Mean field dynamics of boson stars

By Alexander Elgart, B. Schlein. 2005

316 citations recorded by the source corpus.

We consider a quantum mechanical system of N bosons with relativistic dispersion interacting through a mean field Coulomb potential (attractive or repulsive). We choose the initial wave function to describe a condensate where the N bosons are all in the same one‐particle state. Starting from the N‐body Schrödinger equation, we prove that, in the limit N → ∞, the time evolution of the one‐particle density is governed by the relativistic nonlinear Hartree equation. This equation is used to describe the dynamics of boson stars (Chandrasekhar theory). The corresponding static problem was rigorously solved in [10]. © 2005 Wiley Periodicals, Inc.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/27bf202b09ba1dddded6379cb4c5487166458108

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Mean-Field Dynamics: Singular Potentials and Rate of Convergence (2009, unknown): “) This example generalizes the result of [1].”
Derivation of Hartree's theory for generic mean-field Bose systems (2013, background): “There are many works on the related (but still different) derivation of the time-dependent Hartree theory from the time-dependent Schrödinger equation associated with the Hamiltonian HN , see for instance [29, 25, 63, 7, 20, 21, 3, 22, 24, 54, 34, 51].”
Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems (2005, methodology): “This equation was recently derived in [ 8 ], starting from many-body dynamics, for the case of a Coulomb potential.”
A Simple Derivation of Mean Field Limits for Quantum Systems (2009, result): “Nevertheless our result here is already better than previous results [ 3 ,7,8,16] in the sense that we can handle stronger singularities than Coulomb in the interaction.”
Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations (2020, methodology): “We refer for details to Elgart and Schlein [18], Giulini and Großardt [23], Jones [24], and Schunck and Mielke [40].”
Well-posedness for Semi-relativistic Hartree Equations of Critical Type (2005, background): “Equation (1.1) arises, for instance, as an effective description of boson stars, see, e.g., [ ES05 , LY87], where F(u) is a focusing Hartree nonlinearity given by”
Boson Stars as Solitary Waves (2005, unknown): “As recently shown by Elgart and Schlein in [3], Eq.”
Blowup for nonlinear wave equations describing boson stars (2005, methodology): “For spherically symmetric initial data, u0(x) ∈ C ∞ c (R 3), with negative energy, we prove blowup of u(t, x) in H1/2-norm within a finite time.”
Quantitative Derivation of the Gross‐Pitaevskii Equation (2012, background): “This general scheme, first introduced in [23] for bounded interactions, was later extended to potentials with Coulomb singularities in [11] (and in [4], for bosons with relativistic dispersions).”
Sharp threshold of blow-up and scattering for the fractional Hartree equation (2017, background): “1) models the dynamics of (pseudo-relativistic) boson stars, where the potential 1 |x| is the Newtonian gravitational potential in the appropriate physical units (see[10, 30]).”
Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics (2007, methodology): “In [4], the Hartree equation with Coulomb interaction was derived for semirelativistic bosons; in the semirelativistic setting, the dispersion of the bosons only grows linearly in the momentum (for large momenta), and thus the control of the Coulomb singularity is more delicate.”
Effective Evolution Equations from Quantum Dynamics (2015, methodology): “The BBGKY technique has been later extended to potentials with Coulomb singularity in [30, 9] and, for semi-relativistic bosons, in [26].”
Uniqueness of ground states for pseudorelativistic Hartree equations (2008, background): “MR 2007m:35249 Zbl 1122.35119 [Elgart and Schlein 2007] A. Elgart and B. Schlein, “Mean field dynamics of boson stars”, Comm. Pure Appl.”
Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity (2015, unknown): “10 [19] A. Elgart, B. Schlein, Mean field dynamics of boson stars, Comm. Pure Appl.”