共查询到20条相似文献,搜索用时 15 毫秒
1.
Alexander Blokh Michał Misiurewicz Nándor Simányi 《Communications in Mathematical Physics》2006,266(1):239-265
We investigate the rotation sets of billiards on the m-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, measures the change of the position of a point in the universal covering of the torus (that is, in the Euclidean space), in the second case it measures the rotation around the obstacle. A substantial part of the rotation set has usual strong properties of rotation sets.The first author was partially supported by NSF grant DMS 0456748.The second author was partially supported by NSF grant DMS 0456526.The third author was partially supported by NSF grant DMS 0457168. 相似文献
2.
J. Kiukas 《Optics and Spectroscopy》2007,103(3):429-433
We consider questions related to the following quantization scheme: a classical variable f: Ω → ℝ on a phase space Ω is associated with a unique semispectral measure E
f
, such that the kth moment operator of E
f
is required to coincide with the operator integral L(f
k
, E) of f
k
with respect to a certain fixed phase space semispectral measure E. Mainly, we take the phase space Ω to be a locally compact unimodular group. In the concrete case where Ω = ℝ2 and E is a translation covariant semispectral measure, we determine explicitly the relevant operators L(f
k
, E) for certain variables f. In addition, we consider the question under what conditions a positive operator measure is projection valued.
The text was submitted by the author in English. 相似文献
3.
Xianwen Zhang 《Journal of statistical physics》2010,141(3):566-588
Global-in-time existence of weak solutions to the Cauchy problem of the three dimensional Vlasov-Poisson-BGK system is shown
for initial data belonging to the space L
p
(ℝ3×ℝ3) with p>9 and having finite second order velocity moments. This result solves partially the well-posed problem for the Vlasov-Poisson-BGK
system proposed by B. Perthame: “Higher moments for kinetic equations: the Vlasov-Poisson and Fokker-Planck cases,” Math.
Meth. Appl. Sci. 13:441–452, 1990. 相似文献
4.
The distribution μ of a Gibbs cluster point process in χ = ℝd (with n-point clusters) is studied via the projection of an auxiliary Gibbs measure defined on the space of configurations in χ × χ
n. We show that μ is quasi-invariant with respect to the group Diff0(χ) of compactly supported diffeomorphisms of χ and prove an integration-by-parts formula for μ. The corresponding equilibrium stochastic dynamics is then constructed by
using the method of Dirichlet forms.
Dedicated to the memory of Vladimir Geyler
Research supported in part by DFG Grant 436 RUS 113/722. 相似文献
5.
Jaume Llibre Marco Antonio Teixeira Joan Torregrosa 《Mathematical Physics, Analysis and Geometry》2007,10(3):237-249
The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum
periodic orbits of a k-dimensional isochronous center contained in ℝ
n
with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential
system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from
the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree.
As far as we know this is one of the first examples that this study can be made for a polynomial differential system having
a center and a non-rational first integral.
The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550.
The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the
joint project CAPES–MECD grant HBP2003-0017. 相似文献
6.
We consider invertible discrete-time dynamical systems having a hyperbolic product structure in some region of the phase space
with infinitely many branches and variable return time. We show that the decay of correlations of the SRB measure associated
to that hyperbolic structure is related to the tail of the recurrence times. We also give sufficient conditions for the validity
of the Central Limit Theorem. This extends previous results by Young in (Ann. Math. 147: 585–650, [1998]; Israel J. Math. 110: 153–188, [1999]).
Work carried out at the Federal University of Bahia, University of Porto and IMPA. J.F.A. was partially supported by FCT through
CMUP and POCI/MAT/61237/2004. V.P. was partially supported by PADCT/CNPq and POCI/MAT/61237/2004. 相似文献
7.
We consider an equilibrium stochastic dynamics of spatial spin systems in ℝ
d
involving both a birth-and-death dynamics and a spin flip dynamics as well. Using a general approach to the spectral analysis
of corresponding Markov generator, we estimate the spectral gap and construct one-particle invariant subspaces for the generator.
Dedicated to our admired teacher and friend Robert Minlos on occasion of his 75th birthday.
The financial support of SFB-701, Bielefeld University, is gratefully acknowledged. The work is partially supported by RFBR
grant 05-01-00449, Scientific School grant 934.2003.1, CRDF grant RUM1-2693-MO-05. 相似文献
8.
Let ϰ
i
(H
l
(V)) denote the negative eigenvalues of the operatorH
l
u≔(−Δ)
l
u−V≧0,x ℝ
d
onL
2(ℝ
d
). We prove the two-sided estimate
. We discuss bounds on the Riesz means
.
The first author was supported by the EPSRC grant GR/J 32084. The second author was supported byDeutsche Forschungsgemeinschaft grant We 1964-1. 相似文献
9.
Anton Kapustin Alexander Kuznetsov Dmitri Orlov 《Communications in Mathematical Physics》2001,221(2):385-432
Recently N. Nekrasov and A. Schwarz proposed a modification of the ADHM construction of instantons which produces instantons
on a noncommutative deformation of ℝ4. In this paper we study the relation between their construction and algebraic bundles on noncommutative projective spaces.
We exhibit one-to-one correspondences between three classes of objects: framed bundles on a noncommutative ℙ2, certain complexes of sheaves on a noncommutative ℙ3, and the modified ADHM data. The modified ADHM construction itself is interpreted in terms of a noncommutative version of
the twistor transform. We also prove that the moduli space of framed bundles on the noncommutative ℙ2 has a natural hyperk?hler metric and is isomorphic as a hyperk?hler manifold to the moduli space of framed torsion free sheaves
on the commutative ℙ2. The natural complex structures on the two moduli spaces do not
coincide but are related by an SO(3) rotation. Finally, we propose a construction of instantons on a more general noncommutative
ℝ4 than the one considered by Nekrasov and Schwarz (a q-deformed ℝ4).
Received: 3 May 2000 / Accepted: 3 April 2001 相似文献
10.
I. Schmelzer 《Foundations of Physics》2009,39(1):73-107
We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice
space (Aff(3)⊗ℂ)(ℤ3). This space allows a simple physical interpretation as a phase space of a lattice of cells.
We find the SM SU(3)
c
×SU(2)
L
×U(1)
Y
action on (Aff(3)⊗ℂ⊗Λ)(ℝ3) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson
gauge fields and correction terms for lattice deformations.
The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ2-valued (spin) field theory.
A metric theory of gravity compatible with this model is presented too. 相似文献
11.
Given a globally hyperbolic spacetime M, we show the existence of a smooth spacelike Cauchy hypersurface S and, thus, a global diffeomorphism between M and ×S.The second-named author has been partially supported by a MCyT-FEDER Grant BFM2001-2871-C04-01. 相似文献
12.
13.
Remarks on potential spaces and Besov spaces in a Lipschitz domain and on Whitney arrays on its boundary 总被引:1,自引:0,他引:1
M. S. Agranovich 《Russian Journal of Mathematical Physics》2008,15(2):146-155
In this note, we propose to remove some small gaps in the theory of potential spaces H
p
s
(Ω) and Besov spaces B
p
s
(Ω), 1 < p < ∞, s ∈ ℝ, for a bounded Lipschitz domain Ω ⊂ ℝ
n
, n ⩾ 2. Namely, we discuss 1) the unified definitions of these spaces with s of any sign, the unified duality theorems and interpolation relations, 2) the possibility of constructing a function in these
spaces with given array of traces of its derivatives on the boundary.
To the memory of Leonid Romanovich Volevich
The work was partially supported by the RFBR grant no. 07-01-00287. 相似文献
14.
We discuss the Lie Poisson group structures associated to splittings of the loop group LGL(N,ℂ), due to Sklyanin. Concentrating on the finite dimensional leaves of the associated Poisson structure, we show that the geometry
of the leaves is intimately related to a complex algebraic ruled surface with a ℂ
*-invariant Poisson structure. In particular, Sklyanin's Lie Poisson structure admits a suitable abelianisation, once one passes
to an appropriate spectral curve. The Sklyanin structure is then equivalent to one considered by Mukai, Tyurin and Bottacin
on a moduli space of sheaves on the Poisson surface. The abelianization procedure gives rise to natural Darboux coordinates
for these leaves, as well as separation of variables for the integrable Hamiltonian systems associated to invariant functions
on the group.
