Computational approaches to many-body dynamics of unstable nuclear systems

TL;DR

This paper reviews computational techniques for studying the complex quantum many-body dynamics of unstable nuclear systems, focusing on scattering, tunneling, and decay processes using various numerical methods.

Contribution

It introduces and compares multiple computational approaches, including projection, variable phase, and Trotter-Suzuki methods, for analyzing unstable quantum systems.

Findings

Effective non-Hermitian Hamiltonian formulations aid in modeling decay dynamics.

Time-dependent solutions reveal internal decay mechanisms.

Virtual channels significantly influence scattering and tunneling processes.

Abstract

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.