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1.
P. Moylan 《Czechoslovak Journal of Physics》1997,47(12):1251-1258
We show that it is possible to express the basis elements of the Lie algebra of the Euclidean group,E(2), as simple irrational functions of certainq deformed expressions involving the generators of the quantum algebraU
q
(so(2, 1)). We consider implications of these results for the representation theory of the Lie algebra ofE(2). We briefly discess analogous results forU
q
(so(2, 2)).
Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June
1997. 相似文献
2.
Harold Steinacker 《Communications in Mathematical Physics》1998,192(3):687-706
We study irreducible unitary representations of U
q
(SO(2,1)) and U
q
(SO(2,?3)) for q a root of unity, which are finite dimensional. Among others, unitary representations corresponding to all classical one-particle
representations with integral weights are found for , with M being large enough. In the “massless” case with spin bigger than or equal to 1 in 4 dimensions, they are unitarizable only
after factoring out a subspace of “pure gauges” as classically. A truncated associative tensor product describing unitary
many-particle representations is defined for .
Received: 27 November 1996 / Accepted: 28 July 1997 相似文献
3.
A Cartan-Weyl basis for the quantum affine superalgebraU
q
(osp(1|2)) is constructed in an explicit form.
Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June
1997.
Supported by KNB grant No. 2P 30208706.
Supported by Russian Foundation for Fundamental Research, grant No. 96-01-01421. 相似文献
4.
The phase diagram of a two-dimensional mesoscopic system of charges or dipoles, whose realizations could be electrons in a
semiconductor quantum dot or indirect excitons in a system of two vertically coupled quantum dots, is investigated. Quantum
calculations using ab initio Monte Carlo integration along trajectories determine the properties of such objects in the temperature-quantum de-Boer-parameter
plane. At zero (sufficiently low) temperature, as the quantum fluctuations of the particles increase, two types of quantum
disordering phenomena occur with increasing quantum de Boer parameter q: first, for q∼10−5 the systems transform into a radially ordered but orientationally disordered state wherein various shells of the “atom” rotate
relative to one another. For much larger q∼0.1, a transition occurs to a disordered state (a superfluid in the case of a system of bosons).
Fiz. Tverd. Tela (St. Petersburg) 41, 1856–1862 (October 1999) 相似文献
5.
Peter Mittelstaedt 《International Journal of Theoretical Physics》2008,47(1):104-113
The goal of quantum logic is the “bottom-top” reconstruction of quantum mechanics. Starting from a weak quantum ontology,
a long sequence of arguments leads to quantum logic, to an orthomodular lattice, and to the classical Hilbert spaces. However,
this abstract theory does not yet contain Planck’s constant ℏ. We argue, that ℏ can be obtained, if the empty theory is applied to real entities and extended by concepts that are usually considered as
classical notions. Introducing the concepts of localizability and homogeneity we define objects by symmetry groups and systems
of imprimitivity. For elementary systems, the irreducible representations of the Galileo group are projective and determined
only up to a parameter z, which is given by z=m/ℏ, where m is the mass of the particle and ℏ Planck’s constant. We show that ℏ has a meaning within quantum mechanics, irrespective of use the of classical concepts in our derivation. 相似文献
6.
In this paper we give a logical analysis of both classical and quantum correlations. We propose a new logical system to reason
about the information carried by a complex system composed of several parts. Our formalism is based on an extension of epistemic
logic with operators for “group knowledge” (the logic GEL), further extended with atomic sentences describing the results of “joint observations” (the logic LCK). As models we introduce correlation models, as a generalization of the standard representation of epistemic models as vector models. We give sound and complete axiomatizations
for our logics, and we use this setting to investigate the relationship between the information carried by each of the parts
of a complex system and the information carried by the whole system. In particular we distinguish between the “distributed
information”, obtainable by simply pooling together all the information that can be separately observed in any of the parts,
and “correlated information”, obtainable only by doing joint observations of the parts (and pooling together the results).
Our formalism throws a new light on the difference between classical and quantum information and gives rise to an informational-logical
characterization of the notion of “quantum entanglement”. 相似文献
7.
M. Welk 《Czechoslovak Journal of Physics》2000,50(11):1379-1384
We study covariant differential calculus on the quantum Euclidean spheres S
q
N−1
which are quantum homogeneous spaces with coactions of the quantum groups O
q
(N). First order differential calculi on the quantum Euclidean spheres satisfying a dimension constraint are found and classified:
ForN≥6, there exist exactly two such calculi one of which is closely related to the classical differential calculus in the commutative
case. Higher order differential forms and symmetry are discussed.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. 相似文献
8.
A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebrau(n) and its quantum analogU
q(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for
the subalgebrau(n−1) (U
q(u(n−1))). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form of the projection
operator ofu(n) andU
q(u(n)). It is shown that theU
q(u(n)) CGCs can be presented in terms of theU
q(u)(n−1)) q−9j-symbols.
Presented at the 9th International Colloquium: “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.
Supported by Russian Foundation for Fundamental Research, grant 99-01-01163.
Supported in part by the U.S. National Science Foundation under Grant PHY-9970769 and Cooperative Agreement EPS-9720652 that
includes matching from the Louisiana Board of Regents Support Fund. 相似文献
9.
