The Experts below are selected from a list of 4308 Experts worldwide ranked by ideXlab platform
Andre Grosardt - One of the best experts on this subject based on the ideXlab platform.
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optomechanical test of the schrodinger Newton Equation
Physical Review D, 2016Co-Authors: Andre Grosardt, James Bateman, Hendrik Ulbricht, Angelo BassiAbstract:The Schrodinger-Newton Equation has been proposed as an experimentally testable alternative to quantum gravity, accessible at low energies. It contains self-gravitational terms, which slightly modify the quantum dynamics. Here we show that it distorts the spectrum of a harmonic system. Based on this effect, we propose an optomechanical experiment with a trapped microdisc to test the Schrodinger-Newton Equation, and we show that it can be realized with existing technology.
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the schrodinger Newton Equation and its foundations
New Journal of Physics, 2014Co-Authors: Andre Grosardt, Angelo Bassi, Mohammad Bahrami, Sandro DonadiAbstract:The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of a fundamentally semi-classical theory of gravity, in the weak-field non-relativistic limit. We show that, while in the former case the Schrodinger Equation stays linear, in the latter case one ends up with the so-called Schrodinger–Newton Equation, which involves a nonlinear, non-local gravitational contribution. We further discuss that the Schrodinger–Newton Equation does not describe the collapse of the wave-function, although it was initially proposed for exactly this purpose. Together with the standard collapse postulate, fundamentally semi-classical gravity gives rise to superluminal signalling. A consistent fundamentally semi-classical theory of gravity can therefore only be achieved together with a suitable prescription of the wave-function collapse. We further discuss, how collapse models avoid such superluminal signalling and compare the nonlinearities appearing in these models with those in the Schrodinger–Newton Equation.
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gravitationally induced inhibitions of dispersion according to a modified schrodinger Newton Equation for a homogeneous sphere potential
Classical and Quantum Gravity, 2013Co-Authors: Domenico Giulini, Andre GrosardtAbstract:We modify the time-dependent Schrodinger–Newton Equation by using a potential for a solid sphere suggested by Jaaskelainen (2012 Phys. Rev. A 86 052105) as well as a hollow-sphere potential. Compared to our recent paper (Giulini and Grosardt 2011 Class. Quantum Grav. 28 195026) where a single point particle, i.e. a Coulomb potential, was considered, this has been suggested to be a more realistic model for a molecule. Surprisingly, compared to our previous results, inhibitions of dispersion of a Gaussian wave packet occur at even smaller masses for the solid-sphere potential, given that the width of the wave packet is not exceeded by the radius of the sphere.
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the schrodinger Newton Equation as a non relativistic limit of self gravitating klein gordon and dirac fields
Classical and Quantum Gravity, 2012Co-Authors: Domenico Giulini, Andre GrosardtAbstract:In this paper, we show that the Schrodinger–Newton Equation for spherically symmetric gravitational fields can be derived in a WKB-like expansion in 1/c from the Einstein–Klein–Gordon and Einstein–Dirac systems.
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gravitationally induced inhibitions of dispersion according to the schrodinger Newton Equation
Classical and Quantum Gravity, 2011Co-Authors: Domenico Giulini, Andre GrosardtAbstract:We reconsider the time-dependent Schrodinger–Newton Equation as a model for the self-gravitational interaction of a quantum system. We numerically locate the onset of gravitationally induced inhibitions of dispersion of Gaussian wave packets and find them to occur at mass values more than six orders of magnitude higher than reported by Salzman and Carlip (Salzman and Carlip 2006, arXiv:gr-qc/0606120, Carlip 2008 Class. Quantum Grav. 25 107–44), namely at about 1010 u. This fits much better to simple analytical estimates but unfortunately also questions the experimental realizability of the proposed laboratory test of quantum gravity in the foreseeable future, not just because of large masses, but also because of the need to provide sufficiently long coherence times.
Alexandre Jollivet - One of the best experts on this subject based on the ideXlab platform.
