2014/12/19 by Alexander Volya, Volya, Alexander
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Nuclear Theory (nucl-th) #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.1412.6335
openalex publication_date 2014/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this presentation is to highlight various computational techniques used to study dynamics of quantum many-body systems. We examine the projection and variable phase methods being applied to multi-channel problems of scattering and tunneling; here the virtual, energy-forbidden channels and their treatment are of particular importance. The direct time-dependent solutions using Trotter-Suzuki propagator expansion provide yet another approach to exploring the complex dynamics of unstable systems. While presenting computational tools, we briefly revisit the general theory of the quantum decay of unstable states. The list of questions here includes those of the internal dynamics in decaying systems, formation and evolution of the radiating state, and low-energy background that dominates at remote times. Mathematical formulations and numerical approaches to time-dependent problems are discussed using the quasi-stationary methods involving effective Non-Hermitian Hamiltonian formulation.