共查询到20条相似文献,搜索用时 31 毫秒
1.
We consider infinite dimensional Hamiltonian systems. We prove the existence of “Cantor manifolds” of elliptic tori–of any
finite higher dimension–accumulating on a given elliptic KAM torus. Then, close to an elliptic equilibrium, we show the existence
of Cantor manifolds of elliptic tori which are “branching” points of other Cantor manifolds of higher dimensional tori. We
also answer to a conjecture of Bourgain, proving the existence of invariant elliptic tori with tangential frequency along
a pre-assigned direction. The proofs are based on an improved KAM theorem. Its main advantages are an explicit characterization
of the Cantor set of parameters and weaker smallness conditions on the perturbation. We apply these results to the nonlinear
wave equation. 相似文献
2.
Paul Seidel 《Communications in Mathematical Physics》2010,297(2):515-528
We describe the behaviour of Fukaya categories under “suspension”, which means passing from the fibre of a Lefschetz fibration
to the double cover of the total space branched along that fibre. As an application, we consider the mirrors of canonical
bundles of toric Fano surfaces. 相似文献
3.
S. Paycha 《Communications in Mathematical Physics》1992,147(1):163-180
A generalisation of the finite dimensional presentation of the Faddeev-Popov perocedure is derived, in an infinite dimensional framework for gauge theories with finite dimensional moduli space using heat-kernel regularised determinants. It is shown that the infinite dimensional Faddeev-Popov determinant is-up to a finite dimensional determinant determined by a choice of a slice-canonically determined by the geometrical data defining the gauge theory, namely a fibre bundlePP/G with structure groupG and the invariance group of a metric structure given on the total spaceP. The case of (closed) bosonic string theory is discussed. 相似文献
4.
Yoshiaki Maeda Steven Rosenberg Philippe Tondeur 《Journal of Geometry and Physics》1997,23(3-4):319-349
The group of diffeomorphisms of a compact manifold acts isometrically on the space of Riemannian metrics with its L2 metric. Following Arnaudon and Paycha (1995) and Maeda, Rosenberg and Tondeur (1993), we define minimal orbits for this action by a zeta function regularization. We show that odd dimensional isotropy irreducible homogeneous spaces give rise to minimal orbits, the first known examples of minimal submanifolds of infinite dimension and codimension. We also find a flat 2-torus giving a stable minimal orbit. We prove that isolated orbits are minimal, as in finite dimensions. 相似文献
5.
We introduce a new coupled map lattice model in which the weak interaction takes place via rare “collisions”. By “collision”
we mean a strong (possibly discontinuous) change in the system. For such models we prove uniqueness of the SRB measure and
exponential space-time decay of correlations. 相似文献
6.
T. V. Dudnikova A. I. Komech E. A. Kopylova Suhov 《Communications in Mathematical Physics》2002,225(1):1-32
Consider the Klein–Gordon equation (KGE) in ℝ
n
, n≥ 2, with constant or variable coefficients. We study the distribution μ
t
of the random solution at time t∈ℝ. We assume that the initial probability measure μ0 has zero mean, a translation-invariant covariance, and a finite mean energy density. We also assume that μ0 satisfies a Rosenblatt- or Ibragimov–Linnik-type mixing condition. The main result is the convergence of μ
t
to a Gaussian probability measure as t→∞ which gives a Central Limit Theorem for the KGE. The proof for the case of constant coefficients is based on an analysis
of long time asymptotics of the solution in the Fourier representation and Bernstein's “room-corridor” argument. The case
of variable coefficients is treated by using an “averaged” version ofthe scattering theory for infinite energy solutions,
based on Vainberg's results on local energy decay.
Received: 4 January 2001 / Accepted: 2 July 2001 相似文献
7.
Shahn Majid 《Communications in Mathematical Physics》2002,225(1):131-170
We construct noncommutative “Riemannian manifold” structures on dual quasitriangular Hopf algebras such as ℂ
q
[SU
2] with its standard bicovariant differential calculus, using the quantum frame bundle approach introduced previously. The
metric is provided by the braided-Killing form on the braided-Lie algebra on the tangent space and the n-bein by the Maurer–Cartan form. We also apply the theory to finite sets and in particular to finite group function algebras
ℂ[G] with differential calculi and Killing forms determined by a conjugacy class. The case of the permutation group ℂ[S
3] is worked out in full detail and a unique torsion free and cotorsion free or “Levi–Civita” connection is obtained with noncommutative
Ricci curvature essentially proportional to the metric (an Einstein space). We also construct Dirac operators in the metric background, including on finite groups such as S
3. In the process we clarify the construction of connections from gauge fields with nonuniversal calculi on quantum principal
bundles of tensor product form.
Received: 22 June 2000 / Accepted: 26 August 2001 相似文献
8.
In this paper, one-dimensional (1D) nonlinear wave equations
with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function vanishing together with its derivative at u≡0. It is proved that for “most” potentials V(x), the above equation admits small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant
tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theorem which
allows for multiple normal frequencies.
Received: 2 August 1999 / Accepted: 7 January 2000 相似文献
9.
M. Combescot M.-A. Dupertuis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(3):459-464
We show that the carrier “antibinding” observed recently in
semiconductor quantum dots, i.e., the fact that the ground state
energy of two electron-hole pairs goes above twice the ground-state
energy of one pair, can entirely be assigned to a charge separation
effect, whatever its origin. In the absence of external electric field, this charge
separation comes from different “spreading-out” of the electron and
hole wavefunctions linked to the finite height of the barriers. When
the dot size shrinks, the two-pair energy always stays below when the
barriers are infinite. On the opposite, because barriers are less
efficient for small dots, the energy of two-pairs in a dot with
finite barriers, ends by behaving like the one in bulk, i.e., by
going above twice the one-pair energy when the pairs get too close.
For a full understanding of this “antibinding” effect, we have also
reconsidered the case of one pair plus one carrier. We find that,
while the carriers just have to spread out of the dot differently for
the “antibinding” of two-pairs to appear, this “antibinding” for
one pair plus one carrier only appears if this carrier is the one
which spreads out the less. In addition a remarkable sum rule exists
between the “binding energies” of two pairs and of one pair plus one carrier. 相似文献
10.
A. I. Belousova Yu. E. Lozovikb 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,8(2):251-264
A two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. This system can
be used as a model for rare electrons in semiconductor structures near a metal electrode, indirect excitons in coupled quantum
dots etc. For clusters of N ≤ 80 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are found.
Monte-Carlo and molecular dynamic methods are used to study the order-disorder transition (the “melting” of clusters). In
mesoscopic clusters (N < 37) there is a hierarchy of transitions: at lower temperatures an intershell orientational disordering of pairs of shells
takes place; at higher temperatures the intershell diffusion sets in and the shell structure disappears. In “macroscopic”
clusters (N > 37) an orientational “melting” of only the outer shell is possible. The most stable clusters (having both maximal lowest
nonzero eigenfrequencies and maximal temperatures of total melting) are those of completed crystal shells which are concentric
groups of nodes of 2D hexagonal lattice with a number of nodes placed in the center of them. The picture of disordering in
clusters is compared with that in an infinite 2D dipole system. The study of the radial diffusion constant, the structure
factor, the local minima distribution and other quantities shows that the melting temperature is a nonmonotonic function of
the number of particles in the system. The dynamical equilibrium between “solid-like” and “orientationally disordered” forms
of clusters is considered. 相似文献
11.
In this paper we study the asymptotic behavior (in the sense of meromorphic functions) of the zeta function of a Laplace-type
operator on a closed manifold when the underlying manifold is stretched in the direction normal to a dividing hypersurface,
separating the manifold into two manifolds with infinite cylindrical ends. We also study the related problem on a manifold
with boundary as the manifold is stretched in the direction normal to its boundary, forming a manifold with an infinite cylindrical
end. Such singular deformations fall under the category of “analytic surgery”, developed originally by Hassell (Comm Anal
Geom 6:255–289, 1998), Hassell et al. (Comm Anal Geom 3:115–222, 1995) and Mazzeo and Melrose (Geom Funct Anal 5:14–75, 1995) in the context of eta invariants and determinants. 相似文献
12.
