Anisotropic time-dependent coupled oscillators

1990 ◽  
Vol 41 (7) ◽  
pp. 3775-3781 ◽  
Author(s):  
M. Sebawe Abdalla
Keyword(s):  
Coupled Oscillators ◽  
Time Dependent

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.

A Continuation Approach to the Periodic Boundary Value Problem for a Class of Nonlinear Coupled Oscillators with Potential Depending on Time

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Chao Wang
Keyword(s):  
Coupled Oscillators ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Continuation Theorem ◽  
Coupled Systems ◽  
Time Dependent ◽  
Periodic Boundary Value Problems ◽  
Nonlinear Coupled Oscillators ◽  
Dependent Potential ◽  
Nonlinear Vector

AbstractIn this paper, we prove a new continuation theorem for the solvability of periodic boundary value problems for nonlinear vector equations. By applying the continuation theorem, we prove the existence of a periodic solution for a class of semi-linear weekly-coupled systems with time-dependent potential.

scholarly journals Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators

2021 ◽  
Vol 3 (4) ◽  
pp. 684-702
Author(s):  
Radouan Hab-arrih ◽  
Ahmed Jellal ◽  
Dionisis Stefanatos ◽  
Abdeldjalil Merdaci
Keyword(s):  
Coupled Oscillators ◽  
Quantum Dynamics ◽  
Quantum Systems ◽  
Time Dependent ◽  
Strongly Correlated ◽  
Classical Analog ◽  
Photon Excitation ◽  
The Stability ◽  
Shed Light ◽  
Photon Excitations

In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering π periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations Nj) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators.

QUANTUM TREATMENT OF TIME DEPENDENT COUPLED OSCILLATORS

2002 ◽  
Vol 16 (19) ◽  
pp. 2837-2855 ◽  
Author(s):  
M. SEBAWE ABDALLA
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Time Dependent ◽  
Expectation Values ◽  
Quadratic Invariants ◽  
Quantum Treatment ◽  
Schrödinger Picture

In this paper we consider the most quadratic time dependent Hamiltonian. An exact solution of the wave function in both the Schrödinger picture and coherent states representation is given. Linear and quadratic invariants are discussed. The eigenvalues and the corresponding eigenfunctions are obtained. The expectation values for the energy are also given.

scholarly journals Squeezing in coupled oscillators having neither nonlinear terms nor time-dependent parameters

2001 ◽  
Vol 31 (4) ◽  
pp. 562-566
Author(s):  
H. Rodrigues ◽  
D. Portes Jr. ◽  
S.B. Duarte ◽  
B. Baseia
Keyword(s):  
Coupled Oscillators ◽  
Time Dependent

WAVE FUNCTIONS OF TIME-DEPENDENT TWO COUPLED OSCILLATORS BY LEWIS–RIESENFELD METHOD

2006 ◽  
Vol 20 (09) ◽  
pp. 1087-1096 ◽  
Author(s):  
HONG-YI FAN ◽  
ZHONG-HUA JIANG
Keyword(s):  
Schrödinger Equation ◽  
Operator Theory ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
General Solutions ◽  
Eigenvectors And Eigenvalues

For the two time-dependent coupled oscillators model we derive its time-dependent invariant in the context of Lewis–Riesenfeld invariant operator theory. It is based on the general solutions to the Schrödinger equation which is obtained and turns out to be the superposition of the generalized atomic coherent states in the Schwinger bosonic realization. The energy eigenvectors and eigenvalues of the corresponding time-independent Hamiltonian are also obtained as a by-product.

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