Random Interactions

Connections between Classical Integrable Models, Log Gas and Random Matrix Theory

by Prof. Manas Kulkarni (TIFR-ICTS, Bangalore)

Tuesday, February 5, 2019 from to (Asia/Kolkata)
at A 304
We present a deep connection between the classical Calogero-Moser (CM) model, Log-gas (LG) model and Random Matrix Theory (RMT). We show that CM model has some remarkable connections with the 1D LG model. Both models have the same minimum energy configuration with the particle positions given by the zeros of the Hermite potential. Moreover the Hessian describing small oscillations around equilibrium are also related for the two models. We explore this connection further by studying finite temperature equilibrium properties of the CM model through Monte-Carlo simulations and comparing them with known LG results. In particular, our findings indicate that the single particle distribution and the marginal distribution of the boundary particle of CM model are also given by Wigner semi-circle and the Tracy- Widom distribution respectively (similar to LG model). Comparisons are made with analytical predictions from the small oscillation theory and we find very good agreement. Parallels are also drawn with rigorous mathematical results from RMT and implications of finite-size as well as finite- temperature effects are observed. We also present some preliminary results on large deviations in CM model by using field theory.