Initial value representation for the SU(n) semiclassical propagator

TL;DR

This paper introduces an initial value representation for the SU(n) semiclassical propagator, enabling efficient analysis of bosonic dynamics in multi-mode systems like Bose-Einstein condensates.

Contribution

It recasts the SU(n) semiclassical propagator into an initial value form using trajectory filtering, improving computational efficiency for many-body quantum systems.

Findings

Demonstrates the method on a Bose-Einstein condensate in a triple-well potential

Shows improved accuracy and efficiency over traditional boundary-based approaches

Provides detailed analysis of the method's applicability to bosonic systems

Abstract

The semiclassical propagator in the representation of SU(n) coherent states is characterized by isolated classical trajectories subjected to boundary conditions in a doubled phase space. In this paper we recast this expression in terms of an integral over a set of initial-valued trajectories. These trajectories are monitored by a filter that collects only the appropriate contributions to the semiclassical approximation. This framework is suitable for the study of bosonic dynamics in n modes with fixed total number of particles. We exemplify the method for a Bose-Einstein condensate trapped in a triple-well potential, providing a detailed discussion on the accuracy and efficiency of the procedure.