Quantum spin dynamics in Fock space following quenches: Caustics and vortices

TL;DR

This paper explores how caustics and vortices manifest in the quantum spin dynamics of many-body systems after a quench, revealing quantum-specific modifications to classical catastrophe phenomena.

Contribution

It demonstrates the formation of caustics in Fock space amplitudes of quantum spins post-quench and describes how quantum granularity alters classical singularities and vortex structures.

Findings

Caustics form in Fock space amplitudes after a quench.

Quantum granularity removes classical singularities and vortices.

Discrete scaling laws replace continuous ones in quantum catastrophes.

Abstract

Caustics occur widely in dynamics and take on shapes classified by catastrophe theory. At finite wavelengths they produce interference patterns containing networks of vortices (phase singularities). Here we investigate caustics in quantized fields, focusing on the collective dynamics of quantum spins. We show that, following a quench, caustics are generated in the Fock space amplitudes specifying the many-body configuration and which are accessible in experiments with cold atoms, ions or photons. The granularity of quantum fields removes all singularities, including phase singularities, converting point vortices into nonlocal vortices that annihilate in pairs as the quantization scale is increased. Furthermore, the continuous scaling laws of wave catastrophes are replaced by discrete versions. Such `quantum catastrophes' are expected to be universal dynamical features of quantized fields.