G. A. Kozlov 《Physics of Particles and Nuclei》2010,41(6):954-956
A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle (“ungluon”). The model
is formulated in terms of Lagrangian which features the source field S(x) which becomes a local pseudo-Goldstone field of conformal symmetry — the pseudodilaton mode and from which the gauge non-primary
unparticle field is derived by B
μ(x) ∼ ∂μ
S(x). Because the conformal sector is strongly coupled, the mode S(x) may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters
in the “ungluon” exchange pattern — the “ungluon” propagator. 相似文献
13.
Summary In this paper we examine the dynamic of solitons in the presence of external forces expressed by an-degree polynomial perturbative term or by a combination of polynomial and differential terms in the dependent variable. Under
the action of these forces the soliton profile will no longer be a simple translation: asymptotic behaviour of the wave amplitude
to threshold values (stationary equilibrium states) are now possible and “explosions” may occur at some finite “critical time”
at which the soliton amplitude becomes infinite. 相似文献
14.
In this paper we introduce a kind of “noncommutative neighbourhood” of a semiclassical parameter corresponding to the Planck
constant. This construction is defined as a certain filtered and graded algebra with an infinite number of generators indexed
by planar binary leaf-labelled trees. The associated graded algebra (the classical shadow) is interpreted as a “distortion”
of the algebra of classical observables of a physical system. It is proven that there exists a q-analogue of the Weyl quantization, where q is a matrix of formal variables, which induces a nontrivial noncommutative analogue of a Poisson bracket on the classical
shadow. 相似文献
15.
In a series of μ+ experiments either at UT-MSL BOOM or at TRIUMF, we have found that the positive muon can create an interesting and systematic
“after-effect” in the well-known organic semiconductor polymer polyacetylene, (CH)x or (CD)x: the localized unpaired electron at nearby carbon sites is produced in cis-polyacetylene, to form a muon radical; in trans-polyacetylene,
the electron becomes mobile and takes “soliton”-like one dimensional rapid motion along the chain. Recently experiments were
extended towards the following three directions: a) diffusion properties of the muon produced solition in trans-polyacetylene;
b) the details of radical structure in cis-polyacetylene, and c) μSR experiments on I-doped polyacetylene. These works are
reviewed along with the possible future perspectives. 相似文献
16.
17.
A. L. Carey M. G. Eastwood K. C. Hannabuss 《Communications in Mathematical Physics》1991,139(2):217-236
We introduce a class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a gauge group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. 相似文献
18.
19.
S. G. Basiladze 《Physics of Particles and Nuclei》2009,40(6):773-800
A classical signal which agrees with the ideas of mathematical analysis on infinitesimal quantities possesses an infinite
information capacity, which contradicts the concept of information that is finite by definition. A real signal should have
some “threshold” for determining a finite step between its distinguishable states and the “limit” for the possible number
of states.
This paper considers the influence of the level of required energy, performance, and noise of the receiver on the capability
of distinguishing the set of states in the signal. It is shown that the generalized threshold is the constraint on the spectral
density of the signal energy and the limit is the constraint on the energy density with respect to time or spatial coordinate. 相似文献
20.
Alan L. Carey Diarmuid Crowley Michael K. Murray 《Communications in Mathematical Physics》1998,193(1):171-196
A systematic consideration of the problem of the reduction and “lifting” of the structure group of a principal bundle is made
and a variety of techniques in each case are explored and related to one another. We apply these to the study of the Dixmier-Douady
class in various contexts including string structures, bundles and other examples motivated by considerations from quantum field theory.
Received: 26 February 1997 / Accepted: 5 August 1997 相似文献