共查询到20条相似文献,搜索用时 125 毫秒
1.
The thermodynamic limits of SRB-measures for uniformly hyperbolic sets are smoothly dependent on the map in an appropriate
functional space.
Received: 26 April 1999 / Accepted: 17 November 1999 相似文献
2.
Fumio Hiroshima 《Communications in Mathematical Physics》2000,211(3):585-613
The Hamiltonian of a system of quantum particles minimally coupled to a quantum field is considered for arbitrary coupling constants. The Hamiltonian has a translation invariant part. By means of functional integral representations the
existence of an invariant domain under the action of the heat semigroup generated by a self-adjoint extension of the translation
invariant part is shown. With a non-perturbative approach it is proved that the Hamiltonian is essentially self-adjoint on
a domain. A typical example is the Pauli–Fierz model with spin 1/2 in nonrelativistic quantum electrodynamics for arbitrary
coupling constants.
Received: 26 May 1999 / Accepted: 9 November 1999 相似文献
3.
A Generalized Hypergeometric Function¶Satisfying Four Analytic Difference Equations¶of Askey--Wilson Type 总被引:3,自引:3,他引:0
S. N. M. Ruijsenaars 《Communications in Mathematical Physics》1999,206(3):639-690
The hypergeometric function 2
F
1 can be written in terms of a contour integral involving gamma functions. We generalize this (Barnes) representation by using
a certain generalized gamma function as a building block. In this way we obtain a new 2
F
1-generalization with various symmetry features. We determine the analyticity properties of the R-function in all of its eight arguments, and show that it is a joint eigenfunction of four distinct Askey–Wilson type difference
operators, two acting on v and two on . The Askey–Wilson polynomials can be obtained by a suitable discretization of v or .
Received: 21 December 1998 / Accepted: 14 April 1999 相似文献
4.
Haisheng Li 《Communications in Mathematical Physics》2001,217(3):653-696
We generalize Feigin and Miwa's construction of extended vertex operator (super)algebras A
k
(sl(2)) for other types of simple Lie algebras. For all the constructed extended vertex operator (super)algebras, irreducible
modules are classified, complete reducibility of every module is proved and fusion rules are determined modulo the fusion
rules for vertex operator algebras of affine type.
Received: 7 March 2000 / Accepted: 10 November 2000 相似文献
5.
Roberto Peirone 《Communications in Mathematical Physics》1999,207(1):67-80
I prove that in (sufficiently small) tubular ρ$-neighborhoods of a given C
3 manifold of codimension 1, any two points can be connected by a billiard trajectory, and that in addition there exists such
a trajectory having at most collision points, for a suitable H>0, provided the manifold is of class C
3.
Received: 19 June 1998 / Accepted: 7 April 1999 相似文献
6.
Marcos Mariño Gregory Moore Grigor Peradze 《Communications in Mathematical Physics》1999,205(3):691-735
The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide nontrivial information about four-manifold
topology. In particular, in the example of gauge group SU(2) with one doublet hypermultiplet, we derive a theorem relating classical topological invariants such as the Euler character
and signature to sum rules for Seiberg–Witten invariants. A short account of this paper can be found in [1].
Received: 19 December 1998 / Accepted: 7 March 1999 相似文献
7.
We study the model of a strongly non-linear chain of particles coupled to two heat baths at different temperatures. Our main result is the existence and uniqueness of a stationary state at all temperatures. This result extends those of Eckmann, Pillet, Rey-Bellet [EPR99a, EPR99b] to potentials with essentially arbitrary growth at infinity. This extension is possible by introducing a stronger version of Hörmander's theorem for Kolmogorov equations to vector fields with polynomially bounded coefficients on unbounded domains. 相似文献
8.
The correlation functions of the random variables det(λ−X), in which X is an hermitian N×N random matrix, are known to exhibit universal local statistics in the large N limit. We study here the correlation of those same random variables for real symmetric matrices (GOE). The derivation relies
on an exact dual representation of the problem: the k-point functions are expressed in terms of finite integrals over (quaternionic) k×k matrices. However the control of the Dyson limit, in which the distance of the various parameters λ's is of the order of
the mean spacing, requires an integration over the symplectic group. It is shown that a generalization of the Itzykson–Zuber
method holds for this problem, but contrary to the unitary case, the semi-classical
result requires a finite number of corrections to be exact. We have also considered the problem of an external matrix source coupled to the random
matrix, and obtain explicit integral formulae, which are useful for the analysis of the large N limit.
Received: 19 March 2001 / Accepted: 21 June 2001 相似文献
9.
Consider a Schr?dinger operator on L
2 of the line, or of a half line with appropriate boundary conditions. If the potential tends to zero and is a finite sum of
terms, each of which has a derivative of some order in L
1+L
p
for some exponent p<2, then an essential support of the the absolutely continuous spectrum equals ℝ+. Almost every generalized eigenfunction is bounded, and satisfies certain WKB-type asymptotics at infinity. If moreover these
derivatives belong to L
p
with respect to a weight |x|γ with γ >0, then the Hausdorff dimension of the singular component of the spectral measure is strictly less than one.
Received: 27 July 2000 / Accepted: 23 October 2000 相似文献
10.
On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement
the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the Knizhnik–Zamolodchikov
connection and have finite order. When all primary fields are fixed points, the isomorphisms are endomorphisms; in this case,
the bundle of chiral blocks is typically a reducible vector bundle. A conjecture for the trace of such endomorphisms is presented;
the proposed relation generalizes the Verlinde formula. Our results have applications to conformal field theories based on
non-simply connected groups and to the classification of boundary conditions in such theories.
Received: 11 May 1998 / Accepted: 17 April 1999 相似文献
11.
