Relativistic effects on the Schrödinger-Newton equation

Brizuela, David; Duran-Cabacés, Albert

doi:10.1103/physrevd.106.124038

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…The Schrödinger-Newton equation was first proposed to study self-gravitating bosonic stars by Ruffini and Bonazzola [260]. Since this model was completely non-relativistic, some authors recently considered a modification of the Schrödinger-Newton equation by taking into account certain relativistic corrections [261], with a particular focus on gravitomagnetic corrections [262]. Under the above approximation, Zhao et al [263] considered a short distance modification of the Schrödinger-Newton equation which also results in a short distance modification of the quantum mechanical virial theorem.…”

Section: Quantum Effectsmentioning

confidence: 99%

A tale of analogies: a review on gravitomagnetic effects, rotating sources, observers and all that

Ruggiero,

Astesiano

2023

J. Phys. Commun.

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Gravitoelectromagnetic analogies are somewhat ubiquitous in General Relativity, and they are often used to explain peculiar effects of Einstein's theory of gravity in terms of familiar results from classical electromagnetism. Perhaps, the best known of these analogy pertains to the similarity between the equations of electromagnetism and those of the linearized theory of General Relativity. But the analogy is somewhat deeper and ultimately rooted in the splitting of spacetime, which is preliminary to the definition of the measurement process in General Relativity.In this paper we review the various approaches that lead to the introduction of a magnetic-like part of the gravitational interaction, briefly called \textit{gravitomagnetic} and, then, we provide a survey of the recent developments both from the theoretical and experimental viewpoints.

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Section: Quantum Effectsmentioning

confidence: 99%

A tale of analogies: a review on gravitomagnetic effects, rotating sources, observers and all that

Ruggiero,

Astesiano

2023

J. Phys. Commun.

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“…In general, the wave function of a free particle in the S-N-Λ system was found to split into a core region that collapses due to gravitational selfattraction and an outer region that undergoes accelerated diffusion due to the presence of dark energy [54]. While the former behaviour is present in the standard S-N model [57], the latter is unique to the S-N-Λ system. The order of magnitude of the critical radius separating collapse from expansion was found to match analytical estimates of the classical turnaround radius for a massive compact object in the presence of a cosmological constant [58].…”

Section: Introductionmentioning

confidence: 99%

Series Solution of the Time-Dependent Schrödinger–Newton Equations in the Presence of Dark Energy via the Adomian Decomposition Method

2023

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The Schrödinger–Newton model is a nonlinear system obtained by coupling the linear Schrödinger equation of canonical quantum mechanics with the Poisson equation of Newtonian mechanics. In this paper, we investigate the effects of dark energy on the time-dependent Schrödinger–Newton equations by including a new source term with energy density proportional to the cosmological constant Λ, in addition to the particle-mass source term. The resulting Schrödinger–Newton–Λ (S-N-Λ) system cannot be solved exactly, in closed form, and one must resort to either numerical or semianalytical (i.e., series) solution methods. We apply the Adomian Decomposition Method, a very powerful method for solving a large class of nonlinear ordinary and partial differential equations, to obtain accurate series solutions of the S-N-Λ system, for the first time. The dark energy dominated regime is also investigated in detail. We then compare our results to existing numerical solutions and analytical estimates and show that they are consistent with previous findings. Finally, we outline the advantages of using the Adomian Decomposition Method, which allows accurate solutions of the S-N-Λ system to be obtained quickly, even with minimal computational resources. The extensive use of the Adomian Decomposition Method in the field of quantum mechanics and quantum field theory may open new mathematical, and physical, perspectives on obtaining semi-analytical solutions for some complex problems of quantum theory.

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Gravitational soliton solutions to self-coupled Klein-Gordon and Schrödinger equations

Chabysheva

Hiller

2023

Phys. Rev. D

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Relativistic effects on the Schrödinger-Newton equation

Cited by 3 publications

References 23 publications

A tale of analogies: a review on gravitomagnetic effects, rotating sources, observers and all that

A tale of analogies: a review on gravitomagnetic effects, rotating sources, observers and all that

Series Solution of the Time-Dependent Schrödinger–Newton Equations in the Presence of Dark Energy via the Adomian Decomposition Method

Gravitational soliton solutions to self-coupled Klein-Gordon and Schrödinger equations

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