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On inverse scattering at high energies for the multidimensional nonrelativistic Newton Equation in electromagnetic field
Journal of Inverse and Ill-posed Problems, 2020Co-Authors: Alexandre JollivetAbstract:We consider the multidimensional nonrelativistic Newton Equation in a static electromagnetic field ẍ = F (x, ẋ), F (x, ẋ) := −∇V (x) +B(x)ẋ, ẋ = dx dt , x ∈ C(R,R), (∗) where V ∈ C(R,R), B(x) is the n × n real antisymmetric matrix with elements Bi,k(x), Bi,k ∈ C(R,R) (and B satisfies the closure condition), and |∂1 x V (x)| + |∂2 x Bi,k(x)| ≤ β|j1|(1 + |x|)−(α+|j1|) for x ∈ R, 1 ≤ |j1| ≤ 2, 0 ≤ |j2| ≤ 1, |j2| = |j1| − 1, i, k = 1 . . . n and some α > 1. We give estimates and asymptotics for scattering solutions and scattering data for the Equation (∗) for the case of small angle scattering. We show that at high energies the velocity valued component of the scattering operator uniquely determines the X-ray transforms P∇V and PBi,k (on sufficiently rich sets of straight lines). Applying results on inversion of the X-ray transform P we obtain that for n ≥ 2 the velocity valued component of the scattering operator at high energies uniquely determines (∇V,B). We also consider the problem of recovering (∇V,B) from our high energies asymptotics found for the configuration valued component of the scattering operator. Results of the present work were obtained by developing the inverse scattering approach of [R. Novikov, 1999] for (∗) with B ≡ 0 and of [Jollivet, 2005] for the relativistic version of (∗). We emphasize that there is an interesting difference in asymptotics for scattering solutions and scattering data for (∗) on the one hand and for its relativistic version on the other.
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inverse scattering at high energies for the multidimensional Newton Equation in a long range potential
Asymptotic Analysis, 2014Co-Authors: Alexandre JollivetAbstract:We dene scattering data for the Newton Equation in a potential V 2 C 2 (R n ;R), n 2, that decays at innity like r for some 2 (0; 1]. We provide estimates on the scattering solutions and scattering data and we prove, in particular, that the scattering data at high energies uniquely determine the short range part of the potential up to the knowledge of the long range tail of the potential. The Born approximation at xed energy of the scattering data is also considered. We then change the denition of the scattering data to study inverse scattering in other asymptotic regimes. These results were obtained by developing the inverse scattering approach of [Novikov, 1999].
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On inverse scattering at high energies for the multidimensional relativistic Newton Equation in a long range electromagnetic eld
arXiv: Mathematical Physics, 2013Co-Authors: Alexandre JollivetAbstract:We dene scattering data for the relativistic Newton Equation in an electric eld r V 2 C 1 (R n ;R n ), n 2, and in a magnetic eld
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inverse scattering at high energies for the multidimensional Newton Equation in a long range potential
arXiv: Mathematical Physics, 2013Co-Authors: Alexandre JollivetAbstract:We define scattering data for the Newton Equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and we prove, in particular, that the scattering data at high energies uniquely determine the short range part of the potential up to the knowledge of the long range tail of the potential. The Born approximation at fixed energy of the scattering data is also considered. We then change the definition of the scattering data to study inverse scattering in other asymptotic regimes. These results were obtained by developing the inverse scattering approach of [Novikov, 1999].
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On inverse scattering at fixed energy for the multidimensional Newton Equation in a non-compactly supported field
Journal of Inverse and Ill-posed Problems, 2013Co-Authors: Alexandre JollivetAbstract:We consider the inverse scattering problem at fixed and sufficiently large energy for the nonrelativistic and relativistic Newton Equation in Rn, n ≥ 2, with a smooth and short-range electromagnetic field (V,B). Proceeding from different known results we obtain, in particular, that the scattering map at a fixed and sufficiently large energy uniquely determines (V,B) when B is assumed to be zero in a neighborhood of infinity and V is assumed to be spherically symmetric in a neighborhood of infinity.
