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1.
In the qubit semantics the meaning of any sentence α is represented by a quregister: a unit vector of the n–fold tensor product ⊗n ℂ2, where n depends on the number of occurrences of atomic sentences in α (see Cattaneo et al.). The logic characterized by this semantics, called quantum computational logic (QCL), is unsharp, because the noncontradiction principle is violated. We show that QCL does not admit any logical truth. In this framework,
any sentence α gives rise to a quantum tree, consisting of a sequence of unitary operators. The quantum tree of α can be regarded as a quantum circuit that transforms
the quregister associated to the occurrences of atomic subformulas of α into the quregister associated to α. 相似文献
2.
New classes of unitary irreducible representations of Sp(n, 1) which can be useful for applications in physics are obtained. The infinitesimal operators of these representations of Sp(n, 1) and of irreducible representations of Sp(n+1) with highest weights (m, m, m3,…,mn+1) and (m1, m2, 0,…,0) are expressed in terms of the simple Clebsch–Gordancoefficients for Sp(n). For Sp(3) and Sp(2, 1) they are found in an explicit form. 相似文献
3.
We prove that an irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of theSL(2, ) current algebra by putting a constraint on the latter using the Becchi-Rouet-Stora-Tyutin formalism. Thus there is aSL(2, ) symmetry in the Virasoro algebra, but it is gauged and hidden. This construction of the Virasoro algebra is the quantum analogue of the Hamiltonian reduction. We then are naturally lead to consider a constrainedSL(2, ) Wess-Zumino-Witten model. This system is also related to quantum field theory of coadjoint orbit of the Virasoro group. Based on this result, we present a canonical derivation of theSL(2, ) current algebra in Polyakov's theory of two-dimensional gravity; it is a manifestation of theSL(2, ) symmetry in conformal field theory hidden by the quantum Hamiltonian reduction. We also discuss the quantum Hamiltonian reduction of theSL(2, ) current algebra and its relation to theW
n
-algebra of Zamolodchikov. This makes it possible to define a natural generalization of the geometric action for theW
n
-algebra despite its non-Lie-algebraic nature.This paper is dedicated to the memory of Vadik G. Knizhnik 相似文献
4.
Heinrich Saller 《International Journal of Theoretical Physics》1997,36(12):2783-2826
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds
are parametrized by the classes of the positive unitary operations in all complex operations, i.e., by the homogenous spacesD(n)=GL(C
R
n
)/U(n) withn=1 for mechanics andn=2 for relativistic fields. The rankn gives the number of both the discrete and continuous invariants used in the harmonic analysis, i.e., two characteristic masses
in the relativistic case. ‘Canonical’ field theories with the familiar divergencies are inappropriate realizations of the
real 4-dimensional causal manifoldD(2). Faithful timespace realizations do not lead to divergencies. In general they are reducible, but nondecomposable—in addition
to representations with eigenvectors (states, particle), they incorporate principal vectors without a particle (eigenvector)
basis as exemplified by the Coulomb field.
In theorthogonal andunitary groupsO(N
+,N
−), respectively, thepositive orthogonal and unitary ones areO(N) andU(N), respectively. 相似文献
5.
The luminescence properties of Re(I) complexes incorporating the dcbpy ligand (dcbpy = n,n′-dicarboxylic acid-2,2′-bipyridine; n = 3, 4) were investigated as well as their utility as Pb2+ sensors. An unusual binuclear complex of the 3,3′- species was isolated. The emission intensity and lifetime for all complexes
were found to be highly temperature-dependent, with quantum yields and lifetimes dramatically greater at 77 K than at room
temperature. The monomeric 3,3′-dcbpy Re(I) complex demonstrates nearly 1:1 binding with Pb2+. The effect of this lead binding on the emission intensity is great, but the low quantum yields allow only for detection
of the metal at the micromolar level. The binding of Pb2+ to the 4,4′-dcbpy complex is modeled and the interaction is demonstrated to involve two binding sites. 相似文献
6.
No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical
field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical
variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures
ρ on Ω having zero mean value and dispersion σ2(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based
on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ2(ρ) = hn (for n = 2 we obtain the conventional quantum formalism). 相似文献
7.
