共查询到20条相似文献,搜索用时 93 毫秒
1.
M. Zyskin 《Letters in Mathematical Physics》1996,36(4):427-439
We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum field O(k) and the regularization. 相似文献
2.
We discuss the parametrization of quantum groups in terms of independent operators. We find that this consideration leads to the parametrization ofSU q(2) in terms of aq-oscillator plus a commuting phase. The commuting phase is naturally identified with the subgroupU(1) and the remaining cosetSU q(2)/U(1)=CP q(1) consists of aq-oscillator. For unitary quantum groupsSU q (n), the analogous construction results in the quantum projective spaceSU q(n+1)/U q (n)=CP q (n) being identified with then-dimensionalq-oscillator. This yields a nonlinear action of the quantum groupSU q(n+1) on then-dimensionalq-oscillator. 相似文献
3.
In this work, we explore a new connection between quantum groups and Tsallis entropy through the energy spectrum of a Hamiltonian with SUq(2) symmetry. Identifying the deformation parameter of the entropy with the parameter of deformation of the associated quantum group, we deduce Tsallis entropy for states related to such a system with SUq(2) symmetry and conducted an investigation of quantum entanglement. 相似文献
4.
Franklin E. Schroeck Jr. 《Foundations of Physics》1982,12(9):825-841
Various formalisms for recasting quantum mechanics in the framework of classical mechanics on phase space are reviewed and compared. Recent results in stochastic quantum mechanics are shown to avoid the difficulties encountered by the earlier approach of Wigner, as well as to avoid the well-known incompatibilities of relativity and ordinary quantum theory. Specific mappings among the various formalisms are given. 相似文献
5.
There are four reasons why our present knowledge and understanding of quantum mechanics can be regarded as incomplete. (1)
The principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than
about a thousand atoms. (2) There is no universally agreed upon explanation for the process of quantum measurement. (3) There
is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of
position eigenstates. (4) Most importantly, the concept of time is classical and hence external to quantum mechanics: there
should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we
argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important
at the Planck mass scale. Such a nonlinearity can provide insights into the aforesaid problems. We use a physically motivated
model for a nonlinear Schr?dinger equation to show that nonlinearity can help in understanding quantum measurement. We also
show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a
quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain
the observed absence of position superpositions in macroscopic objects (lifetime is too small). It also suggests that ongoing
laboratory experiments may be able to detect the finite superposition lifetime for mesoscopic objects in the near future. 相似文献
6.
D. Arnaudon L. Frappat E. Ragoucy J. Avan M. Rossi 《Czechoslovak Journal of Physics》2001,51(12):1254-1259
We construct Drinfel’d twists that define deformed Hopf structures. In particular, we obtain deformed double Yangians and
dynamical double Yangians.
Presented by D. Arnaudon at the 10th Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23
June, 2001. 相似文献
7.
Lassen M Delaubert V Janousek J Wagner K Bachor HA Lam PK Treps N Buchhave P Fabre C Harb CC 《Physical review letters》2007,98(8):083602
We present the key elements required for continuous variable parallel quantum information protocols based on spatial multimode quantum correlations. We describe techniques for encoding, combining and detecting spatial quantum information with high efficiency in the individual transverse modes. Until now, the missing feature for the implementation of such protocols was the generation of squeezing in higher order transverse Hermite-Gauss modes. We experimentally demonstrate squeezing in selective modes by fine-tuning the phase matching condition of the nonlinear chi(2) material and the cavity resonance condition of an optical parametric amplifier. Combined, these results open the way to practical multimode optical quantum information systems. 相似文献
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A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems. 相似文献
11.
Popper's idea of propensities constituting the physical background of predictable probabilities is reviewed and developed by introducing a suitable formalism compatible with standard probability calculus and with its frequency interpretation. Quantum statistical ensembles described as pure cases (eigenstates) are shown to be necessarily not homogeneous if propensities are actually at work in nature. An extension of the theory to EPR experiments with local propensities leads to a new and more general proof of Bell's theorem. No joint probabilities for incompatible observables need to be introduced. 相似文献
12.
Henry P. Stapp 《Foundations of Physics》1982,12(4):363-399
A theory of psychophysical phenomena is proposed. It resolves simultaneously four basic problems of science, namely the problems of the connections between:(1) mind and matter,(2) quantum theory and reality,(3) relativity theory and becoming, and (4) relativity theory and Bell's theorem.This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract W-7405-EN-G-48. 相似文献
13.
It is shown that (a) the conscious observer plays no essential part in the measurement process, and (b) environmental perturbations of whatever kind fail to account for the evolution of systems into mixtures or dynamically decoupled systems. 相似文献
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A recently developed unified theory of classical and quantum chaos, based on the de Broglie-Bohm (Hamilton-Jacobi) formulation
of quantum mechanics is presented and its consequences are discussed. The quantum dynamics is rigorously defined to be chaotic
if the Lyapunov number, associated with the quantum trajectories in de Broglie-Bohm phase space, is positive definite. This
definition of quantum chaos which under classical conditions goes over to the well-known definition of classical chaos in
terms of positivity of Lyapunov numbers, provides a rigorous unified definition of chaos on the same footing for both the
dynamics. A demonstration of the existence of positive Lyapunov numbers in a simple quantum system is given analytically,
proving the existence of quantum chaos. Breaking of the time-reversal symmetry in the corresponding quantum dynamics under
chaotic evolution is demonstrated. It is shown that the rigorous deterministic quantum chaos provides an intrinsic mechanism
towards irreversibility of the Schrodinger evolution of the wave function, without invoking ‘wave function collapse’ or ‘measurements’ 相似文献
17.
Bernhard Drabant 《Czechoslovak Journal of Physics》1992,42(12):1293-1302
We construct complex quantum groups associated with the Lie algebras of typeA
n–1
,B
n
,C
n
andD
n
which are considered as real algebras. Following the ideas of Faddeev, Reshetikhin and Takhtayan, we obtain the Hopf algebras of regular functionalsU
R
, on these real complexified quantum groups. Theq-analogues of the left invariant vector fields of the quantum enveloping algebras are defined. These quantum vector fields are functionals over the corresponding real formA of the complex quantum groupA. The equivalence of the Hopf algebra of regular functionals and the algebra of complex quantum vector fields is shown 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. In the special exampleA
1
, we derive theq-deformed real complexified enveloping algebraU
q
sl(2, ) with six generators.Presented at the Colloquium on the Quantum Groups, Prague, 18–20 June, 1992.Based on the papers: [i]Drabant B., Schlieker M., Weich W., and Zumino B.: PreprintLMU-TPW 1991-5 (to appear in Commun. Math. Phys.) [ii]Chryssomalakos C., Drabant B., Schlieker M., Weich W., and Zumino B.: Preprint UCB 92/03 (to appear in Commun. Math. Phys.) [iii]Drabant B., Juro B., Schlieker M., Weich W., and Zumino B.: Preprint MPI-Ph/92-39 (submitted to Lett. Math. Phys.) 相似文献
18.
Michael D Scadron 《Annals of Physics》1983,148(2):257-281
The dynamical theory of spontaneous breakdown correctly predicts the bound states and relates the order parameters of electron-phonon superconductivity and quark-gluon chiral symmetry. A similar statement cannot be made for the standard electroweak gauge symmetry. 相似文献
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