Quantum Perfect State Transfer in a 2D Lattice

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• 作者：Sarah Post (1)
  
  1. Department of Mathematics ; University of Hawai鈥榠 ; Honolulu ; HI ; 96822 ; USA
  
• 关键词：Discrete models ; Spin systems ; Harmonic oscillator ; Orthogonal polynomials
• 刊名：Acta Applicandae Mathematicae
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：135
• 期：1
• 页码：209-224
• 全文大小：588 KB
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• 刊物主题：Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9036

文摘

A finite oscillator model based on two-variable Krawtchouk polynomials is presented and its application to spin dynamics is discussed. The model is defined on a triangular lattice. The conditions that the system admit a form of perfect state transfer where the excitation spectrum is isolated to the boundary of the domain is investigated. We give the necessary bounds on the parameters of the model and a sufficient condition on the ratios of the frequencies of the Hamiltonian. The stronger case where the excitation is isolated at a point is also investigated and shown to exist only in degenerate cases. We then focus on systems with rational frequencies, namely the superintegrable cases and their perfect state transfer properties. We see that these systems interpolate between two, one-dimensional spin chains. By using a parameter in the model as a control parameter, we show that it is possible to steer the excitation spectrum to be isolated at either of the two vertices of the triangle with perfect fidelity.