Random k-Body Ensembles for Chaos and Thermalization in Isolated Systems

Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.

Study of Tracer Diffusion Mechanism in Amorphous Metal

The statistical relaxation (SR) simulation has been conducted to study the behavior of simplexes and bubbles (BB) in amorphous Co metal containing 2×105 atoms. The simulation reveals that the fraction of 4-simplex increases and n-simplex (n>4) decreases depending upon relaxation degree. The simulation found that a large number of BB vary upon relaxation degree, which could play a role of diffusion vehicle for Co atoms in amorphous matrix. The idea of the diffusion mechanism in amorphous metal is described as follows: the elemental atomic movement includes a jump of neighboring atom into the BB and then a collective displacement of a large number of atoms around BB.