共查询到20条相似文献,搜索用时 15 毫秒
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We study some aspects of the theory of non-commutative differential calculi over complex algebras, especially over the Hopf algebras associated to compact quantum groups in the sense of S.L. Woronowicz. Our principal emphasis is on the theory of twisted graded traces and their associated twisted cyclic cocycles. One of our principal results is a new method of constructing differential calculi, using twisted graded traces. 相似文献
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Clement Ampadu 《中国物理 B》2014,(3):109-111
We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT. 相似文献
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In this Letter, we introduce the Hopf algebra structure of the quantum quaternionic group GL(1, H1) and discuss the isomorphism between the quantum symplectic group SPq(1) and the quantum unitary group SUq(2). 相似文献
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We present a differential calculus on the extension of the quantum plane obtained by considering that the (bosonic) generator x is invertible and by working with polynomials in ln x instead of polynomials in x. We construct the quantum Lie algebra associated with this extension and obtain its Hopf algebra structure and its dual Hopf algebra. 相似文献
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We give the complete set of irreducible representations of U(SU(2))q when q is a mth root of unity. In particular, we show that their dimensions are less or equal to m. Some of them are not highest-weight representations. 相似文献
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《Physics letters. [Part B]》1987,194(1):91-96
The SU(2) Yang-Mills quantum field is studied by Coulomb-gauge continuum-hamiltonian methods using a variational approximation. The field amplitudes are represented by a truncated momentum expansion in the spatial domain S3. The calculations support Gribov's scenario for the generation of a mass gap in the spectrum of physical states and the confinement of color. 相似文献
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The problem of the interaction between two quantum systems namely SU(1,1) and SU(2) is considered. Using the evolution operator technique, an exact solution of the wave function and consequently the density matrix are obtained. The entropy squeezing is examined and it has shown that, different values of the relative phase angle ? as well as the coupling parameter λ lead to different observation of the squeezing in the quadratures. In the meantime, we have shown that the entropy squeezing is also sensitive to the variation in the state angle θ, the detuning parameter Δ in addition to the excitation number m. Moreover, for a large value of the detuning parameter there is a weak entanglement between the atom and the quantum system and vice versa. Furthermore, we find that the Q-function is sensitive to the variation in the excitation number m in addition to the Bargmann index k where the nonclassical effect is pronounced for the even parity. 相似文献
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The nonlinear differential equation resulting from the use of the ’t Hooft-Corrigan-Fairlie-Wilczek ansatz in SU(2) Yang-Mills
gauge theory is solved by the bilinear operator method. The solutions which are singular are interpreted as fluctuations involving
no flux transport. However, these objects may play a tunnelling role similar to that of merons. 相似文献
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New 3-mode bosonic operator realization of SU(2) Lie algebra: From the point of view of squeezing 下载免费PDF全文
We consider the quantum mechanical SU(2) transformation e2λ JzJ± e-2λJz= e±2λJ± as if the meaning of squeezing with e±2λbeing squeezing parameter. By studying SU(2) operators(J±,Jz) from the point of view of squeezing we find that(J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation(the eigenvectors of J+ or J-) of the 3-mode squeezing operator e2λ Jz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators. 相似文献
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Making use of the general theory of connections invariant under a symmetry group which acts transitively on fibers, explicit solutions are derived for SU(2)×SU(2)-symmetric multi-instantons over S
2×S
2, with SU(2) structure group. These multi-instantons correspond to a principal fiber bundle characterized by a second Chern number given by 2m
2, with m an integer. 相似文献
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A.A. Zvyagin D.M. Apal'kov 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):565-569
We present a Bethe Ansatz based investigation of a one-dimensional (1D) Heisenberg spin chain in a real 3D crystal lattice.
We have shown that due to an influence of the lattice distortion on a crystalline field of ligands of magnetic ions, a Heisenberg
antiferromagnetic spin chain is unstable under the appearance of a magnetic anisotropy of the “easy-plane” type. The effects of an external magnetic
field and nonzero temperature onto such a phase transition are studied.
Received: 19 January 1998 / Revised: 16 March 1998 / Accepted: 17 March 1998 相似文献
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We propose a rational quantum deformed nonlocal currentsin the homogeneous space SU(2)k/U(1),and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level k=c is obtained.In the classical limit h→0,the quantum nonlocal currents become SU(2)k parafermion,and the realization of Yangian double becomes the parafermion realization of SU(2)k current algebra. 相似文献
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In this paper, we introduce a new way to obtain the Q-P (P-Q) ordering of quantum mechanical operators, i.e., from the classical correspondence of Q-P (P-Q) ordered operators by replacing q and p with coordinate and momentum operators, respectively. Some operator identities are derived concisely. As for its applications, the single (two-) mode squeezed operators and Fresnel operator are examined. It is shown that the classical correspondence of Fresnel operator’s Q-P (P-Q) ordering is just the integration kernel of Fresnel transformation. In addition, a new photo-counting formula is constructed by the Q-P ordering of operators. 相似文献
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R. Loll 《Nuclear Physics B》1991,350(3):831-860
Starting from Rovelli-Smolin's infinite-dimensional graded Poisson-bracket algebra of loop variables, we propose a new way of constructing a corresponding quantum representation. After eliminating certain quadratic constraints, we “integrate” an infinite-dimensional subalgebra of loop variables, using a formal group law expansion. With the help of techniques from the representation theory of semidirect-product groups, we find an exact quantum representation of the full classical Poisson-bracket algebra of loop variables, without any higher-order correction terms. This opens new ways of tackling the quantum dynamics for both canonical gravity and Yang-Mills theory. 相似文献
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It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SLq(2)) is a free module of finite rank over the coordinate ring of the classical group SL(2). An explicit set of generators is provided. 相似文献