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

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.

17 pages, 7 figures

References in corpus (4)

• Spin dependent point potentials in one and three dimensions
• Semiclassical wave-packets emerging from interaction with an environment
• De coherence for a heavy particle interacting with a light one: new analysis and numerics
• Joint excitation probability for two harmonic oscillators in dimension one and the Mott problem

Cited by in corpus (3)

• Decoherence and determinism in a one-dimensional cloud-chamber model
• Transverse quantum decoherence of a fast particle in a gas
• An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions