title: Semiclassical propagator to evaluate off-diagonal matrix elements of the evolution operator between quantum states.
abstract: We present a powerful semiclassical expression to evaluate off-diagonal matrix elements of the evolution operator between quantum states constructed in the neighborhood of unstable short periodic orbits, which is valid up to the Heisenberg time. The expression is much easier to evaluate than the Van Vleck propagator and consists of a sum over the set of heteroclinic orbits, where each term of the series is computed by canonical invariants. Here we introduce relevant canonical invariants of heteroclinic orbits and with them at hand, the semiclassical expression is derived. Finally, our formula is successfully verified in the hyperbola billiard.
authors.affiliation: Departamento de Física, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250, C1429BNP Buenos Aires, Argentina and Escuela de Ciencia y Tecnología, Universidad Nacional de General San Martín, Alem 3901, B1653HIM Villa Ballester, Argentina.
authors.forename: Eduardo G
authors.initials: EG
authors.lastname: Vergini