Asymmetry Amplification by a Nonadiabatic Passage through a Critical Point

TL;DR

This paper introduces a minimal, integrable model of a nonadiabatic passage through a second-order phase transition that results in strong asymmetry and provides exact scaling exponents for quasi-particle excitation densities.

Contribution

It generalizes the Painleve'-2 Hamiltonian dynamics to many degrees of freedom while preserving integrability, revealing a mechanism for asymmetry amplification during phase transitions.

Findings

Asymmetry persists regardless of weak symmetry breaking.

Exact scaling exponents for quasi-particle density are derived.

Model demonstrates strong asymmetry in quasi-particle production.

Abstract

We propose and solve a minimal model of dynamic passage through a second-order phase transition in the presence of symmetry breaking interactions and no dissipation. Our model generalizes the Hamiltonian dynamics of the Painleve'-2 equation to the case with many degrees of freedom, while maintaining the integrability property. The evolution eventually leads to a highly asymmetric state, no matter how weak the symmetry breaking parameter of the Hamiltonian is. This suggests a potential mechanism for strong asymmetry in the production of quasi-particles with nearly identical characteristics. The model's integrability also yields exact exponents for the scaling of the density of the nonadiabatically excited quasi-particles.