Spin lattices, state transfer and bivariate Krawtchouk polynomials

Abstract

The quantum state transfer properties of a class of two-dimensional spin lattices on a triangular domain are investigated. Systems for which the 1-excitation dynamics is exactly solvable are identified. The exact solutions are expressed in terms of the bivariate Krawtchouk polynomials that arise as matrix elements of the unitary representations of the rotation group on the states of the three-dimensional harmonic oscillator.

Proceedings of Theory Canada 9, Waterloo, June 2014. Based on invited talk given by Luc Vinet at this conference

References in corpus (5)

• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Mirror Inversion of Quantum States in Linear Registers
• The multivariate Meixner polynomials as matrix elements of $SO(d,1)$ representations on oscillator states
• The Rahman Polynomials Are Bispectral
• The multivariate Charlier polynomials as matrix elements of the Euclidean group representation on oscillator states

Cited by in corpus (2)

• Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results
• Rahman polynomials