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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.

The standard tunneling model describes quite satisfactorily the thermal properties of amorphous solids at temperatures $T

We performed a nuclear magnetometry study on quantum Hall ferromagnet with a bilayer total filling factor of $\nu_{\rm{tot}} = 2$. We found not only a rapid nuclear relaxation but also a sudden change in the nuclear spin polarization distribution after a one-second interaction with a canted antiferromagnetic phase. We discuss the possibility of observing cooperative phenomena coming from nuclear spin ensemble triggered by electrons with collective spin interactions.

The content of an ab-initio time-dependent theory of quantum molecular dynamics of electrons and atomic nuclei is presented. Employing the time-dependent variational principle and a family of approximate state vectors yields a set of dynamical equations approximating the time-dependent Schrodinger equation. These equations govern the time evolution of the relevant state vector parameters as molecular orbital coefficients, nuclear positions and momenta. This approach does not impose the Born-Oppenheimer approximation, does not use potential energy surfaces and takes into account electron-nuclear coupling. Basic conservation laws are fully obeyed. The simplest model of the theory employs a single determinantal state for the electrons and classical nuclei and is implemented in the computer code ENDyne. Results from this ab-initio theory are reported for ion-atom and ion-molecule collisions.

Computerized simulation of low frequency dynamics of liquid hydrogen flow in nuclear rocket engine