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1.
Fabio Gavarini 《Czechoslovak Journal of Physics》2001,51(12):1330-1335
The “quantum duality principle” states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal
Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie bialgebra as
well. We extend this to a much more general result: namely, for any principal ideal domainR and for each primepεR we establish an “inner” Galois’ correspondence on the categoryHA of torsionless Hopf algebras overR, using two functors (fromHA to itself) such that the image of the first and the second is the full subcategory of those Hopf algebras which are commutative
and cocommutative, modulop, respectively (i.e., they are“quantum function algebras” (=QFA) and“quantum universal enveloping algebras” (=QUEA), atp, respectively). In particular we provide a machine to get two quantum groups — a QFA and a QUEA — out of any Hopf algebraH over a fieldk: apply the functors tok[ν] ⊗k H forp=ν.
A relevant example occurring in quantum electro-dynamics is studied in some detail.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001 相似文献
2.
Bertfried Fauser 《Czechoslovak Journal of Physics》2000,50(11):1221-1228
In a recent work we have shown that quantum Clifford algebras — i.e. Clifford algebras of an arbitrary bilinear form — are
closely related to the deformed structures asq-spin groups, Hecke algebras,q-Young operators and deformed tensor products. The question to relate Manin’s approach to quantum Clifford algebras is addressed
here. Explicit computations using the CLIFFORD Maple package are exhibited. The meaning of non-commutative geometry is reexamined
and interpreted in Clifford algebraic terms.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. 相似文献
3.
Robert Oeckl 《Czechoslovak Journal of Physics》2001,51(12):1401-1406
The natural generalization of the notion of bundle in quantum geometry is that of bimodule. If the base space has quantum
group symmetries, one is particularly interested in bimodules covariant (equivariant) under these symmetries. Most attention
has so far been focused on the case with maximal symmetry — where the base space is a quantum group and the bimodules are
bicovariant. The structure of bicovariant bimodules is well understood through their correspondence with crossed modules.
We investigate the “next best” case — where the base space is a quantum homogeneous space and the bimodules are covariant.
We present a structure theorem that resembles the one for bicovariant bimodules. Thus, there is a correspondence between covariant
bimodules and a new kind of “crossed” modules which we define. The latter are attached to the pair of quantum groups which
defines the quantum homogeneous space.
We apply our structure theorem to differential calculi on quantum homogeneous spaces and discuss a related notion of induced
differential calculus.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001.
This work was supported by a NATO fellowship grant. 相似文献
4.
We introduce and study two new examples of noncommutative spheres: the half-liberated sphere, and the free sphere. Together
with the usual sphere, these two spheres have the property that the corresponding quantum isometry group is “easy”, in the
representation theory sense. We present as well some general comments on the axiomatization problem, and on the “untwisted”
and “non-easy” case. 相似文献
5.
An algorithm has been proposed to build an estimate of the half-life of a “daughter” nucleus in case, when it is unknown,
which nucleus is its “mother” (“indefinite start time”). For a decay of the “mother” at an instant t we can determine P—a probability of such a decay, if we assume that each “mother”, which has been decayed before t has equal chances to be “mother” of this “daughter”:
$
\sum\limits_{i = 1}^{n_t } {exp\left( { - \frac{{t - t_i }}
{\tau }} \right)} ,
$
\sum\limits_{i = 1}^{n_t } {exp\left( { - \frac{{t - t_i }}
{\tau }} \right)} ,
相似文献
6.
Giuseppe Castagnoli 《International Journal of Theoretical Physics》2010,49(2):304-315
By extending the representation of quantum algorithms to problem-solution interdependence, the unitary evolution part of the
algorithm entangles the register containing the problem with the register containing the solution. Entanglement becomes correlation,
or mutual causality, between the two measurement outcomes: the string of bits encoding the problem and that encoding the solution.
In former work, we showed that this is equivalent to the algorithm knowing in advance 50% of the bits of the solution it will
find in the future, which explains the quantum speed up.
Mutual causality between bits of information is also equivalent to seeing quantum measurement as a many body interaction between
the parts of a perfect classical machine whose normalized coordinates represent the qubit populations. This “hidden machine”
represents the problem to be solved. The many body interaction (measurement) satisfies all the constraints of a nonlinear
Boolean network “together and at the same time”—in one go—thus producing the solution. 相似文献
7.
