Arrival time from Hamiltonian with non-hermitian boundary term

TL;DR

This paper introduces a novel method to compute quantum arrival time probabilities using a non-Hermitian boundary term in the Hamiltonian, linking the probability flux to the arrival density.

Contribution

It presents a new approach to quantum arrival time measurement by incorporating a non-Hermitian boundary term related to probability flux.

Findings

Arrival probability density equals the flux of the probability current.

The method connects non-Hermitian boundary terms with physical flux measurements.

Provides a theoretical framework for quantum arrival time analysis.

Abstract

We develop a new method for finding the quantum probability density of arrival at the detector. The evolution of the quantum state restricted to the region outside of the detector is described by a restricted Hamiltonian that contains a non-hermitian boundary term. The non-hermitian term is shown to be proportional to the flux of the probability current operator through the boundary, which implies that the arrival probability density is equal to the flux of the probability current.