Received: 8 August 2001/Accepted: 29 April 2002 Published online: 14 October 2002
RID="★"
ID="★" The first author of this article would like to thank NSERC and FCAR for their support
RID="★★"
ID="★★" The second author was partially supported by NSF grant number DMS-9802532 相似文献
15.
On Noncommutative Multi-Solitons 总被引:2,自引:0,他引:2
Rajesh Gopakumar Matthew Headrick Marcus Spradlin 《Communications in Mathematical Physics》2003,233(2):355-381
We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The
existence of a non-trivial moduli space at leading order in 1/θ is a consequence of a Bogomolnyi bound obeyed by the kinetic
energy of the θ=∞ solitons. In two spatial dimensions, the parameter space for k solitons is a K?hler de-singularization of the symmetric product (ℝ2)
k
/S
k
. We exploit the existence of this moduli space to construct solitons on quotient spaces of the plane: ℝ2/ℤ
k
, cylinder, and T
2
. However, we show that tori of area less than or equal to 2πθ do not admit stable solitons. In four dimensions the moduli
space provides an explicit K?hler resolution of (ℝ4)
k
/S
k
. In general spatial dimension 2d, we show it is isomorphic to the Hilbert scheme of k points in ℂ
d
, which for d>2 (and k>3) is not smooth and can have multiple branches.
Received: 29 May 2001 / Accepted: 16 August 2002 Published online: 7 November 2002
Communicated by R.H. Dijkgraaf 相似文献
16.
A quantum sl(2,ℝ) coalgebra (with deformation parameter z) is shown to underly the construction of a large class of superintegrable potentials on 3D curved spaces, that include the
nonconstant curvature analog of the spherical, hyperbolic, and (anti-)de Sitter spaces. The connection and curvature tensors
for these “deformed“ spaces are fully studied by working on two different phase spaces. The former directly comes from a 3D
symplectic realization of the deformed coalgebra, while the latter is obtained through a map leading to a spherical-type phase
space. In this framework, the nondeformed limit z → 0 is identified with the flat contraction leading to the Euclidean and Minkowskian spaces/potentials. The resulting Hamiltonians
always admit, at least, three functionally independent constants of motion coming from the coalgebra structure. Furthermore,
the intrinsic oscillator and Kepler potentials on such Riemannian and Lorentzian spaces of nonconstant curvature are identified,
and several examples of them are explicitly presented. 相似文献
17.
Markov Partitions for some classes of billiards in two-dimensional domains on 2 or two-dimensional torus are constructed. Using these partitions we represent the microcanonical distribution of the corresponding dynamical system in the form of a limit Gibbs state and investigate the character of its approximations by finite Markov chains.Dedicated to the memory of Rufus Bowen 相似文献
18.
S. E. Matskevich 《Russian Journal of Mathematical Physics》2009,16(4):508-517
In the paper, a representation of a solution of the Burgers equation in ℝ
n
is obtained by using integrals with respect to the Wiener measure on the space of trajectories in ℝ
n
. The Burgers equation is considered in a rigged Hilbert space. It is proved that, in the infinite-dimensional case, there
is an analog of the Cole-Hopf transformation relating the Burgers equation and an analog of the heat equation with respect
to measures. The Feynman-Kac formula for the heat equation (with potential) with respect to measures in a rigged Hilbert space
is obtained. 相似文献
19.
20.
Y. Yan J. Y. Zhang T. Cui Y. Li Y. M. Ma J. Gong Z. G. Zong G. T. Zou 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,61(4):397-403
The lattice dynamics of lithium nitride (Li3N) under high pressure are extensively investigated to probe its phase transformations by using the pseudopotential plane-wave
method within the density functional theory. A new second order α↦α′-Li3N phase transition is identified for the first time. The newly proposed α′-phase possesses a hexagonal symmetry with four ions in the unit cell having a space group of P-3m1. Further enthalpy and
phonon calculations support the existence of this phase, which stabilizes in a narrow pressure range of 2.8 – 3.6 GPa at zero
temperature. Upon further compression, transitions to denser packed phases of β-and γ-Li3N are typical first order. The analysis of the electronic densities of states suggests that all the high pressure modifications
of Li3N are insulators and, interestingly, the typical behavior of compression is to broaden the band gap. 相似文献