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary R-matrices, namely unitary solutions to the Yang-Baxter equation, afford explicitly local unitary representations of braid groups. Inspired by topological quantum computation, we study whether or not it is possible
to reassemble the irreducible summands appearing in the unitary braid group representations from a unitary braided fusion
category with possibly different positive multiplicities to get representations that are uniformly equivalent to the ones
from a unitary R-matrix. Such an equivalence will be called a localization of the unitary braid group representations. We show that the q = e
πi/6 specialization of the unitary Jones representation of the braid groups can be localized by a unitary 9 × 9 R-matrix. Actually this Jones representation is the first one in a family of theories (SO(N), 2) for an odd prime N > 1, which are conjectured to be localizable. We formulate several general conjectures and discuss possible connections to
physics and computer science. 相似文献
8.
We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers. 相似文献
9.
We state and prove a generalized adiabatic theorem for Markov chains and provide examples and applications related to Glauber
dynamics of the Ising model over ℤ
d
/nℤ
d
. The theorems derived in this paper describe a type of adiabatic dynamics for
l1(\mathbbRn+)\ell^{1}(\mathbb{R}^{n}_{+}) norm preserving, time inhomogeneous Markov transformations, while quantum adiabatic theorems deal with ℓ
2(ℂ
n
) norm preserving ones, i.e. gradually changing unitary dynamics in ℂ
n
. 相似文献
10.
We study the interaction of vector mesons with the octet of stable baryons in the framework of the local hidden gauge formalism
using a coupled-channels unitary approach, including also the pseudoscalar-baryon channels which couple to the same quantum
numbers. We examine the scattering amplitudes and their poles, which can be associated to the known J
P = 1/2−, 3/2− baryon resonances, and determine the role of the pseudoscalar-baryon channels, changing the width and eventually the mass
of the resonances generated with only the basis of vector-baryon states. 相似文献
11.
J.N. Fuchs M. Holzmann F. Laloë 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(4):463-478
The purpose of this article is to discuss cluster expansions in dense quantum systems, as well as their interconnection with
exchange cycles. We show in general how the Ursell operators of order l≥ 3 contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual - in other words, the mean-field correction is expressed in terms of a modification
of a local Boltzmann equilibrium. In a first part, we consider classical statistical mechanics and recall the relation between
the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the
linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the
subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles)
and show that each Ursell operator Un with n≥ 3 contains a “tree-reducible part”, which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles
in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles
interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles,
and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered
at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach,
in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum
statistics and dynamics.
Received 18 October 2001 相似文献
12.
N. S. Malyshev G. V. Golubkov M. G. Golubkov R. J. Buenker H. P. Lieberman 《Russian Journal of Physical Chemistry B, Focus on Physics》2011,5(6):931-939
The potential curves of the nl(2Λ) electronically excited states of the K**-He quasimolecule (n, l, and Λ are the principal quantum number, angular momentum, and its projection on the molecular axis) are calculated. To describe
the interaction of the weakly bound electron with the singly charged potassium ion and the ground-state helium atom (with
taking into account their long-range electrostatic interactions), the formalism of two-center scattering theory and the finite-range
pseudopotential method are used. A comparison with the results of calculations performed by the MRD CI method is carried out.
The findings showed that, for small principal quantum numbers n, these methods complement each other, because the first is more reliable for large interatomic distances, R ≥ n, whereas second for small, R < n. The characteristic features of the behavior of the potential curves of the K**-He quasimolecule at large n and l are discussed. 相似文献
13.
The solutions of the nonlinear matrix equation in the Atiyah-Hitchin-Drifeld-Manin (AHDM) construction that determine the
Yang-Mills self-dual fields with topological charge k = 4 for symplectic gauge groups are discussed. In the case of Sp(n), n > 2, it is possible to use a procedure that was proposed earlier for generating solutions with k = 3. It is shown that for SU(2) = Sp(1) the AHDM matrix can be generated by using cubic equation solutions with coefficients
that depend on 8k — 3 parameters. 相似文献
14.
Matthias Christandl Robert König Graeme Mitchison Renato Renner 《Communications in Mathematical Physics》2007,273(2):473-498
When n − k systems of an n-partite permutation-invariant state are traced out, the resulting state can be approximated by a convex combination of tensor
product states. This is the quantum de Finetti theorem. In this paper, we show that an upper bound on the trace distance of
this approximation is given by , where d is the dimension of the individual system, thereby improving previously known bounds. Our result follows from a more general
approximation theorem for representations of the unitary group. Consider a pure state that lies in the irreducible representation
of the unitary group U(d), for highest weights μ, ν and μ + ν. Let ξμ be the state obtained by tracing out U
ν. Then ξμ is close to a convex combination of the coherent states , where and is the highest weight vector in U
μ.