Angelo Bassi - One of the best experts on this subject based on the ideXlab platform.
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optomechanical test of the schrodinger Newton Equation
Physical Review D, 2016Co-Authors: Andre Grosardt, James Bateman, Hendrik Ulbricht, Angelo BassiAbstract:The Schrodinger-Newton Equation has been proposed as an experimentally testable alternative to quantum gravity, accessible at low energies. It contains self-gravitational terms, which slightly modify the quantum dynamics. Here we show that it distorts the spectrum of a harmonic system. Based on this effect, we propose an optomechanical experiment with a trapped microdisc to test the Schrodinger-Newton Equation, and we show that it can be realized with existing technology.
-
the schrodinger Newton Equation and its foundations
New Journal of Physics, 2014Co-Authors: Andre Grosardt, Angelo Bassi, Mohammad Bahrami, Sandro DonadiAbstract:The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of a fundamentally semi-classical theory of gravity, in the weak-field non-relativistic limit. We show that, while in the former case the Schrodinger Equation stays linear, in the latter case one ends up with the so-called Schrodinger–Newton Equation, which involves a nonlinear, non-local gravitational contribution. We further discuss that the Schrodinger–Newton Equation does not describe the collapse of the wave-function, although it was initially proposed for exactly this purpose. Together with the standard collapse postulate, fundamentally semi-classical gravity gives rise to superluminal signalling. A consistent fundamentally semi-classical theory of gravity can therefore only be achieved together with a suitable prescription of the wave-function collapse. We further discuss, how collapse models avoid such superluminal signalling and compare the nonlinearities appearing in these models with those in the Schrodinger–Newton Equation.
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The Schrödinger–Newton Equation and its foundations
New Journal of Physics, 2014Co-Authors: Mohammad Bahrami, Sandro Donadi, André Großardt, Angelo BassiAbstract:The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of a fundamentally semi-classical theory of gravity, in the weak-field non-relativistic limit. We show that, while in the former case the Schrodinger Equation stays linear, in the latter case one ends up with the so-called Schrodinger–Newton Equation, which involves a nonlinear, non-local gravitational contribution. We further discuss that the Schrodinger–Newton Equation does not describe the collapse of the wave-function, although it was initially proposed for exactly this purpose. Together with the standard collapse postulate, fundamentally semi-classical gravity gives rise to superluminal signalling. A consistent fundamentally semi-classical theory of gravity can therefore only be achieved together with a suitable prescription of the wave-function collapse. We further discuss, how collapse models avoid such superluminal signalling and compare the nonlinearities appearing in these models with those in the Schrodinger–Newton Equation.
Marc Josien - One of the best experts on this subject based on the ideXlab platform.
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from the Newton Equation to the wave Equation the case of shock waves
Applied Mathematics Research Express, 2017Co-Authors: Xavier Blanc, Marc JosienAbstract:Nous considerons la limite macroscopique d'une chaine d'atomes interagissant de proche en proche par l'Equation de Newton. Depuis les travaux de Blanc, Le Bris et Lions, on sait que cette limite est la solution d'une Equation des ondes non-lineaire, a la condition que celle-ci demeure suffisamment reguliere. Si les ecarts inter-atomiques demeurent bornes et si le potentiel d'interaction est convexe a derivee convexe, nous demontrons que ce n'est plus le cas lorsque des chocs se produisent. Des simulations numeriques viennent etayer cette etude.
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from the Newton Equation to the wave Equation the case of shock waves
arXiv: Analysis of PDEs, 2016Co-Authors: Xavier Blanc, Marc JosienAbstract:We study the macroscopic limit of a chain of atoms governed by the Newton Equation. It is known from the work of Blanc, Le Bris, Lions, that this limit is the solution of a nonlinear wave Equation, as long as this solution remains smooth. We show, numerically and mathematically that, if the distances between particles remain bounded, it is not the case any more when there are shocks -at least for a convex nearest-neighbour interaction potential with convex derivative.