M. Combescot O. Betbeder-Matibet 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(1):63-76
The purpose of this paper is to show how the diagrammatic expansion
in fermion exchanges of scalar products of N-composite-boson
(“coboson”) states can be obtained in a practical way. The hard
algebra on which this expansion is based, will be given in an independent publication.
Due to the composite nature of the particles, the scalar products
of N-coboson states do not reduce to a set of Kronecker symbols, as
for elementary bosons, but contain subtle exchange terms between two or
more cobosons. These terms originate from Pauli exclusion between the
fermionic components of the particles. While our many-body
theory for composite bosons leads to write these scalar products as
complicated sums of products of “Pauli scatterings” between
two cobosons, they in fact correspond to fermion exchanges
between any number P of quantum particles, with
2 ≤P≤N. These P-body exchanges are nicely represented by the
so-called “Shiva diagrams”, which are topologically different from
Feynman diagrams, due to the intrinsic many-body nature of the Pauli
exclusion from which they originate. These Shiva diagrams in fact
constitute the novel part of our composite-exciton many-body theory
which was up to now missing to get its full
diagrammatic representation. Using them, we can now “see” through
diagrams the physics of any quantity in which enters N interacting
excitons — or more generally N composite bosons —, with fermion
exchanges included in an
exact — and transparent — way. 相似文献
8.
An apparatus is developed for investigating the dynamic deformation properties of cryoinsulation coatings in the temperature
range 8–293 K. One type of cryo-insulation material — polyurethane foam — is chosen as the object of investigation. Test measurements
on a polyurethane foam “pack” (metal substrate with a polyurethane foam coating) are performed at 0.01 Hz in the temperature
range 8–293 K. A jump in the temperature dependence of the dynamic shear modulus (by two orders of magnitude) is observed
in the temperature range 54–63 K. This feature is attributed to the solidification of the air present in the pores of the
polyurethane foam. Such a transition results in cementation of the polyurethane skeleton of the coating by the nitrogen and
oxygen “ice” that is formed.
Zh. Tekh. Fiz. 69, 116–118 (February 1999) 相似文献
9.
U. Mohrhoff 《Foundations of Physics》2009,39(2):137-155
This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves,
Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion
beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including
the claim that different pure states may legitimately be assigned to the same system at the same time, and the claim that
the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard
the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads
to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are
neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible
outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the
only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these
are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation
of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic.
This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory.
Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various
reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify
an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians
refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the
macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests
itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental
in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in
the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms
of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe
its manifestation. 相似文献
10.
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincaré invariance
and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation
of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated
in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework
for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status,
and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for
the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum
field theory is constructed in a local and covariant manner from the spacetime metric and other background structure, such
as time and space orientations), a microlocal spectrum condition, an “associativity” condition, and the requirement that the
coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved
spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of
our new viewpoint on quantum field theory are discussed. 相似文献
11.
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
12.
M. Combescot O. Betbeder-Matibet F. Dubin 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(2):181-189
We have recently constructed a many-body theory for composite excitons, in
which the possible carrier exchanges between N excitons can be treated
exactly through a set of dimensionless “Pauli scatterings” between two
excitons. Many-body effects with free excitons turn out to be rather
simple because these excitons are the exact one-pair
eigenstates of the semiconductor Hamiltonian, in the absence of localized
traps. They consequently form a complete orthogonal basis for one-pair
states. As essentially all quantum particles known as bosons are
composite bosons, it is highly desirable to
extend this free exciton many-body theory to other kinds of
“cobosons” — a contraction for composite bosons — the physically
relevant ones being possibly not the exact one-pair eigenstates of
the system Hamiltonian. The purpose of this paper is
to derive the “Pauli scatterings” and the “interaction scatterings” of
these cobosons in terms of their wave functions and the interactions
which exist between the fermions from which they are
constructed. It is also explained how to calculate many-body effects in
such a very general composite boson system. 相似文献
13.
