scholarly journals Simple representation of the quantum entanglement of coupled harmonic oscillators in terms of the reflection coefficient

2021 ◽  
Vol 2086 (1) ◽  
pp. 012171
Author(s):  
Yu V Tsykareva ◽  
D N Makarov
Keyword(s):  
Reflection Coefficient ◽  
Harmonic Oscillator ◽  
Quantum Entanglement ◽  
Simple Form ◽  
Harmonic Oscillators ◽  
Quantum Metrology ◽  
Molecular Chemistry ◽  
Coupled Harmonic Oscillators ◽  
Modern Physics ◽  
Coupled Harmonic Oscillator

Abstract Quantum entanglement of coupled harmonic oscillators is frequently applied in quantum and non-linear physics, molecular chemistry and biophysics, which is why its study is of a great interest for modern physics. In this work a quantum entanglement of a coupled harmonic oscillator in a simple form was found. This simple form is presented as a single parameter – reflection coefficient R. All parameters of the studied system are included in the R coefficient. It is shown that the derivation of the expression can have applications in quantum optics, in particular in quantum metrology.

scholarly journals Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions

2019 ◽  
Vol 1 (1) ◽  
pp. 82-90 ◽  
Author(s):  
Alejandro R. Urzúa ◽  
Irán Ramos-Prieto ◽  
Manuel Fernández-Guasti ◽  
Héctor M. Moya-Cessa
Keyword(s):  
Coupled Oscillators ◽  
Quantum Physics ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Unitary Operators ◽  
Orthogonal Functions ◽  
Molecular Chemistry ◽  
Coupled Harmonic Oscillators ◽  
Generalized Orthogonal

We show that by using the quantum orthogonal functions invariant, we found a solution to coupled time-dependent harmonic oscillators where all the time-dependent frequencies are arbitrary. This system may be found in many applications such as nonlinear and quantum physics, biophysics, molecular chemistry, and cosmology. We solve the time-dependent coupled harmonic oscillators by transforming the Hamiltonian of the interaction using a set of unitary operators. In passing, we show that N time-dependent and coupled oscillators have a generalized orthogonal functions invariant from which we can write a Ermakov–Lewis invariant.

Harmonic Oscillators with Nonlinear Damping

2017 ◽  
Vol 27 (11) ◽  
pp. 1730037 ◽  
Author(s):  
J. C. Sprott ◽  
W. G. Hoover
Keyword(s):  
Dynamical Systems ◽  
Harmonic Oscillator ◽  
Strange Attractor ◽  
Nonlinear Damping ◽  
Harmonic Oscillators ◽  
Coexisting Attractors ◽  
Simple Harmonic Oscillator ◽  
Interesting Behavior

Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

Adaptive cluster synchronisation of coupled harmonic oscillators with multiple leaders

2013 ◽  
Vol 7 (5) ◽  
pp. 765-772 ◽  
Author(s):  
Housheng Su ◽  
Hongwei Wang ◽  
Michael Z. Q. Chen ◽  
Najl V. Valeyev ◽  
Xiaofan Wang
Keyword(s):  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators ◽  
Multiple Leaders
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