Coherent states of a damped harmonic oscillator

Pramana ◽  
1985 ◽  
Vol 24 (4) ◽  
pp. 591-594 ◽  
Author(s):  
S K Bose ◽  
U B Dubey ◽  
V N Tewari
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Damped Harmonic Oscillator

scholarly journals Lewis-Riesenfeld quantization and SU(1, 1) coherent states for 2D damped harmonic oscillator

2018 ◽  
Vol 59 (11) ◽  
pp. 112101 ◽  
Author(s):  
Latévi M. Lawson ◽  
Gabriel Y. H. Avossevou ◽  
Laure Gouba
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Damped Harmonic Oscillator

Coherent states for the damped harmonic oscillator

1987 ◽  
Vol 36 (11) ◽  
pp. 5287-5291 ◽  
Author(s):  
K. H. Yeon ◽  
C. I. Um ◽  
Thomas F. George
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Damped Harmonic Oscillator

Adiabatic and nonadiabatic evolution of a generalized damped harmonic oscillator

2021 ◽  
pp. 2150201
Author(s):  
I. A. Pedrosa
Keyword(s):  
Harmonic Oscillator ◽  
Geometric Phase ◽  
Coherent States ◽  
Time Dependent ◽  
Expectation Values ◽  
Damped Harmonic Oscillator ◽  
Quantum Properties ◽  
Uncertainty Product ◽  
Dynamical Invariants ◽  
Damped Oscillator

In this work we present a simple and elegant approach to study the adiabatic and nonadiabatic evolution of a generalized damped harmonic oscillator which is described by the generalized Caldirola–Kanai Hamiltonian, in both classical and quantum contexts. Based on time-dependent dynamical invariants, we find that the geometric phase acquired when the damped oscillator evolves adiabatically in time provides a direct connection between the classical Hannay’s angle and the quantum Berry’s phase. In addition, we solve the time-dependent Schrödinger equation for this system and calculate various quantum properties of the damped generalized harmonic one, such as coherent states, expectation values of the position and momentum operators, their quantum fluctuations and the associated uncertainty product.

Dynamics of SU(1,1) coherent states driven by a damped harmonic oscillator

1989 ◽  
Vol 39 (2) ◽  
pp. 668-674 ◽  
Author(s):  
Christopher C. Gerry ◽  
Philip K. Ma ◽  
Edward R. Vrscay
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Damped Harmonic Oscillator

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.

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