David Finkelstein 《International Journal of Theoretical Physics》1982,21(6-7):489-503
The mathematical language presently used for quantum physics is a high-level language. As a lowest-level or basic language
I construct a quantum set theory in three stages: (1) Classical set theory, formulated as a Clifford algebra of “S numbers” generated by a single monadic operation, “bracing,” Br = {…}. (2) Indefinite set theory, a modification of set theory
dealing with the modal logical concept of possibility. (3) Quantum set theory. The quantum set is constructed from the null
set by the familiar quantum techniques of tensor product and antisymmetrization. There are both a Clifford and a Grassmann
algebra with sets as basis elements. Rank and cardinality operators are analogous to Schroedinger coordinates of the theory,
in that they are multiplication or “Q-type” operators. “P-type” operators analogous to Schroedinger momenta, in that they transform theQ-type quantities, are bracing (Br), Clifford multiplication by a setX, and the creator ofX, represented by Grassmann multiplicationc(X) by the setX. Br and its adjoint Br* form a Bose-Einstein canonical pair, andc(X) and its adjointc(X)* form a Fermi-Dirac or anticanonical pair. Many coefficient number systems can be employed in this quantization. I use the
integers for a discrete quantum theory, with the usual complex quantum theory as limit. Quantum set theory may be applied
to a quantum time space and a quantum automaton.
This material is based upon work supported in part by NSF Grant No. PHY8007921. 相似文献
14.
15.
Yu. Kh. Vekilov I. A. Gordeev É. I. Isaev 《Journal of Experimental and Theoretical Physics》1999,89(5):995-999
The electronic spectrum and wave functions of a new quasicrystal structure—a two-dimensional Fibonacci lattice—are investigated
in the tight-binding approximation using the method of the level statistics. This is a self-similar structure consisting of
three elementary structural units. The “central” and “nodal” decoration of this structure are examined. It is shown that the
electronic energy spectrum of a two-dimensional Fibonacci lattice contains a singular part, but in contrast to a one-dimensional
Fibonacci lattice the spectrum does not contain a hierarchical gap structure. The measure of allowed states (Lebesgue measure)
of the spectrum is different from zero, and for “central” decoration it is close to 1. The character of the localization of
the wave functions is investigated, and it is found that the wave functions are “critical.”
Zh. éksp. Teor. Fiz. 116, 1834–1842 (November 1999) 相似文献
16.
《Physics Reports》2005,412(4):191-275
It was predicted that frequently repeated measurements on an unstable quantum state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. The results are based on the quantum measurement theory, which is also reviewed briefly. As a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. This measurement is an indirect negative-result one, for which the curiosity of the QZE and AZE is emphasized. It is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. In a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. However, drastic differences emerge in general cases where the detector responds only to limited photon modes. For example, against predictions of the conventional theories, the QZE or AZE may take place even for states that exactly follow the exponential decay law. We also discuss relation to the cavity quantum electrodynamics. 相似文献
17.
The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail
that quantum particles of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible
sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems
therefore unavoidable that even classical particles of the same kind must all be in the same state—in clear conflict with
what we know about classical particles. In this article we analyze the origin of this paradox. We shall argue that in the
classical limit classical particles emerge, as new entities that do not correspond to the “particle indices” defined in quantum mechanics. Put differently, we show
that the quantum mechanical symmetrization postulates do not pertain to particles, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises
the question of whether many discussions in the literature about the status of identical quantum particles have not been misguided. 相似文献
18.
Kurt Bernardo Wolf 《Czechoslovak Journal of Physics》2005,55(11):1527-1534
Various harmonic oscillator models define — in a sense to be explained here — fractional Fourier transforms (up to a phase).
The fractionalization of the Fourier integral transform is well understood; the finite case is less. There are several discrete
and finite oscillator models that contract to the continuous, integral model. The Ankara model can be thought as a ring of
point masses joined by springs to their equilibrium positions and to each other; the Cuernavaca model uses the su(2) algebra
with a distinct physical interpretation.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
19.
Michael H. Freedman Alexei Kitaev Zhenghan Wang 《Communications in Mathematical Physics》2002,227(3):587-603
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates,
which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned “topological models”
having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the
state is discrete, H≡ 0. These are called topological quantum field theories (TQFTs). These exotic physical systems are proved to be efficiently
simulated on a quantum computer. The conclusion is two-fold:
1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model “BQP”.
2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might
suggest a new quantum algorithm.
Received: 4 May 2001 / Accepted: 16 January 2002 相似文献
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