Quantum expansion of the dynamics of interacting bosons: semiclassical approximation and beyond
Abstract
We develop a perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover the semiclassical (also known as truncated Wigner) approximation, where the evolution is still classical but the initial conditions are distributed according to the Wigner transform of the initial density matrix. Further corrections can be characterized as quantum scattering processes, which appear in the form of a nonlinear response of an observable to an infinitesimal displacement of the field along its classical evolution. We compare results obtained within this scheme with the exact ones for a few solvable examples.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 2004
- Bibcode:
- 2004APS..MARS28013P