共查询到20条相似文献,搜索用时 15 毫秒
1.
Two interpretations ofq-special functions based on quantum groups and algebras have been presented in the literature. The connection between these approaches is explained using as an example the case whereU
q
(sl(2)) is the basic structure.Supported in part by the National Sciences and Engineering Research Council (NSERC) of Canada. 相似文献
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Yu. A. Kurochkin V. S. Otchik L. G. Mardoyan D. R. Petrosyan G. S. Pogosyan 《Physics of Atomic Nuclei》2017,80(4):739-746
The classical Kepler–Coulomb problem on the single-sheeted hyperboloid H 3 1 is solved in the framework of the Hamilton–Jacobi equation. We have proven that all the bounded orbits are closed and periodic. The paths are ellipses or circles for finite motion. 相似文献
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Cheng Xiang 《中国物理 B》2022,31(3):30306-030306
We propose three alternative measures for non-Gaussianity of quantum states: sine distance, Bures angle, and Bures distance, which are based on quantum fidelity introduced by Wang [Phys. Lett. A 373 58 (2008)]. Using them, we evaluate the non-Gaussianity of some relevant single-mode and two-mode non-Gaussian states and find a good consistency of the three examined measures. In addition, we show that such metrics can exactly quantify the degree of Gaussianity of even Schrödinger-cat-like states of small amplitudes that can not be measured by other known non-Gaussianity measures such as the Hilbert—Schmidt metric and the relative entropy metric. We make a comparative study between all existing non-Gaussianity measures according to the metric axioms and point out that the sine distance is the best candidate among them. 相似文献
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Bernhard Baumgartner 《Communications in Mathematical Physics》1980,75(1):25-41
Explicit bounds on the quantum partition functions are given in terms of classical partition functions, incorporating effective pair potentials, which account for Fermi- and Bose-statistics, respectively. The bounds may be used for the limit 0 and eventually for showing the interchangeability of the classical with the thermodynamic limit. A simple derivation of the thermodynamic limit for free particles with general dispersions is given.Work supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. 3569. 相似文献
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The Inönü-Wigner contraction from the SO(2, 1) group to the Euclidean E(2) and E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the four corresponding two-dimensional homogeneous spaces: two-dimensional hyperboloids and two-dimensional Euclidean and pseudo-Euclidean spaces. We show how the nine systems of coordinates on the two-dimensional hyperboloids contracted to the four systems of coordinates on E 2 and eight on E 1,1. The text was submitted by the authors in English. 相似文献
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Andrei Tănăsescu Mihai-Zicu Mina Pantelimon George Popescu 《Physics letters. A》2019,383(18):2168-2171
Non-local implementations of quantum gates are a vital part of quantum networks. We find an optimal non-local implementation of quantum functions, the quantum gate equivalent of a switch statement. Then, we apply this result to the Deutsch-Jozsa problem, obtaining a distributed Deutsch-Jozsa algorithm and we show the relative efficiency improvement. As an application, we find a non-cooperative game based upon the original Deutsch-Jozsa problem where a classical agent has at most a 50% probability of winning, while a quantum agent can win every time. 相似文献
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A free particle moving on a one-sheeted hyperboloid is discussed both at the classical and quantum levels. 相似文献
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The concept of correlation function is widely used in classical statistical mechanics to characterize how two or more variables depend on each other. In quantum mechanics, on the other hand, there are observables that cannot be measured at the same time; the so-called incompatible observables. This prospect imposes a limitation on the definition of a quantum analog for the correlation function in terms of a sequence of measurements. Here, based on the notion of sequential weak measurements, we circumvent this limitation by introducing a framework to measure general quantum correlation functions, in principle, independently of the state of the system and the operators involved. To illustrate, we propose an experimental configuration to obtain explicitly the quantum correlation function between two Pauli operators, in which the input state is an arbitrary mixed qubit state encoded on the polarization of photons. 相似文献
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Gerhard C. Hegerfeldt 《Reports on Mathematical Physics》1975,7(3):403-409
