共查询到20条相似文献,搜索用时 0 毫秒
1.
In our previous work (Grillakis et al. in Commun Math Phys 294:273–301, 2010; Adv Math 228:1788–1815, 2011) we introduced a correction to the mean field approximation of interacting Bosons. This correction describes the evolution of pairs of particles that leave the condensate and subsequently evolve on a background formed by the condensate. In Grillakis et al. (Adv Math 228:1788–1815, 2011) we carried out the analysis assuming that the interactions are independent of the number of particles N. Here we consider the case of stronger interactions. We offer a new transparent derivation for the evolution of pair excitations. Indeed, we obtain a pair of linear equations describing their evolution. Furthermore, we obtain a priori estimates independent of the number of particles and use these to compare the exact with the approximate dynamics. 相似文献
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Robert Seiringer 《Communications in Mathematical Physics》2011,306(2):565-578
We investigate the low energy excitation spectrum of a Bose gas with weak, long range repulsive interactions. In particular,
we prove that the Bogoliubov spectrum of elementary excitations with linear dispersion relation for small momentum becomes
exact in the mean-field limit. 相似文献
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We investigate the low-energy excitation spectrum of a Bose gas confined in a trap, with weak long-range repulsive interactions. In particular, we prove that the spectrum can be described in terms of the eigenvalues of an effective one-particle operator, as predicted by the Bogoliubov approximation. 相似文献
4.
这项工作利用考虑π介子与胶子效应的夸克平均场模型研究原子核结构的基本性质。在夸克平均场中,核子由三个束缚在谐振子势场中的组分夸克构成。描述强相互作用的量子色动力学必须满足手征对称性,此外夸克之间也需要通过交换胶子相互作用。因此,在夸克平均场模型中,对利用夸克势获得的核子质量考虑π介子修正与胶子修正。通过少数稳定有限核的结合能与半径实验值确定模型中的未知参数,获得了一组夸克平均场相互作用参数,QMF-NK。利用该组参数计算40Ca和208Pb的电荷密度分布,发现与实验值符合很好。随后获得了与经验值一致的对称核物质的饱和性质。包含π介子修正和胶子修正的夸克平均场模型能够更好地描述有限核和核物质的性质。The basic properties of nuclear structure are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account. In QMF, the nucleon is made up of three constituent quarks confined by a harmonic oscillator potential. The quantum chromodynamics describing the strong interaction must satisfy the chiral symmetry and quarks interact with each other through exchange of gluons. Therefore pion correction and gluon correction are included in the nucleon mass obtained by using quark confinement potential in quark mean field model. We determine the unknown parameters in the model by fitting the experimental data of the binding energies and radii of several stable finite nuclei and obtain a set of parameters of quark mean field interaction, named QMF-NK. The charge density distributions of 40Ca and 208Pb are calculated, which are in good agreement with the experimental data. Later the saturation properties of symmetric nuclear matter which are consistent with the empirical data are obtained. With the pion and gluon corrections, the QMF model could treat finite nuclei and nuclear matter better. 相似文献
5.
In the framework of one generation technicolor model we calculated the virtual effects from heavy PG bosons to the Zbb vertex. Within parameter space the largest reduction from thk charged PGB's and top quark to the partial width Γb was 71 MeV while the maximum correction to the branching ratio Rb was about 14%. From the comparison of theoretical. predictions with the corresponding data we are able to put an "primary" upper bound on the mass of P8±: Mp2 < 280 GeV for given Mt = 200 GeV. 相似文献
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Families of N interacting curves are considered, with long range, mean field type, interaction. They generalize models based on classical interacting point particles to models based on curves. In this new set-up, a mean field result is proven, as \(N\rightarrow \infty \). The limit PDE is vector valued and, in the limit, each curve interacts with a mean field solution of the PDE. This target is reached by a careful formulation of curves and weak solutions of the PDE which makes use of 1-currents and their topologies. The main results are based on the analysis of a nonlinear Lagrangian-type flow equation. Most of the results are deterministic; as a by-product, when the initial conditions are given by families of independent random curves, we prove a propagation of chaos result. The results are local in time for general interaction kernel, global in time under some additional restriction. Our main motivation is the approximation of 3D-inviscid flow dynamics by the interacting dynamics of a large number of vortex filaments, as observed in certain turbulent fluids; in this respect, the present paper is restricted to smoothed interaction kernels, instead of the true Biot–Savart kernel. 相似文献
9.
