Hydrodynamic View of Wave-Packet Interference: Quantum Caves

TL;DR

This paper explores wave-packet interference using a hydrodynamic quantum formalism, revealing topological structures called quantum caves and analyzing their impact on quantum trajectories and interference lifetimes.

Contribution

It introduces the concept of quantum caves in the complex quantum Hamilton-Jacobi formalism and links their topology to interference dynamics and trajectory behavior.

Findings

Quantum caves form from vortical and stagnation tubes in space-time plots.

Trajectories exhibit helical wrapping and hyperbolic deflection around these tubes.

Interference lifetime can be estimated from wrapping time and nodal line rotation.

Abstract

Wave-packet interference is investigated within the complex quantum Hamilton-Jacobi formalism using a hydrodynamic description. Quantum interference leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display counterclockwise helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. The string of alternating stagnation and vortical tubes is sufficient to generate divergent trajectories. Moreover, the average wrapping time for trajectories and the rotational rate of the nodal line in the complex plane can be used to define the lifetime for interference features.