Study of random matrix ensembles for bosonic systems

N. D. Chavda, V. Potbhare, V. K. B. Kota

H. N. Deota

Manan Vyas, T. H. Seligman

Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle (predom-inantly two-particle) interactions. The random matrix models incorporating the few-particle nature of interactions are known as embedded random matrix ensembles. In the present paper, we provide a brief overview of these two ensembles and illustrate how the embedded ensembles can be successfully used to study decoherence of a qubit interacting with an environment, both for fermionic and bosonic embedded ensembles. Numerical calculations show the dependence of decoherence on the nature of the environment.

J. Oitmaa

J. Oitmaa

V. K. B. Kota, N. D. Chavda

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.