The “phase diagram” of a two-dimensional mesoscopic system of bosons is investigated. An example of such a system is a system
of indirect magnetoexcitons in semiconductor double quantum dots. Quantum Monte Carlo calculations show the existence of quantum
orientational melting. At zero (quite low) temperature, as quantum fluctuations of the particles intensify, two quantum disordering
phenomena occur with increasing de Boer parameter q. First, at q≈10−3 the system passes to a radially ordered but orientationally disordered state, where different shells of a cluster rotate
relative to one another. Then at q≈0.16 a transition to a superfluid state occurs.
Pis’ma Zh. éksp. Teor. Fiz. 68, No. 11, 817–822 (10 December 1998) 相似文献
10.
V. L. Golo Yu. M. Evdokimov S. G. Skuridin E. I. Kats 《Journal of Experimental and Theoretical Physics》1999,88(3):517-522
The interaction between hydrogen bonds and conformational elastic degrees of freedom has been investigated using the simplest
model of a double-strand DNA molecule. The hydrogen bonds are described in terms of two-level quantum systems. After excluding
conformational degrees of freedom, one has effective interaction among two-level systems. In the ground state of an ideal
double helix, hydrogen bonds in a DNA molecule also have a helical order induced by conformational degrees of freedom. The
pitch of the hydrogen-bond helix (and even its sign under certain conditions) is different from that of the basic helix pitch
and, generally speaking, is incommensurate with the latter. This effect can, possibly, lead to an inversion of the sign of
the circular dichroism in spectral bands, which was detected in some experiments.
Zh. éksp. Teor. Fiz. 115, 940–950 (March 1999) 相似文献
11.
We consider weighted traces of products of intertwining operators for quantum groups U
q
(?), suitably twisted by a “generalized Belavin–Drinfeld triple”. We derive two commuting sets of difference equations – the
(twisted) Macdonald–Ruijsenaars system and the (twisted) quantum Knizhnik–Zamolodchikov–Bernard (qKZB) system. These systems
involve the nonstandard quantum R-matrices defined in a previous joint work with T. Schedler ([ESS]). When the generalized
Belavin–Drinfeld triple comes from an automorphism of the Lie algebra ?, we also derive two additional sets of difference
equations, the dual Macdonald–Ruijsenaars system and the \textit{dual} qKZB equations.
Received: 20 March 2000 / Accepted: 11 December 2000 相似文献
12.
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
13.
14.
M. Z. Smirnov 《Journal of Experimental and Theoretical Physics》1997,85(3):441-446
An open quantum system, which consists of a “dressed” two-level atom, i.e., an atom interacting with a classical multifrequency
field, and a single quantized mode of an electromagnetic field, is examined. It is shown that when the frequency of the quantized
mode coincides with one of the transition frequencies between the quasienergy levels, two interaction mechanisms, which differ
in the dynamics of the populations of the quasienergy states, can be realized.
Zh. éksp. Teor. Fiz. 112, 818–827 (September 1997) 相似文献
15.
The general expression for the static permittivity ε(q, 0) of the Coulomb system in the region of small wave vectors was derived based on exact limit relations. The relation obtained
describes the function ε(q, 0) in both “metal” and “dielectric” states of the Coulomb system. On this basis, the concept of the “true” dielectric is
introduced and the definition of the “true” screening length was discussed. Exact relations were derived for the function
ε(q, 0) in the region of small wave vectors q within the random phase approximation at an arbitrary degeneracy. 相似文献
16.
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
17.
18.
The structure of all discrete series of unitary irreducible representations of the U
q
(u(3, 1)) and U
q
(u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g′)
q
. The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U
q
(u(n, 1)) ⊇ U
q
(u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) ⊇ u(n) classical algebra. 相似文献
19.
The condition for the appearance of an event horizon is considered in pair-correlated systems (superfluids and superconductors)
in which the fermionic quasiparticles obey “relativistic” equations. In these systems the Landau critical velocity of superflow
corresponds to the speed of light. In conventional systems, such as s-wave superconductors, the superflow remains stable even above the Landau threshold. We show, however, that, in “ relativistic”
systems, the quantum vacuum becomes unstable and the superflow collapses after the “speed of light” is reached, so that the
horizon cannot appear. Thus an equilibrium dissipationless superflow state and the horizon are incompatible on account of
quantum effects. This negative result is consistent with the quantum Hawking radiation from the horizon, which would lead
to a dissipation of the flow.
Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 124–129 (25 January 1998)
Published in English in the original Russian journal. Edited by Steve Torstveit. 相似文献
20.
We propose a general scheme for the “logic” of elementary propositions of physical systems, encompassing both classical and
quantum cases, in the framework given by Non-Commutative Geometry. It involves Baire*-algebras, the non-commutative version of measurable functions, arising as envelope of the C
*-algebras identifying the topology of the (non-commutative) phase space. We outline some consequences of this proposal in
different physical systems. This approach in particular avoids some problematic features appearing in the definition of physical
states in the standard (W
*-)algebraic approach to classical mechanics. 相似文献