Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials

Abstract

Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival is shown to take place in the corresponding quantum walks.

22 pages, 4 figures

References in corpus (9)

• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Mirror Inversion of Quantum States in Linear Registers
• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
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• A graph with fractional revival
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Cited by in corpus (1)

• Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes