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201.
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems.
We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems
which involve the Chern and Lagrange class. Our approach, which uses simple ideas from differential geometry and algebraic
topology, reveals the fundamental role of the integer affine structure on the base space of these bundles. We provide a geometric
proof of the classification of Lagrangian bundles with fixed integer affine structure by their Lagrange class.
相似文献
202.
L. Chierchia 《Regular and Chaotic Dynamics》2008,13(2):130-139
Following closely Kolmogorov’s original paper [1], we give a complete proof of his celebrated Theorem on perturbations of
integrable Hamiltonian systems by including few “straightforward” estimates.
相似文献
203.
图G称为弱泛圈图是指G包含了每个长为t(g(V)≤l≤c(G))的圈,其中g(G),c(v)分别是G的围长与周长.1997年Brandt提出以下猜想:边数大于[n2/4]-n 5的n阶非二部图为弱泛圈图.1999年Bollobas和Thomason证明了边数不小于[n2/4]-n 59的n阶非二部图为弱泛圈图.作者证明了如下结论:设G是n阶Hamilton非二部图,若G的边数不小于[n2/4]-n 12,则G为弱泛圈图. 相似文献
204.
For the periodic Anderson model in the strong correlation regime, we construct the effective Hamiltonian H
eff
up to terms of the fourth order in the parameter V/U, where V is the hybridization interaction intensity and U is the intra-atom
Coulomb repulsion strength. This Hamiltonian contains interactions inducing both magnetic ordering and Cooper instability
under conditions of a mixed valency of rare-earth ions. Based on numerical calculations, we obtain information about the dependences
of the effective interaction parameters on the distance between crystal lattice sites. We demonstrate that realizing exchange
interactions corresponds to a strongly frustrated system of localized spin moments and facilitates the suppression of the
antiferromagnetic order parameter with a possible transition to the state of a quantum spin liquid. It is essential that among
the terms in H
eff
inducing the transition to the superconductivity phase, there are terms resulting in the d-type symmetry of the superconductivity
order parameter; such a symmetry is realized in many heavy-fermion compounds.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 2, pp. 235–249, November, 2008. 相似文献
205.
206.
The effective charge state is an important particle parameter which is required for the calculation of many effects concerning the interaction between radiation and matter such as an estimate of the radial dose of swift heavy projectiles, stopping power and so on. A new method for the determination of effective charge states of heavy ions is based on the measurement of the number of high-energy delta-electrons which are ejected from a target by the penetrating ion. These electrons are detectable with a CCD-detector and their number can be correlated to the effective charge state of the projectile for known particle velocities. This method is even applicable to operation with single swift heavy ions within statistical bounds. 相似文献
207.
Alexander Balakin Heinz Dehnen Alexei Zayats 《General Relativity and Gravitation》2008,40(12):2493-2513
Non-minimal interactions in the pp-wave Einstein–Yang–Mills–Higgs (EYMH) model are shown to give rise to color cross-effects
analogous to the magneto-electricity in the Maxwell theory. In order to illustrate the significance of these color cross-effects,
we reconstruct the effective (associated, color, and color-acoustic) metrics for the pp-wave non-minimal seven-parameter EYMH
model with parallel gauge and scalar background fields. Then these metrics are used as hints for obtaining explicit exact
solutions of the non-minimally extended Yang–Mills and Higgs equations for the test fields propagating in the vacuum interacting
with curvature. The influence of the non-minimal coupling on the test particle motion is interpreted in terms of the so-called
trapped surfaces, introduced in the Analog Gravity theory. 相似文献
208.
In this paper, a class of second order discrete Hamiltonian systems without any periodicity assumptions are considered. Base
on the critical point theory, some sufficient conditions for the existence of homoclinic orbits are obtained. The results
obtained extend the results in [2006] by relaxing the assumptions on the sign of the potential.
相似文献
209.
John D. Ramshaw 《Journal of statistical physics》1989,56(1-2):149-158
Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable. 相似文献
210.
J. I. Abdullaev 《Theoretical and Mathematical Physics》2006,147(1):486-495
We consider the Hamiltonian of a system of two fermions on a one-dimensional integer lattice. We prove that the number of
bound states N(k) is a nondecreasing function of the total quasimomentum of the system k ∈ [0, π]. We describe the set of discontinuity points of N(k) and evaluate the jump N(k +0) − N(k) at the discontinuity points. We establish that the bound-state energy z
n
(k) increases as the total quasimomentum k ∈ [0, π] increases.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 47–57, April, 2006. 相似文献