Complex saddle trajectories for multidimensional quantum wave packet/coherent state propagation: application to a many-body system

TL;DR

This paper introduces a new technique for efficiently finding complex saddle points in multidimensional quantum wave packet propagation, applicable to many-body systems like the Bose-Hubbard model, enabling analysis of complex quantum dynamics.

Contribution

A novel method to locate minimal-dimension real search spaces for saddle points in high-dimensional quantum systems, improving the analysis of wave packet propagation in many-body physics.

Findings

Identifies a minimal real search space for saddle points.

Allows complete saddle set determination up to intermediate times.

Facilitates analysis of dynamical regimes in many-body systems.

Abstract

A practical search technique for finding the complex saddle points used in wave packet or coherent state propagation is developed which works for a large class of Hamiltonian dynamical systems with many degrees of freedom. The method can be applied to problems in atomic, molecular, and optical physics, and other domains. A Bose-Hubbard model is used to illustrate the application to a many-body system where discrete symmetries play an important and fascinating role. For multidimensional wave packet propagation, locating the necessary saddles involves the seemingly insurmountable difficulty of solving a boundary value problem in a high-dimensional complex space, followed by determining whether each particular saddle found actually contributes. In principle, this must be done for each propagation time considered. The method derived here identifies a real search space of minimal dimension, which leads to a complete set of contributing saddles up to intermediate times much longer than the Ehrenfest time scale for the system. The analysis also gives a powerful tool for rapidly identifying the various dynamical regimes of the system.