Birth and death processes and quantum spin chains

Abstract

This papers underscores the intimate connection between the quantum walks generated by certain spin chain Hamiltonians and classical birth and death processes. It is observed that transition amplitudes between single excitation states of the spin chains have an expression in terms of orthogonal polynomials which is analogous to the Karlin-McGregor representation formula of the transition probability functions for classes of birth and death processes. As an application, we present a characterization of spin systems for which the probability to return to the point of origin at some time is 1 or almost 1.

14 pages

References in corpus (4)

• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Mirror Inversion of Quantum States in Linear Registers
• Almost perfect state transfer in quantum spin chains

Cited by in corpus (7)

• Analytic next-to-nearest neighbour XX models with perfect state transfer and fractional revival
• A graph with fractional revival
• Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials
• Exactly solvable inhomogeneous fermion systems
• Quantum vs Classical Birth and Death Processes; Exactly Solvable Examples
• Perfect State Transfer in Laplacian Quantum Walk
• Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes