Can quantum systems succumb to their own (gravitational) attraction?

Abstract

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 to remedy this situation by considering the gravitational influence exerted by a crystalline nanosphere of mesoscopic size on itself, in the semi-classical, mean field, regime. We study in depth the self-localisation process induced by the corresponding non-linear potential of (gravitational) self-interaction. In particular, we characterize the stability of the associated self-collapsed ground state and estimate the magnitude of the corrections that are due to the internal structure of the object (this includes size-effects and corrections due to the discrete, atomic, structure of the sphere). Finally, we derive an approximated, gaussian, dynamics which mimics several essential features of the self-gravitating dynamics and, based on numerical results derived from this model, we propose a concrete experimental setting which we believe might, in the foreseeable future, reveal the existence of gravitational self-interaction effects.

arXiv comment58 pages, 14 figures

References in corpus (21)

• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: I. Analytical results
• Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects
• Gravitation and quantummechanical localization of macroobjects
• Quantum Superposition of Massive Objects and Collapse Models
• Stationary solutions of the one-dimensional nonlinear Schroedinger equation: II. Case of attractive nonlinearity
• Optically Levitating Dielectrics in the Quantum Regime: Theory and Protocols
• Evolution of the Schrödinger--Newton system for a self--gravitating scalar field
• Real-time single-molecule imaging of quantum interference
• The Schrödinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
• Macroscopic Quantum Mechanics in a Classical Spacetime
• Newtonian Collapse of Scalar Field Dark Matter
• Gravitationally induced inhibitions of dispersion according to the Schrödinger-Newton Equation
• Testing spontaneous localization theories with matter-wave interferometry
• Macroscopic quantum resonators (MAQRO)
• Problems with the Newton-Schrödinger Equations
• Parameter Diagrams of the GRW and CSL Theories of Wave Function Collapse
• Newtonian Quantum Gravity
• Schrödinger-Newton "collapse" of the wave function
• Comments on Proposed Gravitational Modifications of Schrodinger Dynamics and their Experimental Implications
• Centre-of-mass motion in multi-particle Schroedinger-Newton dynamics

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• Gravitational Decoherence of Dark Matter
• Crucial tests of macrorealist and semi-classical gravity models with freely falling mesoscopic nanospheres
• General Relativistic Decoherence with Applications to Dark Matter Detection
• Decoherence from General Relativity
• Approximations for the free evolution of self-gravitating quantum particles
• Generalized guidance equation for peaked quantum solitons and effective gravity
• Testing de Broglie's double solution in the mesoscopic regime