The Experts below are selected from a list of 9864 Experts worldwide ranked by ideXlab platform
Shuyu Zhou - One of the best experts on this subject based on the ideXlab platform.
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sonic horizon formation for coupled one dimensional bose einstein condensate in an elongated Harmonic Potential
Modern Physics Letters B, 2018Co-Authors: Ying Wang, Shuyu ZhouAbstract:We theoretically studied the sonic horizon formation problem for coupled one-dimensional Bose–Einstein condensate trapped in an external elongated Harmonic Potential. Based on the coupled (1+1)-dim...
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sonic horizon formation for oscillating bose einstein condensates in isotropic Harmonic Potential
Scientific Reports, 2016Co-Authors: Ying Wang, Yu Zhou, Shuyu ZhouAbstract:: We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic Harmonic Potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study.
Rémi Carles - One of the best experts on this subject based on the ideXlab platform.
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semi classical schrodinger equations with Harmonic Potential and nonlinear perturbation
arXiv: Analysis of PDEs, 2007Co-Authors: Rémi CarlesAbstract:Solutions of semi-classical Schrodinger equation with isotropic Harmonic Potential focus periodically in time. We study the perturbation of this equation by a nonlinear term. If the scaling of this perturbation is critical, each focus crossing is described by a nonlinear scattering operator, which is therefore iterated as many times as the solution passes through a focus. The study of this nonlinear problem is made possible by the introduction of two operators well adapted to Schrodinger equations with Harmonic Potential, and by suitable Strichartz inequalities.
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Semi)classical limit of the Hartree equation with Harmonic Potential
Siam Journal on Applied Mathematics, 2004Co-Authors: Rémi Carles, Norbert J. Mauser, Hans Peter StimmingAbstract:Nonlinear Schrodinger equations (NLS) of the Hartree type occur in the modeling of quantum semiconductor devices. Their "semiclassical" limit of vanishing (scaled) Planck constant is both a mathematical challenge and practically relevant when coupling quantum models to classical models. With the aim of describing the semiclassical limit of the three-dimensional (3D) Schrodinger--Poisson system with an additional Harmonic Potential, we study some semiclassical limits of the Hartree equation with Harmonic Potential in space dimension $n \geq 2$. The Harmonic Potential is confining and causes focusing periodically in time. We prove asymptotics in several cases, showing different possible nonlinear phenomena according to the interplay of the size of the initial data and the power of the Hartree Potential. In the case of the 3D Schrodinger--Poisson system with Harmonic Potential, we can give only a formal computation since the need for modified scattering operators for this long-range scattering case goes beyo...
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nonlinear schrodinger equations with repulsive Harmonic Potential and applications
arXiv: Analysis of PDEs, 2002Co-Authors: Rémi CarlesAbstract:We study the Cauchy problem for Schrodinger equations with repulsive quadratic Potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining Harmonic Potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the nonlinearity is focusing, we prove that choosing the Harmonic Potential sufficiently strong prevents blow-up in finite time. Thanks to quadratic Potentials, we provide a method to anticipate, delay, or prevent wave collapse; this mechanism is explicit for critical nonlinearity.
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critical nonlinear schrodinger equations with and without Harmonic Potential
Mathematical Models and Methods in Applied Sciences, 2002Co-Authors: Rémi CarlesAbstract:We use a change of variables that turns the critical nonlinear Schrodinger equation into the critical nonlinear Schrodinger equation with isotropic Harmonic Potential, in any space dimension. This change of variables is isometric on L2, and bijective on some time intervals. Using the known results for the critical nonlinear Schrodinger equation, this provides information for the properties of Bose–Einstein condensate in space dimension one and two. We discuss in particular the wave collapse phenomenon.
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remarks on nonlinear schrodinger equations with Harmonic Potential
Annales Henri Poincaré, 2002Co-Authors: Rémi CarlesAbstract:Bose-Einstein condensation is usually modeled by nonlinear Schrodinger equations with Harmonic Potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no Potential. For the global problem, we establish an evolution law, which is the analogue of the pseudo-conformal conservation law for the nonlinear Schrodinger equation. With this evolution law, we give wave collapse criteria, as well as an upper bound for the blow up time. Taking the physical scales into account, we finally give a lower bound for the breaking time. This study relies on two explicit operators, suited to nonlinear Schrodinger equations with Harmonic Potential, already known in the linear setting.
Shihang Shen - One of the best experts on this subject based on the ideXlab platform.
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Harmonic Potential theorem extension to spin velocity and density dependent interactions
Physical Review Letters, 2019Co-Authors: S Zanoli, X Rocamaza, G Colo, Shihang ShenAbstract:: One of the few exact results for the description of the time evolution of an inhomogeneous, interacting many-particle system is given by the Harmonic Potential theorem (HPT). The relevance of this theorem is that it sets a tight constraint on time-dependent many-body approximations. In this contribution, we show that the original formulation of the HPT is valid also for the case of spin-, velocity-, and density-dependent interactions. This result is completely general and relevant, among the rest, for nuclear structure theory both in the case of ab initio and of more phenomenological approaches. As an example, we report on a numerical implementation by testing the small-amplitude limit of the time-dependent Hartree-Fock-also known as the random phase approximation-for the translational frequencies of a neutron system trapped in a Harmonic Potential.
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Harmonic Potential theorem extension to spin velocity and density dependent interactions
arXiv: Nuclear Theory, 2019Co-Authors: S Zanoli, X Rocamaza, G Colo, Shihang ShenAbstract:One of the few exact results for the description of the time-evolution of an inhomogeneous, interacting many-particle system is given by the Harmonic Potential Theorem (HPT). The relevance of this theorem is that it sets a tight constraint on time-dependent many-body approximations. In this contribution, we show that the original formulation of the HPT is valid also for the case of spin-, velocity- and density-dependent interactions. This result is completely general and relevant, among the rest, for nuclear structure theory both in the case of ab initio and of more phenomenological approaches. As an example, we report on a numerical implementation by testing the small-amplitude limit of the time-dependent Hartree-Fock -- also known as Random Phase Approximation (RPA) -- for the translational frequencies of a neutron system trapped in a Harmonic Potential.
Ying Wang - One of the best experts on this subject based on the ideXlab platform.
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sonic horizon formation for coupled one dimensional bose einstein condensate in an elongated Harmonic Potential
Modern Physics Letters B, 2018Co-Authors: Ying Wang, Shuyu ZhouAbstract:We theoretically studied the sonic horizon formation problem for coupled one-dimensional Bose–Einstein condensate trapped in an external elongated Harmonic Potential. Based on the coupled (1+1)-dim...
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sonic horizon formation for oscillating bose einstein condensates in isotropic Harmonic Potential
Scientific Reports, 2016Co-Authors: Ying Wang, Yu Zhou, Shuyu ZhouAbstract:: We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic Harmonic Potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study.
Binhua Feng - One of the best experts on this subject based on the ideXlab platform.
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sharp threshold of global existence and instability of standing wave for the schrodinger hartree equation with a Harmonic Potential
Nonlinear Analysis-real World Applications, 2016Co-Authors: Binhua FengAbstract:Abstract In this paper, we consider the Schrodinger–Hartree equation with a Harmonic Potential. By constructing some cross-invariant manifolds of the evolution flow and some variational problems, we obtain the sharp threshold for global existence and blow-up of the solutions. In addition, we discuss the stability and instability of the standing waves. In particular, we give two different characterizations on these problems in the L 2 critical case. Our results extend some earlier results.
