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math-ph2026
Bottleneck Effects and Harmonic-Type Velocity Bounds for Periodic Quantum Walks
Houssam Abdul-Rahman, Thomas A. Jackson, Darren C. Ong
We prove explicit upper bounds on the propagation velocity of one-dimensional quantum walks with periodic coins of arbitrary period. We treat two complementary settings. First, in…
math-ph2018
On a description of the Toda hierarchy using cocycle maps
Darren C. Ong
The Toda hierarchy refers to a family of integrable flows on Jacobi operators that have many applications in mathematics and physics. We demonstrate carefully that an alternative c…
math-ph2017
Spectral Approximation for Ergodic CMV Operators with an Application to Quantum Walks
Jake Fillman, Darren C. Ong, Tom Vandenboom
We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices…