Caustics in quantum many-body dynamics

TL;DR

This paper introduces a new class of nonequilibrium quantum phenomena called quantum caustics, which are singularities in the wavefunction's evolution that can be described using catastrophe theory, revealing universal patterns in quantum many-body dynamics.

Contribution

It extends classical caustic concepts to quantum many-body systems, illustrating their structure and universality using Bose Hubbard models and catastrophe theory.

Findings

Quantum caustics form hierarchical universal patterns.

Discretized caustics in Fock space include fold, cusp, and higher catastrophes.

Identifies new universal phenomena in quantum dynamics related to singularities.

Abstract

We describe a new class of nonequilibrium quantum many-body phenomena in the form of networks of caustics that dominate the many-body wavefunction in the semiclassical regime following a sudden quench. It includes the light cone-like propagation of correlations as a particular case. Caustics are singularities formed by the birth and death of waves and form a hierarchy of universal patterns whose natural mathematical description is via catastrophe theory. Examples in classical waves range from rainbows and gravitational lensing in optics to tidal bores and rogue waves in hydrodynamics. Quantum many-body caustics are discretized by second-quantization (``quantum catastrophes'') and live in Fock space which can potentially have many dimensions. We illustrate these ideas using the Bose Hubbard dimer and trimer models which are simple enough that the caustic structure can be elucidated from first principles and yet run the full range from integrable to nonintegrable dynamics. The dimer gives rise to discretized versions of fold and cusp catastrophes whereas the trimer allows for higher catastrophes including the codimension-3 hyperbolic and elliptic umbilics which are organized by, and projections of, an 8-dimensional corank-2 catastrophe known as $X_9$. These results describe a hitherto unrecognized form of universality in quantum dynamics organized by singularities that manifest as strong fluctuations in mode population probabilities.