A model of a quantum particle in a quantum environment: a numerical study

TL;DR

This paper presents a numerical study of a quantum particle interacting with an environment modeled as localized spins, demonstrating how superposition states evolve into classical-like trajectories similar to a cloud chamber.

Contribution

It introduces a one-dimensional toy-model simulating a quantum particle's decoherence and trajectory formation through interaction with localized spins, mimicking cloud chamber behavior.

Findings

Superposition collapses into a classical-like path.

Environment interaction causes decoherence.

Model reproduces cloud chamber-like behavior.

Abstract

We define and investigate, via numerical analysis, a one dimensional toy-model of a cloud chamber. An energetic quantum particle, whose initial state is a superposition of two identical wave packets with opposite average momentum, interacts during its evolution and exchanges (small amounts of) energy with an array of localized spins. Triggered by the interaction with the environment, the initial superposition state turns into an incoherent sum of two states describing the following situation: or the particle is going to the left and a large number of spins on the left side changed their states, or the same is happening on the right side. This evolution is reminiscent of what happens in a cloud chamber where a quantum particle, emitted as a spherical wave by a radioactive source, marks its passage inside a supersaturated vapour-chamber in the form of a sequence of small liquid bubbles arranging themselves around a possible classical trajectory of the particle.