Algebraic dynamics and time-dependent dynamical symmetry of nonautonomous systems

1993 ◽  
Vol 180 (3) ◽  
pp. 189-196 ◽  
Author(s):  
S.J. Wang ◽  
F.L. Li ◽  
A. Weiguny
Keyword(s):  
Dynamical Symmetry ◽  
Time Dependent ◽  
Algebraic Dynamics ◽  
Nonautonomous Systems

The pseudo Hermitian invariant operator and time-dependent non-Hermitian Hamiltonian exhibiting a SU(1,1) and SU(2) dynamical symmetry

2018 ◽  
Vol 59 (7) ◽  
pp. 072103 ◽  
Author(s):  
Walid Koussa ◽  
Naima Mana ◽  
Oum Kaltoum Djeghiour ◽  
Mustapha Maamache
Keyword(s):  
Dynamical Symmetry ◽  
Invariant Operator ◽  
Time Dependent

Algebraic dynamic study of geometric phase for a homonuclear linear spincluster

2007 ◽  
Vol 85 (8) ◽  
pp. 879-885
Author(s):  
X -X Chen ◽  
J Xue
Keyword(s):  
Magnetic Field ◽  
Coupling Strength ◽  
Geometric Phase ◽  
Time Dependent ◽  
Algebraic Dynamics ◽  
Spin Cluster ◽  
Alternative Expression ◽  
Linear Formula ◽  
External Time ◽  
The Magnetic Field

A homonuclear linear [Formula: see text] coupling spin cluster with the middle particle driven by an external time-dependent magnetic field is investigated by using the method of algebraic dynamics. The exact analytical solutions of the time-dependent Schrodinger equation of the spin cluster system are derived and employed to study the geometric phase. An alternative expression of the geometric phase in each eigenstate is obtained. It is shown that the geometric phase is related to the external magnetic-field parameter θ (the angle between the magnetic field and the Z axis) and the effective coupling strength Jn. Based on the relation, how the geometric phase depends on the coupling strength Jn in different reducible subspace is discussed.PACS Nos.: 33.20.Wr, 03.65.Fd, 03.65.Vf

scholarly journals On a direct method for the determination of an exact invariant for the time-dependent harmonic oscillator

1977 ◽  
Vol 20 (1) ◽  
pp. 97-105 ◽  
Author(s):  
P. G. L. Leach
Keyword(s):  
Direct Method ◽  
Dynamical Symmetry ◽  
Time Dependent ◽  
Symmetry Groups ◽  
New Approach ◽  
One Dimensional ◽  
The One ◽  
A Direct Method ◽  
Exact Invariant

AbstractAn exact invariant is found for the one-dimensional oscillator with equation of motion . The method used is that of linear canonical transformations with time-dependent coeffcients. This is a new approach to the problem and has the advantage of simplicity. When f(t) and g(t) are zero, the invariant is related to the well-known Lewis invariant. The significance of extension to higher dimension of these results is indicated, in particular for the existence of non-invariance dynamical symmetry groups.

Stability of a Pretwisted Blade With Nonconstant Rotating Speed

1992 ◽  
Author(s):  
S. M. Yang ◽  
S. M. Tsao
Keyword(s):  
Fundamental Frequency ◽  
Parametric Resonance ◽  
Multiple Scale ◽  
Time Dependent ◽  
Combination Resonance ◽  
Rotating Speed ◽  
System Parameters ◽  
Scale Method ◽  
Nonautonomous Systems ◽  
Parametric Instabilities

An analytical model is presented to investigate the vibration and stability of a pretwisted blade under nonconstant rotating speed. Two coupled bending displacements in flapwise and edgewise directions are considered. The time-dependent rotating speed leads to nonautonomous systems in which parametric resonance can occur. Six parametric instabilities, including primary and combination resonances, are predicted by using multiple scale method. These instability predictions are compared with those from numerical results of a more detail model. Among all instabilities, the combination resonance when perturbed frequency near twice of the fundamental frequency is found to be most critical and sensitive to system parameters.

scholarly journals Pricing multi-asset financial derivatives with time-dependent parameters—Lie algebraic approach

2002 ◽  
Vol 32 (7) ◽  
pp. 401-410 ◽  
Author(s):  
C. F. Lo ◽  
C. H. Hui
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Closed Form ◽  
Algebraic Approach ◽  
Dynamical Symmetry ◽  
Financial Derivatives ◽  
Time Dependent ◽  
New Method ◽  
New Approach ◽  
Algebraic Technique

We present a Lie algebraic technique for the valuation of multi-asset financial derivatives with time-dependent parameters. Exploiting the dynamical symmetry of the pricing partial differential equations of the financial derivatives, the new method enables us to derive analytical closed-form pricing formulae very straightforwardly. We believe that this new approach will provide an efficient and easy-to-use method for the valuation of financial derivatives.

Sign in / Sign up

Export Citation Format

Share Document