Schrödinger–Newton ‘collapse’ of the wavefunction

  title={Schr{\"o}dinger–Newton ‘collapse’ of the wavefunction},
  author={J. V. Meter},
  journal={Classical and Quantum Gravity},
  • J. V. Meter
  • Published 2011
  • Physics
  • Classical and Quantum Gravity
It has been suggested that the nonlinear Schrodinger–Newton equation might approximate the coupling of quantum mechanics with gravitation, particularly in the context of the Moller–Rosenfeld semiclassical theory. Numerical results for the spherically symmetric, time-dependent, single-particle case are presented, clarifying and extending previous work on the subject. It is found that, for a particle mass greater than 1.14(2/(Gσ))1/3, a wave packet of width σ partially 'collapses' to a… Expand

Figures from this paper

The Dynamics of the Schrodinger-Newton System with Self-Field Coupling
We probe the dynamics of a modified form of the Schrodinger-Newton system of gravity coupled to single particle quantum mechanics. At the masses of interest here, the ones associated with the onsetExpand
Equaquação de Schrödinger-Newton : influência da condição inicial em um modelo semi-clássico para gravitação
In this work we use the semi-classical approximation to try a better understanding of how gravity interacts with matter. This aproximation is studied through the Schrödinger-Newton (SN) Equation,Expand
Initial condition dependence and wave function confinement in the Schrödinger–Newton equation
In this work we study the dynamics of the Schrödinger–Newton (SN) equation upon different choices of initial conditions. Setting up superpositions of Gaussian-like wave packages, a very rich behaviorExpand
Can quantum systems succumb to their own (gravitational) attraction
The gravitational interaction is generally considered to be too weak to be easily submitted to systematic experimental investigation in the quantum, microscopic, domain. In this paper we attempt toExpand
The Schrödinger–Newton system with self-field coupling
We study the Schrodinger–Newton (SN) system of equations with the addition of gravitational field energy sourcing—such additional nonlinearity is to be expected from a theory of gravity (like generalExpand
Generalized guidance equation for peaked quantum solitons: the single particle case
We study certain non-linear generalisations of the Schrodinger equation which admit static solitonic 2 solutions in absence of external potential acting on the particle. We consider a class ofExpand
Towards a theory of wavefunction collapse Part 1: How the Diosi-Penrose criterion and Born's rule can be derived from semiclassical gravity, and how the criterion can be relativistically generalised with help of the Einstein-Hilbert action
A new approach to wavefunction collapse is prepared by an analysis of semiclassical gravity. The fact that, in semiclassical gravity, superposed states must share a common classical spacetimeExpand
The Schrödinger–Newton equations beyond Newton
The scope of this paper is twofold. First, we derive rigorously a low-velocity and Galilei-covariant limit of the gravitoelectromagnetic (GEM) equations. Subsequently, these reduced GEM equations areExpand
Modification of Schrödinger–Newton equation due to braneworld models with minimal length
Abstract We study the correction of the energy spectrum of a gravitational quantum well due to the combined effect of the braneworld model with infinite extra dimensions and generalized uncertaintyExpand
From optics to dark matter: A review on nonlinear Schrödinger–Poisson systems
Abstract We review recent progress in Schrodinger–Poisson systems in 1+2 and 1+3 dimensions in the presence of nonlinear terms. In a mean field approach, this mathematical model describes theExpand


A numerical study of the Schrödinger-Newton equations
The Schrodinger-Newton (S-N) equations were proposed by Penrose [18] as a model for gravitational collapse of the wave-function. The potential in the Schrodinger equation is the gravity due to theExpand
Evolution of the Schrödinger--Newton system for a self--gravitating scalar field
Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein-Klein-Gordon (EKG) system, which results in the soExpand
Spherically symmetric solutions of the Schrodinger-Newton equations
As part of a programme in which quantum state reduction is understood as a gravitational phenomenon, we consider the Schrodinger-Newton equations. For a single particle, this is a coupled systemExpand
Investigation of the time-dependent Schroedinger-Newton equation
The Schrödinger-Newton equation is a highly non-linear integro-partial differential equation that arises from both the theory of semiclassical gravity of Møller and Rosenfeld and as a possibleExpand
Comments on proposed gravitational modifications of schrödinger dynamics and their experimental implications
We discuss aspects of gravitational modifications of Schr?dinger dynamics proposed by Di?si and Penrose. We consider first the Di?si?Penrose criterion for gravitationally induced state vectorExpand
Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
In this book, Robert Wald provides a pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantumExpand
On Gravity's role in Quantum State Reduction
The stability of a quantum superposition of two different stationary mass distributions is examined, where the perturbing effect of each distribution on the space-time structure is taken intoExpand
Testing spontaneous localization theories with matter-wave interferometry
It is a basic unresolved question of quantum mechanics whether the Schrodinger equation holds for truly macro- scopic systems. Unitarity then implies that even mea- surement devices or consciousExpand
Non-linear coupling of quantum theory and classical gravity
Discusses the possibility that the non-linear evolution proposed earlier for a relativistic quantum field theory may be related to its coupling to a classical gravitational field. Formally, in theExpand
Scalar field dark matter: Nonspherical collapse and late-time behavior
Instituto de F´isica y Matem´aticas, Universidad Michoacana de San Nicol´as de Hidalgo. Edificio C-3,Cd. Universitaria, A. P. 2-82, 58040 Morelia, Michoac´an, M´exico.(Dated: February 5, 2008)We showExpand