Domenico Giulini - One of the best experts on this subject based on the ideXlab platform.
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THE SCHR ¨ ODINGER-Newton Equation AS A MODEL FOR SELF-GRAVITATING SYSTEMS
The Thirteenth Marcel Grossmann Meeting, 2015Co-Authors: André Großardt, Domenico Giulini, Am FallturmAbstract:The time-dependent Schrodinger-Newton Equation can be considered as a model for the gravitational self-interaction of a quantum system. We motivate this model as the non- relativistic limit of a gravitationally interacting relativistic field. Namely, we show that the Schrodinger-Newton Equation can be derived in a WKB-like expansion in 1/c from the Einstein-Klein-Gordon and Einstein-Dirac system.
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gravitationally induced inhibitions of dispersion according to a modified schrodinger Newton Equation for a homogeneous sphere potential
Classical and Quantum Gravity, 2013Co-Authors: Domenico Giulini, Andre GrosardtAbstract:We modify the time-dependent Schrodinger–Newton Equation by using a potential for a solid sphere suggested by Jaaskelainen (2012 Phys. Rev. A 86 052105) as well as a hollow-sphere potential. Compared to our recent paper (Giulini and Grosardt 2011 Class. Quantum Grav. 28 195026) where a single point particle, i.e. a Coulomb potential, was considered, this has been suggested to be a more realistic model for a molecule. Surprisingly, compared to our previous results, inhibitions of dispersion of a Gaussian wave packet occur at even smaller masses for the solid-sphere potential, given that the width of the wave packet is not exceeded by the radius of the sphere.
-
the schrodinger Newton Equation as a non relativistic limit of self gravitating klein gordon and dirac fields
Classical and Quantum Gravity, 2012Co-Authors: Domenico Giulini, Andre GrosardtAbstract:In this paper, we show that the Schrodinger–Newton Equation for spherically symmetric gravitational fields can be derived in a WKB-like expansion in 1/c from the Einstein–Klein–Gordon and Einstein–Dirac systems.
-
gravitationally induced inhibitions of dispersion according to the schrodinger Newton Equation
Classical and Quantum Gravity, 2011Co-Authors: Domenico Giulini, Andre GrosardtAbstract:We reconsider the time-dependent Schrodinger–Newton Equation as a model for the self-gravitational interaction of a quantum system. We numerically locate the onset of gravitationally induced inhibitions of dispersion of Gaussian wave packets and find them to occur at mass values more than six orders of magnitude higher than reported by Salzman and Carlip (Salzman and Carlip 2006, arXiv:gr-qc/0606120, Carlip 2008 Class. Quantum Grav. 25 107–44), namely at about 1010 u. This fits much better to simple analytical estimates but unfortunately also questions the experimental realizability of the proposed laboratory test of quantum gravity in the foreseeable future, not just because of large masses, but also because of the need to provide sufficiently long coherence times.
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Gravitationally induced inhibitions of dispersion according to the Schrödinger–Newton Equation
Classical and Quantum Gravity, 2011Co-Authors: Domenico Giulini, André GroßardtAbstract:We reconsider the time-dependent Schrodinger–Newton Equation as a model for the self-gravitational interaction of a quantum system. We numerically locate the onset of gravitationally induced inhibitions of dispersion of Gaussian wave packets and find them to occur at mass values more than six orders of magnitude higher than reported by Salzman and Carlip (Salzman and Carlip 2006, arXiv:gr-qc/0606120, Carlip 2008 Class. Quantum Grav. 25 107–44), namely at about 1010 u. This fits much better to simple analytical estimates but unfortunately also questions the experimental realizability of the proposed laboratory test of quantum gravity in the foreseeable future, not just because of large masses, but also because of the need to provide sufficiently long coherence times.