scholarly journals Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 837
Author(s):  
Salim Medjber ◽  
Salah Menouar ◽  
Jeong Ryeol Choi
Keyword(s):  
Coupled Oscillators ◽  
Three Dimensional ◽  
Original System ◽  
Invariant Operator ◽  
Point Of View ◽  
Wave Functions ◽  
Harmonic Oscillators ◽  
Unitary Operators ◽  
Quantum Invariant ◽  
Full Wave

We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system. We use such a property of the invariant operator in quantizing the system in this work. To this end, we first transform the invariant operator to a simple one by using a unitary operator in order that we can easily manage it. The invariant operator is further simplified through its diagonalization via three-dimensional rotations parameterized by three Euler angles. The coupling terms in the quantum invariant are eventually eliminated thanks to such a diagonalization. As a consequence, transformed quantum invariant is represented in terms of three independent simple harmonic oscillators which have unit masses. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators.

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.

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.

Quantum dynamics of a general time-dependent coupled oscillator

2021 ◽  
pp. 2150230
Author(s):  
Sara Hassoul ◽  
Salah Menouar ◽  
Jeong Ryeol Choi ◽  
Ramazan Sever
Keyword(s):  
Quantum Dynamics ◽  
Oscillatory System ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
Coupled Oscillator ◽  
Quantum Invariant ◽  
Classical Counterpart ◽  
Quantum Dynamical ◽  
General Time

Quantum dynamical properties of a general time-dependent coupled oscillator are investigated based on the theory of two-dimensional (2D) dynamical invariants. The quantum dynamical invariant of the system satisfies the Liouville–von Neumann equation and it coincides with its classical counterpart. The mathematical formula of this invariant involves a cross term which couples the two oscillators mutually. However, we show that, by introducing two pairs of annihilation and creation operators, it is possible to uncouple the original invariant operator so that it becomes the one that describes two independent subsystems. The eigenvalue problem of this decoupled quantum invariant can be solved by using a unitary transformation approach. Through this procedure, we eventually obtain the eigenfunctions of the invariant operator and the wave functions of the system in the Fock state. The wave functions that we have developed are necessary in studying the basic quantum characteristics of the system. In order to show the validity of our theory, we apply our consequences to the derivation of the fluctuations of canonical variables and the uncertainty products for a particular 2D oscillatory system whose masses are exponentially increasing.

Comparison of the reluctance laminated and solid rotor synchronous machine operating at high temperatures

2019 ◽  
Vol 38 (4) ◽  
pp. 1111-1119 ◽  
Author(s):  
Marcin Lefik ◽  
Krzysztof Komeza ◽  
Ewa Napieralska-Juszczak ◽  
Daniel Roger ◽  
Piotr Andrzej Napieralski
Keyword(s):  
High Speed ◽  
Design Methodology ◽  
Three Dimensional ◽  
Synchronous Machine ◽  
Point Of View ◽  
Heat Sources ◽  
Model Calculations ◽  
Content Type ◽  
Thermal Phenomenon ◽  
Practical Implications

Purpose The purpose of this paper is to present a comparison between reluctance synchronous machine-enabling work at high internal temperature (HT° machine) with laminated and solid rotor. Design/methodology/approach To obtain heat sources for the thermal model, calculations of the electromagnetic field were made using the Opera 3D program including effect of rotation and the resulting eddy current losses. To analyse the thermal phenomenon, the 3D coupled thermal-fluid (CFD) model is used. Findings The presented results show clearly that laminated construction is much better from a point of view of efficiency and temperature. However, solid construction can be interesting for high speed machines due to their mechanical robustness. Research limitations/implications The main problem, despite the use of parallel calculations, is the long calculation time. Practical implications The obtained simulation and experimental results show the possibility of building a machine operating at a much higher ambient temperature than it was previously produced for example in the vicinity of the aircraft turbines. Originality/value The paper presents the application of fully three-dimensional coupled electromagnetic and thermal analysis of new machine constructions designed for elevated temperature.

Cyclopean Vision, Size Estimation, and Presence in Orthostereoscopic Images

2001 ◽  
Vol 10 (3) ◽  
pp. 312-330 ◽  
Author(s):  
Bernard Harper ◽  
Richard Latto
Keyword(s):  
Visual System ◽  
Three Dimensional ◽  
Point Of View ◽  
Psychophysical Experiment ◽  
Size Estimation ◽  
Human Form ◽  
Image Capture ◽  
Series Of Experiments ◽  
Abstract Shapes ◽  
And Control

Stereo scene capture and generation is an important facet of presence research in that stereoscopic images have been linked to naturalness as a component of reported presence. Three-dimensional images can be captured and presented in many ways, but it is rare that the most simple and “natural” method is used: full orthostereoscopic image capture and projection. This technique mimics as closely as possible the geometry of the human visual system and uses convergent axis stereography with the cameras separated by the human interocular distance. It simulates human viewing angles, magnification, and convergences so that the point of zero disparity in the captured scene is reproduced without disparity in the display. In a series of experiments, we have used this technique to investigate body image distortion in photographic images. Three psychophysical experiments compared size, weight, or shape estimations (perceived waist-hip ratio) in 2-D and 3-D images for the human form and real or virtual abstract shapes. In all cases, there was a relative slimming effect of binocular disparity. A well-known photographic distortion is the perspective flattening effect of telephoto lenses. A fourth psychophysical experiment using photographic portraits taken at different distances found a fattening effect with telephoto lenses and a slimming effect with wide-angle lenses. We conclude that, where possible, photographic inputs to the visual system should allow it to generate the cyclopean point of view by which we normally see the world. This is best achieved by viewing images made with full orthostereoscopic capture and display geometry. The technique can result in more-accurate estimations of object shape or size and control of ocular suppression. These are assets that have particular utility in the generation of realistic virtual environments.

ON THE OPTICAL POTENTIAL OF AN ATTRACTIVE NONRELATIVISTIC DEGENERATE ELECTRON GAS INTERACTING WITH NUCLEAR MATTER

2012 ◽  
Vol 26 (31) ◽  
pp. 1250210 ◽  
Author(s):  
M. A. GRADO-CAFFARO ◽  
M. GRADO-CAFFARO
Keyword(s):  
Nuclear Matter ◽  
Optical Potential ◽  
Electron Gas ◽  
Three Dimensional ◽  
Harmonic Oscillators ◽  
Fermi Velocity ◽  
Potential Well ◽  
Schwinger Model ◽  
Degenerate Fermi Gas ◽  
Degenerate Electron Gas

The optical potential of an attractive nonrelativistic electron gas interacting with nuclear matter is determined on the basis of the concept of degenerate Fermi gas. In fact, the involved electrons are treated as three-dimensional quantum harmonic oscillators confined at the surface of a spherical (approximately ideal) potential well. Within this picture, the Fermi velocity is calculated as well as the spatial electron density at the surface of the potential well and the attractive force between the electron gas and the nuclear matter. In addition, considerations related to the Lippmann–Schwinger model are made.

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

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