Regensburg 2013 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 26: Quantum Chaos I
DY 26.1: Invited Talk
Thursday, March 14, 2013, 09:30–10:00, H47
Genuine quantum interference in interacting bosonic fields: The semiclassical propagator in Fock space — •Juan Diego Urbina1, Thomas Engl1, Arturo Arguelles2,1, Julien Dujardin2, Peter Schlagheck2, and Klaus Richter1 — 1Institute for Theoretical Physics, University of Regensburg — 2Department of Physics, University of Liege
We present a semiclassical theory of quantum interference effects in interacting bosonic fields. We make special emphasis on the difference between genuine quantum interference (due to the superposition principle in the many-body Hilbert space), and classical interference effects due to the wave character of the classical limit.
First, we discuss how the usual approaches to this problem are unable to provide the characteristic sum of oscilatory terms, each asociated with a solution of the classical equations of motion, required to semiclassically address interference effects. We show then how to solve this problems by a formal construction of the van Vleck-Gutzwiller propagator for bosonic fields as a sum over paths in the associated Fock space and we identify the classical limit as a Gross-Pitaevskii equation with boundary conditions and multiple solutions.
The theory predicts effects akin to weak localization to take place in Fock space, and in particular the enhancement of quantum probability of return due to interference between time-reversed paths there. We support our claims with extensive numerical calculations for a discrete version of an interacting bosonic field.