Marcello Porta Simone Rademacher Chiara Saffirio Benjamin Schlein 《Journal of statistical physics》2017,166(6):1345-1364
We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles. For initial data describing approximate Slater determinants, we prove convergence of the many-body evolution towards Hartree–Fock dynamics. Our result holds under a condition on the solution of the Hartree–Fock equation, that we can only show in a very special situation (translation invariant data, whose Hartree–Fock evolution is trivial), but that we expect to hold more generally. 相似文献
10.
We consider the persistence probability that a site, initially unoccupied, remains unoccupied for a long time t in reaction-diffusion systems. The models considered are bosonic, i.e., multiple occupancy of the sites is allowed and can be exactly diagonalized. The persistence shows a wide variety of time dependences depending on the model, the dimensionality, and even the initial conditions 相似文献
11.
Using the Hamilton–Jacobi equation approach to study genomes of length L, we obtain 1/L corrections for the steady state population distributions and mean fitness functions for horizontal gene transfer model,
as well as for the diploid evolution model with general fitness landscapes. Our numerical solutions confirm the obtained analytic
equations. Our method could be applied to the general case of nonlinear Markov models. 相似文献
12.
Daniel Gandolfo Roger Rodriguez Henry C. Tuckwell 《Journal of statistical physics》2017,166(5):1310-1333
We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean–Vlasov–Fokker–Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh–Nagumo model neurons, which are often used to approximate Hodgkin–Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension. 相似文献
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Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity. The models include the bosonized chiral Schwinger model, the generalized chiral Schwinger model (GCSM) and its gauge invariant formulation. We establish the Lagrangian theories of the models, and then derive the Hamilton's equations in accordance with the Dirac's method and solve the equations of motion, and further analyze the self-duality of the Lagrangian theories in terms of the parent action approach. 相似文献
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Sergey Bravyi David DiVincenzo Daniel Loss 《Communications in Mathematical Physics》2008,284(2):481-507
We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which
interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial in n and δ−1, where n is the number of qubits, and δ is the required precision. Specifically, we consider Hamiltonians of the form , where H
0 describes non-interacting qubits, V is a perturbation that involves arbitrary two-qubit interactions on a graph of bounded degree, and is a small parameter. The algorithm works if is below a certain threshold value that depends only upon the spectral gap of H
0, the maximal degree of the graph, and the maximal norm of the two-qubit interactions. The main technical ingredient of the
algorithm is a generalized Kirkwood-Thomas ansatz for the ground state. The parameters of the ansatz are computed using perturbative
expansions in powers of . Our algorithm is closely related to the coupled cluster method used in quantum chemistry. 相似文献
16.
L. C. Garcia de Andrade 《General Relativity and Gravitation》2001,33(4):679-682
Gauge field corrections to domain walls are obtained by making use of perturbation method on the usual flat domain wall. The gauge vector field introduces a damping term and an external force on the motion equation for the perturbed domain wall. A thin domain wall approximation solution is found. The vector gauge field also introduces a gauge mass term correction into the perturbed Lagrangean. 相似文献
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We develop a theory for the nonequilibrium coherent transport through a mesoscopic region, based on thenonequilibrium Green function technique. The theory requires the weak coupling bet. ween the central mesoscopic regionand the multiple electrodes, but allows arbitrary hopping and interaction in the central region. An equation determiningthe nonequilibrium distribution in the central interacting region is derived and plays an important role in the theory.The theory is applied to two special cases for demonstrations, revealing the novel effects associated with the combinationof phase coherence, Coulomb interaction, and nonequilibrium distribution. 相似文献
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ZHENGTai-Yu HUIPing LIMing 《理论物理通讯》2004,42(3):394-396
We discuss the two-loop radiative correction to the Casimir force of Maxwell Chern Simons Abelian gauge field between two parallel ideal conducting wires in terms of Feynman path integral method. 相似文献
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ZHENG Tai-Yu HUI Ping LI Ming 《理论物理通讯》2004,42(9)
We discuss the two-loop radiative correction to the Casimir force ofMaxwell-Chern-Simons Abelian gaugefield between two parallel ideal conducting wires in terms of Feynman path integral method. 相似文献
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