共查询到20条相似文献,搜索用时 569 毫秒
1.
J. Donin 《Czechoslovak Journal of Physics》1997,47(11):1115-1122
For
we construct a two parametric
-invariant family of algebras,
, that is a quantization of the function algebra
on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric
-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on
. 相似文献
2.
The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy
(where
0$$
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and
0$$
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are two constants). In particular, the perpendicular incidence of an electron with a given value
of the wave vector
is considered. The electron is forward-scattered into the region behind the barrier (region 2:
0$$
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), i. e. the wave function
is composed of plane waves with all wave vectors
such that
and
\left. 0 \right)} $$
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) (where
). Therefore, if
0$$
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, the wave function of the electron is represented as
, where
. An approximate formula is derived for the amplitude
. The authors pay a special attention to the flow density
and calculate this function in two cases: 1. for the plane
and 2. for high values of
is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier. 相似文献
3.
Marcus Pivato 《Journal of statistical physics》2003,110(1-2):247-267
If
, and
is a finite (nonabelian) group, then
is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation
which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of
. We characterize when MCA are group endomorphisms of
, and show that MCA on
inherit a natural structure theory from the structure of
. We apply this structure theory to compute the measurable entropy of MCA, and to study convergence of initial measures to Haar measure. 相似文献
4.
Solutions of the Yang-Baxter equation with spectral parameter for systems with in-variance under a Lie algebra
and for which the quantum space is a Hilbert space different from the auxiliary space are studied. In particular, for the case of
=cn= sp (2n, ), solutions on infinite-dimensional state spaces are constructed. 相似文献
5.
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
6.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
7.
D. Arnaudon 《Czechoslovak Journal of Physics》1997,47(11):1075-1082
Irreducible representations of
at roots of unity in the restricted specialisation are described with the Gelfand-Zetlin basis. This basis is redefined to allow the Casimir operator of the quantum subalgebra
not to be completely diagonalised. Some irreducible representations of
indeed contain indecomposable
-modules. The set of redefined (mixed) states is described as a teepee inside the pyramid made with the whole representation. 相似文献
8.
We derive explicit formulas for the multipoint series of
in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of
. We also obtain explicit formulas for the Hodge integrals
, in the cases i=0 and 1. 相似文献
9.
Given a simple, simply laced, complex Lie algebra
corresponding to the Lie group G, let
be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra
whose underlying graded commutative algebra is given by the cohomology, with respect to
, of the algebra of regular functions on G with values in
. We conjecture that
describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical
string. The conjecture is verified in the two explicitly known cases,
2 (the Virasoro string) and
3 (the
string). 相似文献
10.
It is shown that the elliptic algebra
at the critical level c = –2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and containing the q-deformed Virasoro algebra is constructed on this center. We show also that t(z) close an exchange algebra when p
m = q
c+2 for
, they commute when in addition p = q
2k
for k integer non-zero, and they belong to the center of
when k is odd. The Poisson structures obtained for t(z) in these classical limits contain the q-deformed Virasoro algebra, characterizing the structures at p q
2k
as new
algebras. 相似文献
11.
C. Quesne 《International Journal of Theoretical Physics》1999,38(7):1905-1923
GLh(n) ×GLh(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras
are built in terms of thecorresponding Rh and
-matrices by contracting theGLq(n) ×
-covariant q-bosonic (or q-fermionic) algebras
, = 1, 2.When using a basis of
wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra Uq(gl(n))
, a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingUh(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some Uh(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of
(2, 1). 相似文献
12.
Let
be von Neumann algebras acting on a Hilbert space
and let
be a common cyclic and separating vector. We say that
have the modular intersection property with respect to
if(1)
-half-sided modular inclusions,(2)
(If (1) holds the strong limit exists.) We show that under these conditions the modular groups of
and
generate a 2-dim. Lie group.This observation is the basis for obtaining group representations of Sl(2,
)/Z
2 generated by modular groups. 相似文献
13.
Total electron emission from metals due to the impact of multiply charged ions, , may significantly influence quantitative measurements of ion current in corpuscular diagnostics. The value of (/q) was determined for Xe ions impacting clean polycrystalline copper as a function of ion charge state
and of ion kinetic energy,
keV/q, i.e. in the energy region up to
keV/amu, where there is a lack of such data. For highly charged projectile ions,
was found to have a clear minimum as a function of E
i. With decreasing charge state of the projectile ion this minimum shifts to a lower energy and becomes shallower. This observation is in agreement with compiled results of other authors. Limits for values of
are estimated and discussed. 相似文献
14.
V. Tarasov 《Czechoslovak Journal of Physics》2000,50(1):193-200
We discuss relations between different integral formulae for solutions of the quantized Knizhnik-Zamolodchikov (qKZ) equation at level zero in the Uq (
2) case for q < 1. Smirnov type formulae of M. Jimbo et al. are derived from the general approach of A. Varchenko and the author. The consideration is parallel to the qKZ equation in the rational
2 case done by A. Nakayashiki, S. Pakuliak and the author. 相似文献
15.
We prove the almost sure existence of a pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding densityg has support equal to
, and satisfies
, for some > 0. This includes the case of Gaussian distributions. We show that the almost sure spectrum is
, provided the magnetic field B0. We prove that for each positive integer n, there exists a field strength B
n
, such that for all B>B
n
, the almost sure spectrum is pure point at all energies
except in intervals of width
about each lower Landau level
, for m < n. We also prove that for any B0, the integrated density of states is Lipschitz continuous away from the Landau energiesE
n
(B). This follows from a new Wegner estimate for the finite-area magnetic Hamiltonians with random potentials. 相似文献
16.
A. A. Raduta 《Czechoslovak Journal of Physics》2000,50(4):519-527
Two neutrino double beta (2) Gamow-Teller transitions,
and
, are treated with a many-body Hamiltonian involving a Bonn-type realistic two-body interaction. The states involved in these transitions are described by a pnRQRPA approach. Transition operators are expanded in first order in terms of renormalized bosons. For illustration the formalism is applied to the case
Kr. 相似文献
17.
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
18.
Richard L. Liboff 《International Journal of Theoretical Physics》2002,41(10):1957-1970
Three problems related to the spherical quantum billiard in
are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in
. The second topic addresses the first-excited-state theorem for the spherical quantum billiard in
. Wavefunctions for this system are given by the product form, (
)Z
q+()Y
(n)
, where is dimensionless displacement,
is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written
. It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in
is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in
. In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in
by enumerating independent degenerate product eigenstates of the Laplacian. 相似文献
19.
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group
in the following manner. There is a partition
into disjoint subsets and a bijection between
and the sectors
of the (p,q)-minimal model such that the fusion rules
correspond to
where
. 相似文献
20.
Suppose
g
is the (negative) Laplace–Beltrami operator of a Riemannian metric g on
n
which is Euclidean outside some compact set. It is known that the resolvent R()=(–
g
–2)–1, as the operator from L
2
comp(
n
) to H
2
loc(
n
), has a meromorphic extension from the lower half plane to the complex plane or the logarithmic plane when n is odd or even, respectively. Resonances are defined to be the poles of this meromorphic extension. We prove that when n is 4 or 6, there always exist infinitely many resonances provided that g is not flat. When n is greater than 6 and even, we prove the same result under the condition that the metric is conformally Euclidean or is close to the Euclidean metric. 相似文献