A NEW SEMICLASSICAL DYNAMICS FROM THE INTERACTION REPRESENTATION

2005 ◽  
Vol 04 (04) ◽  
pp. 1093-1100 ◽  
Author(s):  
STEVEN D. SCHWARTZ
Keyword(s):  
Evolution Operator ◽  
Specific Interaction ◽  
Time Dependent ◽  
Zeroth Order ◽  
Exact Quantum ◽  
Semiclassical Dynamics ◽  
Semiclassical Mechanics ◽  
Dependent Interaction

This paper develops a new semiclassical mechanics from an exact quantum prescription. In this formulation, a zeroth order propagation, rather than Hamiltonian, is specified. The exact, full evolution operator is then given from a specific interaction representation of the evolved "perturbation" Hamiltonian. We then investigate a variety of approximate, semiclassical, and mixed Quantum/Classical methods, along with exact methodologies to evaluate this time dependent interaction Hamiltonian. The approximate full evolution operator can be described in a variety of ways including an iterated Lippman-Schwinger like equation, and an expansion of the perturbation propagator generated from the time evolved Hamiltonian.

scholarly journals Study of Time Evolution for Approximation of Two-Body Spinless Salpeter Equation in Presence of Time-Dependent Interaction

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Hadi Sobhani ◽  
Hassan Hassanabadi
Keyword(s):  
Differential Equation ◽  
Time Evolution ◽  
Series Solution ◽  
Evolution Operator ◽  
Heavy Quarks ◽  
Time Dependent ◽  
Time Evolution Operator ◽  
Invariant Method ◽  
The One ◽  
Dependent Interaction

We approximate the two-body spinless Salpeter equation with the one which is valid in heavy quarks limit. We consider the resulting semirelativistic equation in a time-dependent formulation. We use the Lewis-Riesenfeld dynamical invariant method and series solution to obtain the solutions of the differential equation. We have also done some calculations in order to derive the time evolution operator for the considered problem.

scholarly journals Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida
Keyword(s):  
Evolution Operator ◽  
Large Time ◽  
Rigid Motion ◽  
Time Dependent ◽  
Energy Relation ◽  
Exterior Domains ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
Whole Space ◽  
Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

scholarly journals CANONICAL FORM OF THE EVOLUTION OPERATOR OF A TIME-DEPENDENT HAMILTONIAN IN THE THREE LEVEL SYSTEM

2011 ◽  
Vol 08 (03) ◽  
pp. 647-655
Author(s):  
KAZUYUKI FUJII
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Evolution Operator ◽  
Time Dependent ◽  
Level System ◽  
Riccati Differential Equations

In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on SU(3) and its dimension is eight, so we obtain three complex Riccati differential equations interacting with one another (which have been obtained by Fujii and Oike) and two real phase equations. This is a canonical form of the evolution operator.

Sign in / Sign up

Export Citation Format

Share Document