Characterize anomalous transport points in the SU(3) parameter space

Determine the locations and transport behavior of the parameter-space points near the diagonal and antidiagonal regions around β ≈ ±π/2, γ ≈ π/2, and β ≈ ±π, γ ≈ ±π that exhibit enhanced sensitivity and crossover structures in the side-resolved variance and mean-position ratios for the three-component discrete-time quantum walk governed by the SU(3) coin operator.

Background

The paper studies a three-component discrete-time quantum walk on a one-dimensional lattice, with the internal states moving right, remaining stationary, or moving left. Its coin operator is a three-parameter SU(3) construction generated by Gell–Mann matrices, with α fixed at π/4 and β and γ controlling couplings to the third internal component.

Side-resolved observables reveal structured transport boundaries and crossover behavior in the parameter space. In particular, near β ≈ ±π/2 and γ ≈ π/2, the authors observe enhanced probability-current sensitivity and additional crossovers between the left and right halves of the lattice. Similar points occur near diagonal and antidiagonal parameter values around β ≈ ±π and γ ≈ ±π, but the mechanism determining their locations and transport signatures is not resolved.