Semiclassical coherent-states propagator

• Autores: Rivas, Alejandro Mariano Fidel
• Año de publicación: 2013
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Semiclasscial Physica; Quantum propagator; Coherent States
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

In this work, we derived a semiclassical approximation for the matrix elements of a quantum propagator in coherent states (CS) basis that avoids complex trajectories; it only involves real ones. For that purpose, we used the symplectically invariant semiclassical Weyl propagator obtained by performing a stationary phase approximation (SPA) for the path integral in the Weyl representation. After that, for the transformation to CS representation SPA is avoided; instead a quadratic expansion of the complex exponent is used. This procedure also allows us to express the semiclassical CS propagator uniquely in terms of the classical evolution of the initial point without the need of any root search typical of van Vleck–Gutzwiller-based propagators. For the case of chaotic Hamiltonian systems, the explicit time dependence of the CS propagator has been obtained. The comparison with a realistic chaotic system that derives from a quadratic Hamiltonian, the cat map, reveals that the expression here derived is exact up to quadratic Hamiltonian systems.
Fil: Rivas, Alejandro Mariano Fidel. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina