Wavefunction collapse driven by non-Hermitian disturbance

TL;DR

This paper models wavefunction collapse using a non-Hermitian Hamiltonian, simulating how non-Hermitian perturbations influence collapse dynamics and exploring potential deviations from standard quantum mechanics.

Contribution

It introduces a novel approach to wavefunction collapse via non-Hermitian Hamiltonians and analyzes how perturbation parameters affect collapse time.

Findings

Collapse time depends on non-Hermitian perturbation strength

Manipulating the apparatus can challenge standard quantum predictions

Simulation results show non-Hermitian effects influence measurement outcomes

Abstract

In the context of the measurement problem, we propose to model the interaction between a quantum particle and an "apparatus" through a non-Hermitian Hamiltonian term. We simulate the time evolution of a normalized quantum state split into two spin components (via a Stern-Gerlach experiment) and that undergoes a wave-function collapse driven by a non-Hermitian Hatano-Nelson Hamiltonian. We further analyze how the strength and other parameters of the non-Hermitian perturbation influence the time-to-collapse of the wave function obtained under a Schr\"{o}dinger-type evolution. We finally discuss a thought experiment where manipulation of the apparatus could challenge standard quantum mechanics predictions.