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1.
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
2.
Stan Gudder 《Foundations of Physics》1999,29(6):877-897
This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the -effect algebra of effects (fuzzy events)
and the set of probability measures
on a measurable space
. An observable
is defined, where
is the value space of X. It is noted that there exists a one-to-one correspondence between states on
and elements of
and between observables
and -morphisms from
to
. Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map
is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived. 相似文献
3.
We consider the large time asymptotic behavior of solutions to the Cauchy problem for the modified Korteweg–de Vries equation
, with initial data
. We assume that the coefficient
is real, bounded and slowly varying function, such that
, where
. We suppose that the initial data are real-valued and small enough, belonging to the weighted Sobolev space
. In comparison with the previous paper (Internat. Res. Notices
8 (1999), 395–418), here we exclude the condition that the integral of the initial data u
0 is zero. We prove the time decay estimates
and
for all
, where
. We also find the asymptotics for large time of the solution in the neighborhood of the self-similar solution. 相似文献
4.
For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann–Hilbert problem approach is used to derive the leading-order asymptotics as
of solutions
to the Cauchy problem for the defocusing nonlinear Schrödinger equation (
NLSE),
, with finite-density initial data
.The
NLSE dark soliton position shifts in the presence of the continuum are also obtained. 相似文献
5.
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
6.
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$$
" align="middle" border="0">
, 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
7.
8.
Carl M. Bender 《Czechoslovak Journal of Physics》2006,56(9):1047-1062
In this paper, two independent methods are used to show that the non-Hermitian
-symmetric wrong-sign quartic Hamiltonian H = (1/2m)p
2 − gx
4 is exactly equivalent to the conventional Hermitian Hamiltonian
. First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated
by using functional-integration methods. As the linear term in the Hermitian Hamiltonian
is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly
is a consequence of the broken parity symmetry of the original non-Hermitian
-symmetric Hamiltonian. The anomaly term in
remains unchanged if an x
2 term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in
are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states. 相似文献
9.
We examine the effects of mixing induced non-diagonal light-heavy neutrino weak neutral currents on the amplitude for the
process
(with a=e, μ or τ). By imposing constraint that the amplitude should not exceed the perturbative unitarity limit at high energy
, we obtain bounds on light-heavy neutrino mixing parameter sin2
where
is the mixing angle. In the case of one heavy neutrino (mass mξ) or mass degenerate heavy neutrinos, for Λ=1 TeV, no bound is obtained for mξ<0.50 TeV. However, sin2
≤3.8 × 10−6 for mξ=5 TeV and sin
≤6.0 × 10−8 for mξ=10 TeV. For Λ=∞, no constraint is obtained for mξ<0.99 TeV and sin2
≤3.8 × 10−2 (for mξ=5 TeV) and sin2
≤9.6 × 10−3 (for mξ=10 TeV). 相似文献
10.
N. I. Rukhadze P. Beneš Ch. Briançon V. B. Brudanin P. Čermák F. A. Danevich V. G. Egorov K. N. Gusev A. A. Klimenko V. E. Kovalenko A. Kovalik A. V. Salamatin I. Štekl V. V. Timkin V. I. Tretyak Ts. Vylov 《Physics of Atomic Nuclei》2006,69(12):2117-2123
A search for double electron capture of 106Cd was performed at the Modane Underground Laboratory (4800 m w.e.) using a low-background and high-sensitivity multidetector
spectrometer TGV-2 (Telescope Germanium Vertical). New limits on β
+/EC, EC/EC decays of 106Cd were obtained from preliminary calculations of experimental data accumulated for 4800 h of measurement of 10 g of 106Cd with enrichment of 75%. They are
> 9.1 × 1018 yr,
> 1.9 × 1019 yr for transitions to the first 2+, 511.9 keV excited state of 106Pd, and
> 1.3 × 1019 yr,
> 6.2 × 1019 yr for transitions to the ground 0+ state of 106Pd. All limits are given at 90% C.L.
The text was submitted by the authors in English. 相似文献
11.
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
12.
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
13.
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
14.
The zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite-dimensional state space. A generalized BRS operator A such that
being the height of the current algebra representation) acts in
-dimensional indefinite metric space
of quantum group invariant vectors. The generalized cohomologies Ker
are 1-dimensional. Their direct sum spans the physical subquotient of
. 相似文献
15.
We consider solutions to the Dirac equation in the presence of an external axial vector potential
coupled to the spinor field psi through the interaction term
. There turn out to be no bound-state energies in this system consistent with a normalizable wave function. 相似文献
16.
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
17.
18.
We consider a family of Hamiltonian systems
and we prove that it is integrable for
. To show this we use the normal variational equation. 相似文献
19.
The purpose of this Letter is to develop further the Gauss diagram approach to finite-type link invariants. In this context we introduce Gauss diagrams counterparts to chord diagrams, 4T relation, weight systems arising from Lie algebras, and an algebra of unitrivalent graphs modulo the STU relation. The counterparts, respectively, are arrow diagrams, 6T relation, weights arising from the solutions of the classical Yang–Baxter equation, and an algebra
of acyclic arrow graphs (modulo an oriented version
of the STU relation). The algebra
encodes, in a graphical form, the main properties of Lie bialgebras, similarly to the well-known relation of the algebra of unitrivalent graphs to Lie algebras. We show that the oriented
and
relations hold, and that
is isomorphic to the algebra
of arrow diagrams. As an application, we consider an appropriate link-homotopy version
of the algebra
. Using this algebra, we construct a Gauss diagram invariants of string links up to link-homotopy, with values both in the algebra
and in . We observe that this construction gives the universal Milnor's link-homotopy -invariants. 相似文献
20.
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