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A Model of a Quantum Particle in a Quantum Environment: A Numerical Study

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems General quantum mechanics and problems of quantization Partial differential equations, boundary value problems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  03 July 2015

Raffaele Carlone ,
Rodolfo Figari  and
Claudia Negulescu
Raffaele Carlone
Affiliation:
Università Federico II di Napoli, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, MSA I-80126 Napoli, Italy
Rodolfo Figari
Affiliation:
Università Federico II di Napoli, Dipartimento di Fisica e INFN Sezione di Napoli, MSA I-80126 Napoli, Italy
Claudia Negulescu*
Affiliation:
Université de Toulouse & CNRS, UPS, Institut de Mathématiques de Toulouse UMR 5219, F-31062 Toulouse, France
*
Email addresses: raffaele.carlone@unina.it (R. Carlone), figari@na.infn.it (R. Figari), claudia.negulescu@math.univ-toulouse.fr (C. Negulescu)
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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.

Keywords

Schrödinger equationquantum particle+environment modelmulti-channel point interactionsWilson cloud chambertrace formationdecoherencenumerical discretization

MSC classification

Secondary: 35Q41: Time-dependent Schrödinger equations, Dirac equations 65N06: Finite difference methods 65M06: Finite difference methods 81S22: Open systems, reduced dynamics, master equations, decoherence 68U20: Simulation
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 1 , July 2015 , pp. 247 - 262
Copyright
Copyright © Global-Science Press 2015 

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