Interplay of causticity and vorticality within the complex quantum Hamilton-Jacobi formalism

TL;DR

This paper explores how interference in quantum scattering creates complex dynamics and topologies in the quantum Hamilton-Jacobi formalism, highlighting the roles of caustics and vortices in wave packet collisions.

Contribution

It provides a detailed analysis of interference effects using the complex quantum Hamilton-Jacobi formalism, revealing the interplay of caustics and vortices in quantum trajectories.

Findings

Interference leads to rich trajectory topologies in the complex plane.

Caustics are linked to free wave-packet propagation.

Vortices are associated with the collision and interference process.

Abstract

Interference dynamics is analyzed in the light of the complex quantum Hamilton-Jacobi formalism, using as a working model the collision of two Gaussian wave packets. Though simple, this model nicely shows that interference in quantum scattering processes gives rise to rich dynamics and trajectory topologies in the complex plane, both ruled by two types of singularities: caustics and vortices, where the former are associated with the regime of free wave-packet propagation, and the latter with the collision (interference) process. Furthermore, an unambiguous picture connecting the complex and real frameworks is also provided and discussed.