2015
DOI: 10.1088/0264-9381/32/6/065010
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The Schrödinger–Newton system with self-field coupling

Abstract: We study the Schrödinger-Newton system of equations with the addition of gravitational field energy sourcing -such additional nonlinearity is to be expected from a theory of gravity (like general relativity), and its appearance in this simplified scalar setting (one of Einstein's precursors to general relativity) leads to significant changes in the spectrum of the self-gravitating theory.Using an iterative technique, we compare the mass dependence of the ground state energies of both Schrödinger-Newton and the… Show more

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Cited by 7 publications
(12 citation statements)
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References 17 publications
(49 reference statements)
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“…They introduce a characteristic scale length to the gravitational interactions, therefore reducing the potential interactions to finite distances. Gravitational field sources have been introduced into the SN equation [26], which has some resemblance to our present Yukawa model.…”
Section: Introductionmentioning
confidence: 91%
See 1 more Smart Citation
“…They introduce a characteristic scale length to the gravitational interactions, therefore reducing the potential interactions to finite distances. Gravitational field sources have been introduced into the SN equation [26], which has some resemblance to our present Yukawa model.…”
Section: Introductionmentioning
confidence: 91%
“…We can study the evolution of the SN system, associated with matter coupled with a background, as described by the wave-kinetic Equation (26) and the radiation transport Equation (22). We start from a given equilibrium (I 0 , W 0 , n 0 ) and consider perturbations (Ĩ k ,W k ,ñ k ) evolving with frequency ω and wavevector k. Replacing this in Equation ( 26), we obtain, after linearization:…”
Section: Modified Jeans Instabilitymentioning
confidence: 99%
“…2 yields a new richness to the solutions for Newtonian boson stars that we will call "quantum polytropes" for reasons that will become obvious later. Although authors have considered other modifications to the Schrodinger-Poisson equation such as an electromagnetic field [11] or non-linear gravitational terms [12,13], the non-linear coupling of the gravitational source proposed here is novel.…”
Section: Introductionmentioning
confidence: 99%
“…In a recent paper, we studied the spectrum of a modified form of the usual Schrödinger-Newton system (SN) of gravity coupled to quantum mechanics (SN was originally developed in [1]). Now we turn to the spherical dynamics of the self-coupled gravity introduced, in this quantum mechanical setting, in [2]. For the SN system, we have Newtonian gravity determining the potential Φ using the wave function itself to describe the mass density, so the coupled system is…”
Section: Introductionmentioning
confidence: 99%
“…and making a gravitational field equation in (2) that is more like the nonlinear (Einstein tensor) left-hand side of (3) than the linear Poisson equation for gravity found in (1). Both SN and our modification take the source to be m Ψ * Ψ, and the approach can be viewed either as part of a multi-body Hartree approximation, or fundamental (the many-body view would not change the gravitational field equation here -we would still have to incorporate the energy self-coupling).…”
Section: Introductionmentioning
confidence: 99%