Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Grillakis, Manoussos"'
We provide the analysis of a physically inspired model for a trapped dilute Bose gas with repulsive pairwise atomic interactions at zero temperature. Our goal is to describe aspects of the excited many-body quantum states by accounting for the scatte
Externí odkaz:
http://arxiv.org/abs/2106.02152
We prove that certain Sobolev-type norms, slightly stronger than those given by energy conservation, stay bounded uniformly in time and $N$. This allows one to extend the local existence results of the second and third author globally in time. The pr
Externí odkaz:
http://arxiv.org/abs/2008.01753
We establish both a local and a global well-posedness theories for the nonlinear Hartree-Fock equations and its reduced analog in the setting of the modulation spaces on $\mathbb R^d$. In addition, we prove similar results when a harmonic potential i
Externí odkaz:
http://arxiv.org/abs/1908.05862
We prove local in time, uniform in $N$, estimates for the solutions $\phi$, $\Lambda$ and $\Gamma$ of a coupled system of Hartree-Fock-Bogoliubov type with interaction potential $v_N(x-y) =N^{3 \beta} v(N^{\beta}(x-y))$, with $\beta <1$ and $v$ a Sch
Externí odkaz:
http://arxiv.org/abs/1808.06448
This article addresses the large data global regularity for the equivariant case of the $2+1$-dimensional Faddeev model and shows that it holds true for initial data in $H^s\times H^{s-1}(\mathbb{R}^2)$ with $s>3$.
Comment: 35 pages. arXiv admin
Comment: 35 pages. arXiv admin
Externí odkaz:
http://arxiv.org/abs/1709.00331
This article is concerned with the large data global regularity for the equivariant case of the classical Skyrme model and proves that this is valid for initial data in $H^s\times H^{s-1}(\mathbb{R}^3)$ with $s>7/2$.
Comment: 37 pages
Comment: 37 pages
Externí odkaz:
http://arxiv.org/abs/1707.02917
Publikováno v:
Communications in Mathematical Physics, 294, 273-301 (2010)
Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle
Externí odkaz:
http://arxiv.org/abs/0904.0158
We prove new interaction Morawetz type (correlation) estimates in one and two dimensions. In dimension two the estimate corresponds to the nonlinear diagonal analogue of Bourgain's bilinear refinement of Strichartz. For the 2d case we provide a proof
Externí odkaz:
http://arxiv.org/abs/0807.0871
We study the evolution of a many-particle system whose wave function obeys the N-body Schroedinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the absence of an external potential. We derive aprior
Externí odkaz:
http://arxiv.org/abs/0803.2322
Models of quantum computing rely on transformations of the states of a quantum memory. We study mathematical aspects of a model proposed by Wu in which the memory state is changed via the scattering of incoming particles. This operation causes the me
Externí odkaz:
http://arxiv.org/abs/0709.2654