arXiv subjects

Sudhir R. Jain

Publications and source records attributed to Sudhir R. Jain.

39 records · Page 3Linked to original sources

arXiv1996

Semiclassical theory for many-body Fermionic systems

We present a treatment of many-body Fermionic systems that facilitates an expression of the well-known quantities in a series expansion of the Planck's constant. The ensuing semiclassical result contains to a leading order of the response function the classical time correlation function of the observable followed by the Weyl-Wigner series, on top of these terms are the periodic-orbit correction terms. The treatment given here starts from linear response assumption of the many-body theory and in its connection with semiclassical theory, it makes no assumption of the integrability of classical dynamics underlying the one-body quantal system. Applications of the framework are also discussed.

cond-mat↗

arXiv1996

Quantum chaos, random matrix theory, and statistical mechanics in two dimensions - a unified approach

We present a theory where the statistical mechanics for dilute ideal gases can be derived from random matrix approach. We show the connection of this approach with Srednicki approach which connects Berry conjecture with statistical mechanics. We further establish a link between Berry conjecture and random matrix theory, thus providing a unified edifice for quantum chaos, random matrix theory, and statistical mechanics. In the course of arguing for these connections, we observe sum rules associated with the outstanding counting problem in the theory of braid groups. We are able to show that the presented approach leads to the second law of thermodynamics.

chao-dyn↗

arXiv1996

From Random Matrix Theory to Statistical Mechanics - Anyon Gas

Motivated by numerical experiments and studies of quantum systems which are classically chaotic, we take a Random Matrix description of a Hard-sphere gas to Statistical Mechanical description. We apply this to Anyon gas and obtain a formal expression for the momentum distribution. Various limiting situations are discussed and are found in agreement with the well-known results on Hard-sphere gas in low-density regime.

cond-mat↗