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Feb 2013

Volume 54, Issue 2, Articles (02xxxx)

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J. Math. Phys. 54, 021506 (2013); http://dx.doi.org/10.1063/1.4790887 (24 pages)

Gui-Qiang Chen, Vaibhav Kukreja, and Hairong Yuan
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back to top Representation Theory and Algebraic Methods

Generalized Bell states and principal realization of the Yangian Y(mathN)

Ming Liu, Chengming Bai, Mo-Lin Ge, and Naihuan Jing

J. Math. Phys. 54, 021701 (2013); http://dx.doi.org/10.1063/1.4789317 (11 pages)

Online Publication Date: 1 February 2013

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We prove that the action of the Yangian algebra Y(mathN) is better described by the principal generators on the tensor product of the fundamental representation and its dual. The generalized Bell states or maximally entangled states are permuted by the principal generators in a dramatically simple manner on the tensor product. Under the Yangian symmetry the new quantum number J2 is also explicitly computed, which gives an explanation for these maximally entangled states.
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03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)
03.67.Lx Quantum computation architectures and implementations
02.10.-v Logic, set theory, and algebra

Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials

J. T. Hartwig and J. V. Stokman

J. Math. Phys. 54, 021702 (2013); http://dx.doi.org/10.1063/1.4790566 (20 pages)

Online Publication Date: 11 February 2013

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We realize an extended version of the trigonometric Cherednik algebra as affine Dunkl operators involving Heaviside functions. We use the quadratic Casimir element of the extended trigonometric Cherednik algebra to define an explicit nonstationary Schrödinger equation with delta-potential. We use coordinate Bethe ansatz methods to construct solutions of the nonstationary Schrödinger equation in terms of generalized Bethe wave functions. It is shown that the generalized Bethe wave functions satisfy affine difference Knizhnik-Zamolodchikov equations as functions of the momenta. The relation to the vector valued root system analogs of the quantum Bose gas on the circle with delta-function interactions is indicated.
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05.30.Jp Boson systems
02.20.Uw Quantum groups
03.65.Fd Algebraic methods
03.65.Ge Solutions of wave equations: bound states

Group-theoretical derivation of Aharonov-Bohm phase shifts

C. R. Hagen

J. Math. Phys. 54, 021703 (2013); http://dx.doi.org/10.1063/1.4792234 (4 pages)

Online Publication Date: 20 February 2013

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The phase shifts of the Aharonov-Bohm effect are generally determined by means of the partial wave decomposition of the underlying Schrödinger equation. It is shown here that they readily emerge from an math(2,1) calculation of the energy levels employing an added harmonic oscillator potential which discretizes the spectrum.
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03.65.Ge Solutions of wave equations: bound states
03.65.Ta Foundations of quantum mechanics; measurement theory
02.20.-a Group theory
03.65.Fd Algebraic methods
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