It is well known that there is a close connection between (Abelian) fields and probability measures on distribution space, or more generally, on infinite-dimensional vector spaces, and their associated random processes. We establish general criteria for mutual singularity of such measures and apply them to quantum fields. In particular, it is shown that a kind of generalized clustering implies singularity. Then a condition for singularity is given in terms of a natural metric introduced previously. It is used to show that the translate of a measure by a linear functional which is not continuous for this metric is singular to the untranslated measure. The results are applied to processes with independent values at each point, corresponding to the ultra-local model. It is shown that each such measuris singular to any of its translates although its finite-dimensional projections may be equivalent to Lebesgue measure. 相似文献
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Juan Mateos Guilarte JosMaría Muoz Porras Marina de la Torre Mayado 《Journal of Geometry and Physics》1998,27(3-4):297-332
Algebro-geometric methods are applied to the theoretical understanding of the fractionary quantum Hall effect on a periodic lattice. The fermionic Fock space of the many-electron system is precisely identified, and as a consequence, the variational Haldane-Rezayi ground state is decomposed in terms of one-particle wave functions at the first Landau level; the filling factor is thus analytically computed. Quasi-hole and quasi-particle excitations are also analyzed. The center of mass dynamics is described in terms of a section in a very subtle stable vector bundle. The Hall conductance arises as a topological invariant; namely, the slope of the vector bundle previously mentioned. 相似文献
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Kazimierz Bragiel 《Letters in Mathematical Physics》1991,22(3):195-201
Invariance properties of the functions satisfying an integral spherical equation on a compact quantum group are discussed. It is shown that spherical and zonal spherical functions are conncected with the spherical representation of a compact quantum group.Supported by Polish Scientific Grant RPI10. 相似文献
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I. Földesi J. Janszky P. Ádám S. Szabó I. Tarján M. S. Kim 《Acta Physica Hungarica A》1996,3(3-4):269-278
A new, approximate generalized Wigner function based on discrete coherent state superpositions is introduced. It is shown that in contrast to the exact generalized Wigner function that may not exist in some region of its parameter the proposed approximate function exists everywhere. 相似文献
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Jan Fischer 《Czechoslovak Journal of Physics》1958,8(4):379-388
Using the Freese-Matthews-Salam equations for chronological products of field operators, equations are written for Green functions of many electrons and photons. It is shown that in order to find any single Green function an infinite recursive system of these equations has to be solved. After adding terms containing the external electric current and external electromagnetic potential to the Lagrangian, this system is reduced to one equation containing functional derivatives of higher orders. It is shown that all relations and equations become much simpler when the definition of the Green function is appropriately changed.On leave from the Physical Institute of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia. 相似文献
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V. V. Kuryshkin 《Russian Physics Journal》1969,12(4):497-500
A broad class of representations for the density matrix of phase-space functions is proposed. It is shown that all the known quantum distribution functions are particular cases of this representation. The corresponding equations are found. An examination is made of the conditions under which the phase representation may be a quantum distribution function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 111–115, April, 1969.The author thanks Professor Ya. P. Terletskii for valuable advice. 相似文献
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运用量子理论推导和数值计算相结合的方法,本文首先得到了一维势箱函数的示意图及其模型.接着,全面、系统地研究了量子理论中N维势箱函数的波函数、能级和概率密度.最后,运用MATLAB软件对势箱函数的所有特性进行了仿真模拟.我们发现:N维势箱中粒子的能量是量子化的、不连续;量子数n不能为零,且n越大对应的能级越高,而质量m越大,对应的能级越低.一般条件下,一维势箱长度a越大(粒子运动范围越大),对应的能级越低;节点数为n-1,节点越多,波长越短,频率越高,能级越高.二维势箱函数波函数的峰值个数为n x 0x0E?SymboltB@0x0Fn y,且与Ψ=0平面的交线数也为n x 0x0E?SymboltB@0x0Fn y;概率密度分布的极大值个数也为n x 0x0E?SymboltB@0x0Fn y.对于简并度,一般情况下,二维势箱模型下的粒子的简并度是不确定的;但对于二维正方势箱函数模型,其箱内微观粒子的能级简并度分为特殊和一般两种情况.三维势箱函数的简并度为n x+n y+n z.最后,首次借助MATLAB软件的色彩实现了四维表现,得到了三维势箱函数的四维空间切片图.这种可视化的结果与理论结果完全一致,这对于抽象性概念的理解具有重要意义. 相似文献
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《Nuclear Physics B》1996,462(1):99-140
We solve general 1-matrix models without taking the double scaling limit. A method of computing generating functions is presented. We calculate the generating functions for a simple and a double torus. Our method is also applicable to higher genus. Each generating function can be expressed by a “specific heat” function for the sphere. Universal terms, which survived in the double scaling limit can be easily picked out from our exact solutions. We also find that the regular part of the spherical generating function is at most bilinear in the coupling constants of the source terms. 相似文献