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

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.

19 pages, 9 figures

References in corpus (5)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Semiclassical "Divide-and-Conquer" Method for Spectroscopic Calculations of High Dimensional Molecular Systems
• Post-Ehrenfest many-body quantum interferences in ultracold atoms far-out-of-equilibrium
• The semiclassical propagator in fermionic Fock space
• Searching chaotic saddles in high dimensions

Cited by in corpus (12)

• Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators
• Chaos in the three-site Bose-Hubbard model -- classical vs quantum
• Enhancement of many-body quantum interference in chaotic bosonic systems
• Eigenstate thermalization scaling in approaching the classical limit
• Controlling Many-Body Quantum Chaos: Bose-Hubbard systems
• Controlling Quantum Chaos: Optimal Coherent Targeting
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model
• Semiclassical evaluation of expectation values
• A corrected Maslov index for complex saddle trajectories
• Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-Heisenberg time scales
• Semiclassical propagation of coherent states and wave packets: hidden saddles
• Reduced Dimensional Monte Carlo Method: Preliminary Integrations