共查询到20条相似文献,搜索用时 0 毫秒
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Zuhan Liu 《NoDEA : Nonlinear Differential Equations and Applications》2012,19(1):49-65
In the understanding of the spatial behavior of interacting components of multicomponent Bose–Einstein condensates (BECs),
a central problem is to establish whether coexistence of all the components occurs, or the interspecies interaction leads
to extinction, that is, configurations where one or more densities are null. In this paper, for the rotating k-mixture BEC, we prove that the interspecies interaction leads to extinction in the Thomas–Fermi approximation. 相似文献
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Claudio Angione Annalisa Occhipinti Giovanni Stracquadanio Giuseppe Nicosia 《European Journal of Operational Research》2013
This paper is concerned with the complex behavior arising in satisfiability problems. We present a new statistical physics-based characterization of the satisfiability problem. Specifically, we design an algorithm that is able to produce graphs starting from a k-SAT instance, in order to analyze them and show whether a Bose–Einstein condensation occurs. We observe that, analogously to complex networks, the networks of k-SAT instances follow Bose statistics and can undergo Bose–Einstein condensation. In particular, k-SAT instances move from a fit-get-rich network to a winner-takes-all network as the ratio of clauses to variables decreases, and the phase transition of k-SAT approximates the critical temperature for the Bose–Einstein condensation. Finally, we employ the fitness-based classification to enhance SAT solvers (e.g., ChainSAT) and obtain the consistently highest performing SAT solver for CNF formulas, and therefore a new class of efficient hardware and software verification tools. 相似文献
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We consider a minimization problem for the variational functional associated with a Gross–Pitaevskii equation arising in the study of an attractive Bose–Einstein condensate. Under an ellipse-shaped trapping potential, that is, the bottom of the trapping potential is an ellipse, we prove that any minimizer of the minimization problem blows up at one of the endpoints of the major axis of the ellipse if the parameter associated to the attractive interaction strength approaches a critical value. 相似文献
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We solve a model which describes internal degrees of freedom of the spinor Bose–Einstein condensate with dipole-dipole interaction
up to its eigenstates and eigenvalues. A representation of the Hamiltonian of the model in terms of generators of the su(1,
1) algebra allows one to develop the quantum inverse method for its study. The method of solution provides a general framework
within which many related problems can be solved similarly. Bibliography: 15 titles. 相似文献
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We investigate the physical model for a two dimensional rotating Bose–Einstein condensate. We minimize a Gross–Pitaevskii functional defined in under the unit mass constraint. We estimate the critical rotational speeds for having d vortices in the condensate and we determine the location of the vortices. This relies on an asymptotic expansion of the energy. To cite this article: R. Ignat, V. Millot, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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In this paper, we prove existence, symmetry and uniqueness of standing waves for a coupled Gross–Pitaevskii equations modeling component Bose–Einstein condensates BEC with an internal atomic Josephson junction. We will then address the orbital stability of these standing waves and characterize their orbit. 相似文献
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For a system of identical Bose particles sitting at integer energy levels with the probabilities of microstates given by a multiplicative measure with ≥ 2 degrees of freedom, we estimate the probability of the sequence of occupation numbers to be close to the Bose–Einstein distribution as the total energy tends to infinity. We show that a convergence result earlier proved by A.M. Vershik [Functional Anal. Appl. 30 (2), 95–105 (1996)] is a corollary of our theorems. 相似文献
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Coupled dark–bright vector solitons are considered in a two-component Bose–Einstein condensate, and their dynamics are investigated by the variational approach based on the renormalized integrals of motion. The stationary states and their atom population distribution are obtained, and it is found that the dark soliton has obvious robust features. The dynamic mechanism is demonstrated by performing a coordinate of a classical particle moving in an effective potential field, and the switching and self-trapping dynamics of the coupled dark–bright vector solitons are discussed by the evolution of the atom population transferring ratio. 相似文献
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Considering the time-dependent external potential and thermal cloud effects, this paper investigates via symbolic computation the dark-soliton dynamics in a two-species Bose–Einstein condensate (BEC), which can be described by the quasi-one-dimensional coupled Gross–Pitaevskii equations. Under the balance between the harmonic potential and thermal cloud effects, dark multi-soliton solutions are derived for the two-species BEC through the Hirota bilinear method. Regions of the s-wave scattering lengths are ascertained for the existence of the dark solitons in two species. Influence of the scattering lengths and external potential on the background density, soliton width and velocity is examined. Graphical analysis demonstrates that the harmonic and linear potentials can change the propagation paths, collision positions and collision time of the dark solitons, and that the thermal cloud effects can affect the number of atoms in the two-species BEC. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(8):2715-2723
In this paper, we present a perturbation method that utilizes Hamiltonian perturbation theory and averaging to analyze spatio-temporal structures in Gross–Pitaevskii equations and thereby investigate the dynamics of modulated amplitude waves (MAWs) in quasi-one-dimensional Bose–Einstein condensates with mean-field interactions. A good approximation for MAWs is obtained. We also explore dynamics of BECs with the nonresonant external potentials and scatter lengths varying periodically in detail using Hamiltonian perturbation theory and numerical simulations. 相似文献
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Doklady Mathematics - This paper deals with the problem of motion of a system of two point vortices in a Bose–Einstein condensate enclosed in a cylindrical trap. Bifurcation diagram is... 相似文献
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Jimena Royo-Letelier 《Calculus of Variations and Partial Differential Equations》2014,49(1-2):103-124
We study ground states of two-component condensates in a harmonic trap. We prove that in the strongly coupled and weakly interacting regime, the two components segregate while a symmetry breaking occurs. More precisely, we show that when the intercomponent coupling strength is very large and both intracomponent coupling strengths are small, each component is close to the positive or the negative part of a second eigenfunction of the harmonic oscillator in ${\mathbb{R}^2}$ . As a result, the supports of the components approach complementary half-spaces, and they are not radially symmetric. 相似文献