scholarly journals An illustration of canonical quantum-classical dynamics: backreaction, canonical relations and time evolution in the quantum-classical harmonic oscillator

2021 ◽  
Author(s):  
Mustafa Amin ◽  
Mark A. Walton
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Classical Dynamics ◽  
Canonical Quantum

Time evolution of a time-dependent inverted harmonic oscillator in arbitrary dimensions

2012 ◽  
Vol 45 (11) ◽  
pp. 115301
Author(s):  
Guang-Jie Guo ◽  
Zhong-Zhou Ren ◽  
Guo-Xing Ju ◽  
Xiao-Yong Guo
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Time Dependent ◽  
Arbitrary Dimensions

SQUEEZING AND SOME OTHER CHARACTERISTICS OF TIME-DEPENDENT HARMONIC OSCILLATOR WITH VARIABLE MASS

1994 ◽  
Vol 08 (14n15) ◽  
pp. 917-927 ◽  
Author(s):  
A. JOSHI ◽  
S. V. LAWANDE
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Time Evolution ◽  
Evolution Operator ◽  
Variable Mass ◽  
Time Dependent ◽  
Integral Approach ◽  
Feynman Path ◽  
Time Evolution Operator ◽  
General Time

In this paper we investigate the time evolution of a general time-dependent harmonic oscillator (TDHO) with variable mass using Feynman path integral approach. We explicitly evaluate the squeezing in the quadrature components of a general quantum TDHO with variable mass. This calculation is further elaborated for three particular cases of variable mass whose propagator can be written in a closed form. We also obtain an exact form of the time-evolution operator, the wave function, and the time-dependent coherent state for the TDHO. Our results clearly indicate that the time-dependent coherent state is equivalent to the squeezed coherent state.

scholarly journals QUANTUM DYNAMICS OF THE CUBIT SYSTEM IN EXTERNAL FIELDS

2021 ◽  
Vol 26 (4) ◽  
pp. 68-75
Author(s):  
A. V. Gorokhov ◽  
G. I. Eremenko
Keyword(s):  
Symmetry Group ◽  
Time Evolution ◽  
Coherent States ◽  
Quantum Dynamics ◽  
Dynamic Symmetry ◽  
Classical Dynamics ◽  
External Fields

A system of two dipole-dipole interacting two-level elements (qubits) in external fields is considered. It is shown that using the coherent states (CS) of the dynamic symmetry group of the SU(2)SU(2) system, the time evolution can be reduced to the "classical" dynamics of the complex parameters of the CS. The trajectories of the CS are constructed and the time dependences of the probability of finding qubits at the upper levels are calculated.

scholarly journals A PATH INTEGRAL FOR CLASSICAL DYNAMICS, ENTANGLEMENT, AND JAYNES-CUMMINGS MODEL AT THE QUANTUM-CLASSICAL DIVIDE

2011 ◽  
Vol 09 (supp01) ◽  
pp. 203-224 ◽  
Author(s):  
HANS-THOMAS ELZE ◽  
GIOVANNI GAMBAROTTA ◽  
FABIO VALLONE
Keyword(s):  
Time Evolution ◽  
Path Integral ◽  
Statistical Physics ◽  
Hamiltonian Dynamics ◽  
Path Integrals ◽  
Classical Mechanics ◽  
Quantum Evolution ◽  
Classical Dynamics ◽  
Von Neumann ◽  
Feynman Path Integrals

The Liouville equation differs from the von Neumann equation "only" by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. Employing superspace (instead of Hilbert space), we describe time evolution of density matrices in terms of path integrals, which are formally identical for quantum and classical mechanics. They only differ by the interaction contributing to the action. This allows us to import tools developed for Feynman path integrals, in order to deal with superoperators instead of quantum mechanical commutators in real time evolution. Perturbation theory is derived. Besides applications in classical statistical physics, the "classical path integral" and the parallel study of classical and quantum evolution indicate new aspects of (dynamically assisted) entanglement (generation). Our findings suggest to distinguish intra- from inter-space entanglement.

Squeezing caused by a change of mass in a harmonic oscillator

1989 ◽  
Vol 67 (2-3) ◽  
pp. 152-154 ◽  
Author(s):  
Fan Hong-Yi ◽  
H. R. Zaidi
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Mass Change ◽  
Transformation Time

It is shown that a mass change in a harmonic oscillator generates a squeezing transformation. Time-independent as well as time-dependent transformations are investigated. An expression for the interaction Hamiltonian responsible for squeezing and the equations of motion for the time evolution are derived.

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