Time dependent canonical perturbation theory I: General theory

Pramana ◽  
1995 ◽  
Vol 45 (2) ◽  
pp. 141-148 ◽  
Author(s):  
B R Sitaram ◽  
Mitaxi P Mehta
Keyword(s):  
Perturbation Theory ◽  
General Theory ◽  
Time Dependent ◽  
Canonical Perturbation

Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation

1997 ◽  
Author(s):  
Eric A. Butcher ◽  
S. C. Sinha
Keyword(s):  
Perturbation Theory ◽  
Classical Method ◽  
Time Dependent ◽  
Fast Time ◽  
Quadratic Part ◽  
Canonical Perturbation ◽  
Internal Excitation ◽  
Quadratic Hamiltonian ◽  
Unperturbed Part ◽  
Time Periodic

Abstract In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.

Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation

1998 ◽  
Vol 65 (1) ◽  
pp. 209-217 ◽  
Author(s):  
E. A. Butcher ◽  
S. C. Sinha
Keyword(s):  
Perturbation Theory ◽  
Classical Method ◽  
Time Dependent ◽  
Fast Time ◽  
Quadratic Part ◽  
Canonical Perturbation ◽  
Internal Excitation ◽  
Quadratic Hamiltonian ◽  
Unperturbed Part ◽  
Time Periodic

In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.

Kinetic equations for plasmas subjected to a strong time-dependent extenal field. Part 2. The weak-interaction approximation

1974 ◽  
Vol 11 (3) ◽  
pp. 377-387 ◽  
Author(s):  
R. Balescu ◽  
J. H. Misguich
Keyword(s):  
Kinetic Equation ◽  
General Theory ◽  
Weak Interaction ◽  
Weak Coupling ◽  
Kinetic Equations ◽  
Time Dependent ◽  
External Fields ◽  
Interaction Approximation

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.

scholarly journals Symmetry‐adapted perturbation theory of nonadditive three‐body interactions in van der Waals molecules. I. General theory

1995 ◽  
Vol 103 (18) ◽  
pp. 8058-8074 ◽  
Author(s):  
Robert Moszynski ◽  
Paul E. S. Wormer ◽  
Bogumil Jeziorski ◽  
Ad van der Avoird
Keyword(s):  
Perturbation Theory ◽  
General Theory ◽  
Van Der Waals ◽  
Van Der Waals Molecules ◽  
Three Body
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