Sanjaye Ramgoolam: Negative specific heat capacities from gauged matrix and tensor quantum harmonic oscillators.

Wednesday Feb 19, 2025, 3:00 PM → 4:00 PM Europe/Paris

Quantum harmonic oscillator systems with gauged large N symmetries have been shown to have thermodynamic properties similar to expectations from the quantum physics of small black holes in Anti-de-Sitter space. Explicit partition functions for matrix harmonic oscillators for matrix size N with S_N gauge symmetry  are shown to give rise to negative specific heat capacities in the micro-canonical ensemble for energies below a bound scaling as ( N Log N ) for large N.  In the canonical ensemble there is a sharp Hagedorn-like transition at a temperature, derivable from a high temperature  expansion, which approaches zero in the large N limit.  There is evidence, based on representation-theoretic number sequences for the counting of states,  that similar thermodynamic features hold in multi-matrix and tensor systems with U(N) gauge symmetry. The talk is based on https://link.springer.com/article/10.1007/JHEP12(2024)161