Quantum Dynamics in the Thermodynamic Limit

TL;DR

This paper explores how spontaneous symmetry breaking in the thermodynamic limit can lead to classical behavior in quantum systems and proposes an experiment to test this mechanism using exciton polariton condensates.

Contribution

It demonstrates that collective excitations enable quantum systems to spontaneously break time-translation symmetry, linking quantum dynamics to classical physics in the thermodynamic limit.

Findings

Thermodynamic limit allows quantum systems to exhibit classical dynamics.

Presence of thin spectrum enables spontaneous breaking of time-translation symmetry.

Proposes an experiment with exciton polariton condensates to test the theory.

Abstract

The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum mechanical building blocks is one of the cornerstones of modern condensed matter theory and has found applications in many different areas of physics. The theory of spontaneous symmetry breaking however, is inherently an equilibrium theory, which does not address the dynamics of quantum systems in the thermodynamic limit. Here, we will use the example of a particular antiferromagnetic model system to show that the presence of a so-called thin spectrum of collective excitations with vanishing energy -one of the well-known characteristic properties shared by all symmetry-breaking objects- can allow these objects to also spontaneously break time-translation symmetry in the thermodynamic limit. As a result, that limit is found to be able, not only to reduce quantum mechanical equilibrium averages to their classical counterparts, but also to turn individual-state quantum dynamics into classical physics. In the process, we find that the dynamical description of spontaneous symmetry breaking can also be used to shed some light on the possible origins of Born's rule. We conclude by describing an experiment on a condensate of exciton polaritons which could potentially be used to experimentally test the proposed mechanism.