Quantum interference within the complex quantum Hamilton-Jacobi formalism

TL;DR

This paper explores quantum interference within the complex quantum Hamilton-Jacobi formalism, revealing how complex trajectories and nodal line rotations explain interference patterns and allow computation of interference feature lifetimes.

Contribution

It provides a unified framework for understanding quantum interference through complex trajectories and introduces a method to calculate interference lifetimes based on wrapping time.

Findings

Complex trajectories exhibit helical wrapping and hyperbolic deflection.

Interference features are explained by nodal line rotation in the complex plane.

A practical method to compute interference lifetime using average wrapping time.

Abstract

Quantum interference is investigated within the complex quantum Hamilton-Jacobi formalism. As shown in a previous work [Phys. Rev. Lett. 102, 250401 (2009)], complex quantum trajectories display helical wrapping around stagnation tubes and hyperbolic deflection near vortical tubes, these structures being prominent features of quantum caves in space-time Argand plots. Here, we further analyze the divergence and vorticity of the quantum momentum function along streamlines near poles, showing the intricacy of the complex dynamics. Nevertheless, despite this behavior, we show that the appearance of the well-known interference features (on the real axis) can be easily understood in terms of the rotation of the nodal line in the complex plane. This offers a unified description of interference as well as an elegant and practical method to compute the lifetime for interference features, defined in terms of the average wrapping time, i.e., considering such features as a resonant process.