Integrability of Φ⁴ Matrix Model as N-body Harmonic Oscillator System

2023/08/22 by Harald Grosse, Grosse, Harald, Akifumi Sako +1
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Cold Atom Physics and Bose-Einstein Condensates

paper · pdf · doi:10.48550/arxiv.2308.11523

Abstract

We study a Hermitian matrix model with a kinetic term given by Tr (H Φ² ), where H is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential Φ³ replaced by Φ⁴. We show that its partition function solves an integrable Schrödinger-type equation for a non-interacting N-body Harmonic oscillator system.

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