In this article we characterize a certain class of rational solutions of the hierarchy of master symmetries for KdV. The result
is that the generic rational potentials that decay at infinity and remain rational by all the flows of the master-symmetry
KdV hierarchy are bispectral potentials for the Schr?dinger operator. By bispectral potentials we mean that the corresponding
Schr?dinger operators possess families of eigenfunctions that are also eigenfunctions of a differential operator in the spectral
variable. This complements certain results of Airault–McKean–Moser [4], Duistermaat–Grünbaum [10], and Magri–Zubelli [40].
As a consequence of bispectrality, the rational solutions of the master symmetries turn out to be solutions of a (generalized)
string equation.
Received: 28 January 1999 / Accepted: 22 October 1999 相似文献
12.
We obtain the explicit reduction of the Oscillator representation of the symplectic group, on the subgroups of automorphisms of certain vector-valued skew forms | of "Clifford type"-equivalently, of automorphisms of Lie algebras of Heisenberg type. These subgroups are of the form G · \Spin(k), with G a real reductive matrix group, in general not compact, commuting with Spin(k) with finite intersection. The reduction turns out to be free of multiplicity in all the cases studied here, which include some where the factors do not form a Howe pair. If G is maximal compact in G, the restriction to K · \Spin(k) is essentially the action on the symmetric algebra on a space of spinors. The cases when this is multiplicity-free are listed in [R]; our examples show that replacing K by G does make a difference. Our question is motivated to a large extent by the geometric object that comes with such a |: a Fock-space bundle over a sphere, with G acting fiberwise via the oscillator representation. It carries a Dirac operator invariant under G and determines special derivations of the corresponding gauge algebra. 相似文献
13.
Håkan Andréasson 《Communications in Mathematical Physics》1999,206(2):337-365
A global existence theorem, with respect to a geometrically defined time, is shown for Gowdy symmetric globally hyperbolic
solutions of the Einstein–Vlasov system for arbitrary (in size) initial data. The spacetimes being studied contain both matter
and gravitational waves.
Received: 8 December 1998 / Accepted: 20 March 1999 相似文献
14.
We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras.
An example is the factorisation of matrices M
2(ℂ)=ℂℤ2·ℂℤ2. We also further extend the coalgebra version of theory introduced previously, to include frame resolutions and corresponding
covariant derivatives and torsions. As an example, we construct q-monopoles on all the Podleś quantum spheres S
2
q,s
.
Received: 25 September 1998 / Accepted: 23 February 2000 相似文献
15.
C.P. Walkden 《Communications in Mathematical Physics》1999,205(2):263-281
We consider a hyperbolic flow φ
t
defined on an attracting basic set Λ. A map from the first (Čech) cohomology group of Λ into the dynamic cohomology group
is constructed. This map is used to discuss the stable ergodicity and mixing of compact Lie group extensions and velocity
changes of φ
t
.
Received: 17 June 1998 / Accepted: 24 February 1999 相似文献
16.
17.
Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux–Egoroff
equations. This system of partial differential equations appears as a specific subset of the n-component KP hierarchy. KP representation theory and the related Sato infinite Grassmannian are used to construct solutions
of this Darboux–Egoroff system and the related Frobenius manifolds. Finally we show that for these solutions Dubrovin's isomonodromy
tau-function can be expressed in the KP tau-function.
Received: 1 September 1998 / Accepted: 7 March 1999 相似文献
18.
Takashi Hara Tetsuya Hattori Hiroshi Watanabe 《Communications in Mathematical Physics》2001,220(1):13-40
Existence of critical renormalization group trajectory for a hierarchical Ising model in 4 dimensions is shown. After 70
iterations of renormalization group transformations, the critical Ising model is mapped into a vicinity of the Gaussian fixed
point. Convergence of the subsequent trajectory to the Gaussian fixed point is shown by power decay of the effective coupling
constant. The analysis in the strong coupling regime is computer-aided and Newman's inequalities on truncated correlations
are used to give mathematical rigor to the numerical bounds. In order to obtain a criterion for convergence to the Gaussian
fixed point, characteristic functions and Newman's inequalities are systematically used.
Received: 27 April 2000 / Accepted: 5 January 2001 相似文献
19.
C. A. Morales M. J. Pacifico E. R. Pujals 《Communications in Mathematical Physics》2000,211(3):527-558
We study a bifurcation of Axiom A (hyperbolic) vector fields in dimension three leading to robust strange attractors with
singularities. The Axiom A vector fields involved in the bifurcation exhibit a basic set equivalent to the suspension of a
three symbol subshift. The attractors arising from this kind of bifurcation are not equivalent to the geometric Lorenz attractors.
Received: 4 December 1998 / Accepted: 5 October 1999 相似文献
20.
We consider fermionic lattice systems with Hamiltonian H=H
{(0)}+λH
Q
, where H
{(0)} is diagonal in the occupation number basis, while H
Q
is a suitable “quantum perturbation”. We assume that H
{(0)} is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitations, while H
Q
is a finite range or exponentially decaying Hamiltonian that can be written as a sum of even monomials in the fermionic creation
and annihilation operators. Mapping the d dimensional quantum system onto a classical contour system on a d+1 dimensional lattice, we use standard Pirogov–Sinai theory to show that the low temperature phase diagram of the quantum
system is a small perturbation of the zero temperature phase diagram of the classical
system, provided λ is sufficiently small. Particular attention is paid to the sign problems arising from the fermionic nature
of the quantum particles.
As a simple application of our methods, we consider the Hubbard model with an additional nearest neighbor repulsion. For this
model, we rigorously establish the existence of a paramagnetic phase with commensurate staggered charge order for the narrow
band case at sufficiently low temperatures.
Received: 23 December 1996/ Accepted: 7 April 1999 相似文献