共查询到20条相似文献,搜索用时 31 毫秒
1.
The determinants of Laplacians acting in real line bundles over manifolds of the form
相似文献
2.
Models of random systems whose Hamiltonian reads
, where
and
i
,=1,...,n are independent, identically distributed random variables are discussed.J
ij
are assumed to be symmetric, with respect toJ
0, random variables and also symmetric functions of components of
. A question of dependence of a phase diagram on a probability distribution of
is addressed. A class of distributions and interactionsJ
ij
, which give rise to phase diagrams called typical is selected. Then a problem of obtaining typical phase diagrams, containing a certain region with an infinite number of pure phases, is studied. 相似文献
3.
On the Schrödinger equation and the eigenvalue problem 总被引:1,自引:0,他引:1
If
k
is thek
th eigenvalue for the Dirichlet boundary problem on a bounded domain in
n
, H. Weyl's asymptotic formula asserts that
, hence
. We prove that for any domain and for all
. A simple proof for the upper bound of the number of eigenvalues less than or equal to - for the operator –V(x) defined on
n
(n3) in terms of
is also provided.Research partially supported by a Sloan Fellowship and NSF Grant No. 81-07911-A1 相似文献
4.
Lu has shown that any dynamical r-matrix for the pair (
,
) naturally induces a Poisson homogeneous structure on G/U. She also proved that if
is complex simple,
is its Cartan subalgebra and r is quasitriangular, then this correspondence is in fact one-to-one. In this Letter we find some general conditions under which the Lu correspondence is one-to-one. Then we apply this result to describe all triangular Poisson homogeneous structures on G/U for a simple complex group G and its reductive subgroup U containing a Cartan subgroup. 相似文献
5.
Given n2, we put r=min
. Let be a compact, C
r
-smooth surface in n which contains the origin. Let further
be a family of measurable subsets of such that
as
. We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator
in L
2(
n
), where is a positive constant, as
. An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve. 相似文献
6.
Periodic nonlinear Schrödinger equation and invariant measures 总被引:1,自引:1,他引:0
J. Bourgain 《Communications in Mathematical Physics》1994,166(1):1-26
In this paper we continue some investigations on the periodic NLSEiu
u
+iu
xx
+u|u|
p-2
(p6) started in [LRS]. We prove that the equation is globally wellposed for a set of data of full normalized Gibbs measrue
(after suitableL
2-truncation). The set and the measure are invariant under the flow. The proof of a similar result for the KdV and modified KdV equations is outlined. The main ingredients used are some estimates from [B1] on periodic NLS and KdV type equations. 相似文献
7.
The influence of spin dynamics on the Kondo effect manifestations in the Kondo lattices is investigated within perturbation theory with respect to thes-f interaction. It may give rise to Kondo-like divergencies in the electron self-energy already in the second order, resulting in an appreciable effective mass enhancement. As for usual Kondo contributions to thermodynamic and transport properties, the effect of spin dynamics reduces roughly to the replacement ln
, with
the characteristic spin-fluctuation energy. The thermoelectric power of dense Kondo systems is discussed. Singular contributions to the electron self-energies in the ferro-and antiferromagnetic state are considered. Kondo-like corrections to the intersite exchange interactions, saturation magnetic moment and total energy in a magnetically ordered state are calculated. The strong-coupling regionT<T
K
is investigated within the Anderson lattice model. A decrease ofT
K
due to spin fluctuations is demonstrated. 相似文献
8.
Hugo Parr 《Zeitschrift für Physik B Condensed Matter》1976,25(4):359-361
We have calculated analytically the superheating fieldH
sh
for bulk superconductors, correct to second order in. We find
, which agrees well with numerical computations for<0.5. The surface order parameter is
, and the penetration depth is
. 相似文献
9.
Frédéric Klopp 《Communications in Mathematical Physics》1995,167(3):553-569
We study the spectrum of random Schrödinger operators acting onL
2(R
d
) of the following type
. The
are i.i.d. random variables. Under weak assumptions onV, we prove exponential localization forH at the lower edge of its spectrum. In order to do this, we give a new proof of the Wegner estimate that works without sign assumptions onV.
Résumé Dans ce travail, nous étudions le spectre d'opérateurs de Schrödinger aléatoires agissant surL 2(R d ) du type suivant . Les sont des variables aléatoires i.i.d. Sous de faibles hypothèses surV, nous démontrons que le bord inférieur du spectre deH n'est composé que de spectre purement ponctuel et, que les fonctions propres associées sont exponentiellement décroissantes. Pour ce faire nous donnons une nouvelle preuve de l'estimée de Wegner valable sans hypothèses de signe surV. U.R.A. 760 C.N.R.S. 相似文献 10.