For the class of symmetric Werner states, which are invariant under both the permutation and unitary groups, we give a second
de Finetti-style theorem (our “half” theorem). It arises from a combinatorial formula for the distance of certain special
symmetric Werner states to states of fixed spectrum, making a connection to the recently defined shifted Schur functions [1].
This formula also provides us with useful examples that allow us to conclude that finite quantum de Finetti theorems (unlike
their classical counterparts) must depend on the dimension d. The last part of this paper analyses the structure of the set of symmetric Werner states and shows that the product states
in this set do not form a polytope in general. 相似文献
15.
We use the Clifford algebra technique (J. Math. Phys. 43:5782, 2002; J. Math. Phys. 44:4817, 2003), that is nilpotents and projectors which are binomials of the Clifford algebra objects γ
a
with the property {γ
a
,γ
b
}+=2η
ab
, for representing quantum gates and quantum algorithms needed in quantum computers in a simple and an elegant way. We identify
n-qubits with the spinor representations of the group SO(1,3) for a system of n spinors. Representations are expressed in terms of products of projectors and nilpotents; we pay attention also on the nonrelativistic
limit. An algorithm for extracting a particular information out of a general superposition of 2
n
qubit states is presented. It reproduces for a particular choice of the initial state the Grover’s algorithm (Proc. 28th
Annual ACM Symp. Theory Comput. 212, 1996). 相似文献
16.
The influence of neutral species in the E- and D-layers of the Earth’s upper atmosphere on the spectrum of the spontaneous emission (absorption) of Rydberg atoms and molecules
for transitions that occur without changing the principal quantum number (Δn = 0) is examined. Along with the process of l-mixing, the splitting of orbitally degenerate states due to interaction with perturbing neutral species of the medium is
taken into account. The possible types of radiative transitions between them are analyzed. It is demonstrated that, for principal
quantum numbers of n = 10–30, decimeter-band radiation corresponds to transitions between the levels of split states, whereas meter-band radiation,
to transitions between their individual components. It is established that, for these values of n, the ratios of the intensities of the decimeter and meter bands for Δn = 0 transitions to the intensity of IR radiation (Δn = 1) are 10−4 and 10−6, respectively. The issue of satellite signal phase shift because of multiple Raman scattering in the D-layer of the atmosphere is discussed. 相似文献
17.
K. J. Oyewumi 《International Journal of Theoretical Physics》2010,49(6):1302-1316
The dynamical symmetries of the Kratzer-type molecular potentials (generalized Kratzer molecular potentials) are studied by
using the factorization method. The creation and annihilation (ladder) operators for the radial eigenfunctions satisfying
quantum dynamical algebra SU(1,1) are established. Factorization method is a very simple method of calculating the matrix elements from these ladder operators.
The matrix elements of different functions of r,
r\fracddrr\frac{d}{dr}, their sum Γ1 and difference Γ2 are evaluated in a closed form. The exact bound state energy eigenvalues E
n,ℓ
and matrix elements of r,
r\fracddrr\frac{d}{dr}, their sum Γ1 and difference Γ2 are calculated for various values of n and ℓ quantum numbers for CO and NO diatomic molecules for the two potentials. The results obtained are in very good agreement with those obtained by other methods. 相似文献
18.
Jeong Ryeol Choi 《International Journal of Theoretical Physics》2006,45(1):176-196
We showed that the idea of Schleich and Wheeler (1987, Nature 326, 574) for the semiclassical approach of the interference in phase space of harmonic oscillator squeezed states can be extended to that of general time-dependent Hamiltonian system. The quantum phase properties of squeezed states for the general time-dependent Hamiltonian system are investigated by using the quantum distribution function. The weighted overlaps A
n
and phases θ
n
for the system are evaluated in the semiclassical limit. 相似文献
19.
Bernhard Drabant Branislav Jurčo Michael Schlieker Wolfgang Weich Bruno Zumino 《Letters in Mathematical Physics》1992,26(2):91-96
We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A
n
, B
n
, C
n
, and D
n
by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.Humboldt Fellow. 相似文献
20.
In a physical basis of the unitary scheme, analytic formulas for the probabilities B(E2κL → κ′L′) and their isospin factors for the (λ0) and (λ2) representations of the SU(3) group were obtained for even-even nuclei. It was shown that the isospin correction must be taken into account at low L and in the case of off-diagonal transitions in κ. The results obtained in the unitary scheme are compared with the results of other models and with experimental data. At
high L, the transition probabilities B(E2κL → κ′L′) are markedly smaller in the unitary scheme than in the rotational model, while, for L ≪ λ, these probabilities in the unitary scheme and in the rotational model are close. 相似文献