Approximations for the free evolution of self-gravitating quantum particles

André Großardt
Phys. Rev. A 94, 022101 – Published 1 August 2016

Abstract

The evolution of the center-of-mass wave function for a mesoscopic particle according to the Schrödinger-Newton equation can be approximated by a harmonic potential if the wave function is narrow compared to the size of the mesoscopic particle. It was noticed by Colin et al. [Phys. Rev. A 93, 062102 (2016).] that, in the regime where self-gravitational effects are weak, intermediate and wider wave functions may be approximated by a harmonic potential as well but with a width-dependent coupling, leading to a time evolution that is determined only by a differential equation for the width of a Gaussian wave function as a single parameter. Such an approximation results in considerably less computational effort in order to predict the self-gravitational effects on the wave-function dynamics. Here, we provide an alternative approach to this kind of approximation, including a rigorous derivation of the equations of motion for an initially Gaussian wave packet under the assumption that its shape is conserved. Our result deviates to some degree from the result by Colin et al. [Phys. Rev. A 93, 062102 (2016).], specifically in the limit of wide wave functions.

  • Figure
  • Figure
  • Received 21 June 2016

DOI:https://doi.org/10.1103/PhysRevA.94.022101

©2016 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsQuantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

André Großardt*

  • Department of Physics, University of Trieste, 34151 Miramare-Trieste, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy

  • *andre.grossardt@ts.infn.it

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Issue

Vol. 94, Iss. 2 — August 2016

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