The Universe from a Single Particle

TL;DR

This paper investigates how complex many-body phenomena can emerge from fundamental quantum mechanics through spontaneous symmetry breaking, analyzing potentials with unstable and local minima related to random and interacting quantum systems.

Contribution

It introduces a framework connecting random quantum systems and interacting systems via symmetry breaking in potential functionals on Hamiltonians.

Findings

Identification of unstable critical points in Hamiltonian space.

Connection between random ensembles and interacting systems.

Insights into the emergence of many-body physics from quantum mechanics.

Abstract

We explore the emergence of many-body physics from quantum mechanics via spontaneous symmetry breaking. To this end, we study potentials which are functionals on the space of Hamiltonians enjoying an unstable critical point corresponding to a random quantum mechanical system (the Gaussian unitary ensemble), but also less symmetrical local minima corresponding to interacting systems at the level of operators.