSSES

1996 ◽  
Vol 10 (20) ◽  
pp. 981-987
Author(s):  
J. SEKE
Keyword(s):  
Harmonic Oscillator ◽  
Equations Of Motion ◽  
Operator Method ◽  
New Method ◽  
New Technique ◽  
Relaxation Processes ◽  
Total System ◽  
Damped Harmonic Oscillator ◽  
A New Technique ◽  
Reduced Density

In the present paper a new technique for treating relaxation processes, based on the author’s self-consistent projection-operator method, is developed. This new technique, which yields (instead of a master equation for a reduced density operator) equations of motion for probability amplitudes for a reduced set of states of the total system, opens a new way for treating relaxation processes. The applicability of the new method is demonstrated in the case of a damped harmonic oscillator and in that of the Jaynes-Cummings model with cavity losses.

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

Path integral for the damped harmonic oscillator coupled to its dual

1994 ◽  
Vol 35 (3) ◽  
pp. 1185-1191 ◽  
Author(s):  
L. Chetouani ◽  
L. Guechi ◽  
T. F. Hammann ◽  
M. Letlout
Keyword(s):  
Harmonic Oscillator ◽  
Path Integral ◽  
Damped Harmonic Oscillator
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