Let
be the Haag--Kastler net generated by the
(2) chiral current algebra at level 1. We classify the SL(2,
)-covariant subsystems
by showing that they are all fixed points nets
H
for some subgroup H of the gauge automorphisms group SO(3) of
. Then, using the fact that the net
1 generated by the
(1) chiral current can be regarded as a subsystem of
, we classify the subsystems of
1. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem
. 相似文献
11.
We deduce the Lax pair for a new space-dependent KdV equation,
, via the technique of Painlevé analysis. From it, infinitely many conservation laws are deduced and the symplectic structure is obtained. 相似文献
12.
The product of two real spectral triples
and
, the first of which is necessarily even, was defined by A.Connes as
given by
and, in the even-even case, by
. Generically it is assumed that the real structure
obeys the relations
,
,
, where the
-sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes'
>-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this
-sign table. In this Letter, we propose an alternative definition of the product real structure such that the
-sign table is also satisfied by the product. 相似文献
13.
P. C. Hemmer 《Journal of statistical physics》2000,100(1-2):3-11
A binary mixture of long rigid rods of diameters D
i and lengths L
i (i=1, 2) may demix into two isotropic phases, and we give necessary conditions on the molecular size parameters for this transition to exist. These conditions imply that the two diameters must be sufficiently unequal, D
2/D
1>(
+
)2, or D
2/D
1<(
+
)2, while the length ratio is limited to an interval f
–(D
2/D
1)<L
2/L
1<f
+(D
2/D
1). The functions f
± are given explicitly. 相似文献
14.
A simplified construction of representations is presented for the quantized enveloping algebra
q (
), with
being a simple complex Lie algebra belonging to one of the four principal series A\ell, B\ell, C\ell or D\ell. The carrier representation space is the quantized algebra of polynomials in antiholomorphic coordinate functions on the big cell of a coadjoint orbit of K where K is the compact simple Lie group with the Lie algebra
– the compact form of
. 相似文献
15.
Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential
A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }}
16.
R. F. Streater 《Communications in Mathematical Physics》1967,6(4):233-247
We consider a lattice of spin 1/2 ions, described by the discrete form of the current commutation relationsJ
i
J
(i)
=1/2, [J
i
,J
i
]=i
ij
J
i
where =1, 2, 3 andi label the lattice sites. The algebra is realized as the Clifford algebra
over a Hilbert space. The equations of motion are specified by a formal Hamiltonian of the Heisenberg form:
, wheref
ij
0 and only a finite numberQ of ions are linked to any given lattice site. We prove that the Hamiltonian is non-negative in a representation of
, and has a ground state exhibiting ferromagnetism. The time displacement group acts continuously on
, inducing automorphisms.
is asymptotically abelian with respect to the space translations of the lattice.The model is an example of an algebraic quantum field theory and possesses a broken symmetry, the rotation group 0(3). The consequent Goldstone theorem is proved, namely, there is no energy gap in the spectrum ofH. 相似文献
17.
Chains of extended twists are composed of factors
. The set of Jordanian twists {
} can be applied to the initial Hopf algebra
. In this case the remaining (transformed) factors of the chain can serve as extensions for such a multijordanian twist. We study the properties of these generalized extensions and the spectra of deformations of the corresponding Heisenberg-like algebras. The results are explicitly demonstrated for the case when
. 相似文献
18.
We consider the Dirichlet Laplacian for astrip in
with one straight boundary and a width
, where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase,
, the operator has nobound statesfor small
.On the otherhand, a weakly bound state existsprovided
. In thatcase, there are positive c
1,c
2 suchthat the corresponding eigenvalue satisfies
for all
sufficiently small. 相似文献
19.
In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators
. The reduction of the Poisson structure to the symplectic submanifold
gives rise to W-algebras. In this Letter, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: (a) L is pure polynomial in p with multiple roots and (b) L has multiple poles at finite distance. The w-algebra corresponding to the case (a) is defined as
, where
means the multiplicity of roots and to the case (b) is defined by
where
is the multiplicity of poles. We prove that
-algebra is isomorphic via a transformation to
U(1) with m=
. We also give the explicit free fields representations for these W-algebras. 相似文献
20.
Karen K. Uhlenbeck 《Communications in Mathematical Physics》1985,101(4):449-457
AssumeF is the curvature (field) of a connection (potential) onR
4 with finiteL
2 norm
. We show the chern number
(topological quantum number) is an integer. This generalizes previous results which showed that the integrality holds forF satisfying the Yang-Mills equations. We actually prove the natural general result in all even dimensions larger than 2. 相似文献
|