Analytical expressions for real and complex Fano parameters in a simple classical harmonic oscillator system

2021 ◽  
Author(s):  
Seiji MIZUNO
Keyword(s):  
Harmonic Oscillator ◽  
Resonance Frequency ◽  
Real Number ◽  
Wave Phenomenon ◽  
Fano Resonance ◽  
Equation Of Motion ◽  
Coupled Oscillator ◽  
Physical Systems ◽  
Oscillator System ◽  
Analytical Expressions

Abstract We analytically study the Fano resonance in a simple coupled oscillator system. We demonstrate directly from the equation of motion that the resonance profile observed in this system is generally described by the Fano formula with a complex Fano parameter. The analytical expressions are derived for the resonance frequency, resonance width, and Fano parameter, and the conditions under which the Fano parameter becomes a real number are examined. These expressions for the simple system are also expected to be helpful for considering various other physical systems because the Fano resonance is a general wave phenomenon.

scholarly journals Time delay effect in a three coupled oscillator system of the physarum plasmodium

2000 ◽  
Vol 40 (supplement) ◽  
pp. S100
Author(s):  
A. Takamatsu ◽  
T. Fujii ◽  
I. Endo
Keyword(s):  
Time Delay ◽  
Delay Effect ◽  
Coupled Oscillator ◽  
Oscillator System ◽  
Time Delay Effect

(ANTI)COMMUTATIVITY OF THE HARMONIC CREATION AND ANNIHILATION OPERATORS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1808-1818
Author(s):  
S. KUWATA ◽  
A. MARUMOTO
Keyword(s):  
Irreducible Representation ◽  
Harmonic Oscillator ◽  
Linear Algebra ◽  
Commutation Relation ◽  
Complex Number ◽  
Single Mode ◽  
Equation Of Motion ◽  
Sufficient Condition ◽  
Special Linear ◽  
Creation And Annihilation Operators

It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.

Constructing physical systems with dynamical symmetry

2014 ◽  
Vol 92 (4) ◽  
pp. 335-340
Author(s):  
Yan Li ◽  
Fu-Lin Zhang ◽  
Rui-Juan Gu ◽  
Jing-Ling Chen ◽  
L.C. Kwek
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Dynamical Symmetry ◽  
Algebraic Method ◽  
Quantum Systems ◽  
Physical Systems ◽  
Generalized Systems ◽  
Dependent Mass ◽  
Position Dependent Mass

An approach to constructing quantum systems with dynamical symmetry is proposed. As examples, we construct generalized systems of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mass. They have symmetries that are similar to the corresponding ones, and can be solved by using the algebraic method. We also exhibit an example of the method applied to the noncentral field.

MULTI-MODE LINEAR COMPOSITE MOMENTUM REPRESENTATION AND ITS APPLICATION

2009 ◽  
Vol 23 (07) ◽  
pp. 975-988
Author(s):  
SHI-MIN XU ◽  
XING-LEI XU ◽  
JI-JIAN JIANG ◽  
HONG-QI LI ◽  
JI-SUO WANG
Keyword(s):  
Harmonic Oscillator ◽  
Unitary Transformation ◽  
Particle System ◽  
Momentum Representation ◽  
Dynamic Problems ◽  
Quantum Harmonic Oscillator ◽  
Oscillator System ◽  
Kinetic Coupling ◽  
Linear Composite ◽  
Multi Mode

A unitary transformation matrix, n linear-composite coordinate operators and n linear-composite momentum operators are constructed for an n-particle system, and the complete and orthonormal common eigenvectors of the multi-mode linear composite momentum operators are examined by virtue of the technique of integration within an ordered product of operators. The multi-mode linear composite momentum representation is proposed, and its application to a general two-mode forced quantum harmonic oscillator system with kinetic coupling is presented for solving some dynamic problems.

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