5 papers · 1 filter
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…
Exponential Suppression of Transport in Electric Quantum Walks
Houssam Abdul-Rahman, Christopher Cedzich, Günter Stolz +1
We establish exact scalings for the maximal group velocity of translation-invariant quantum walks in periodic electric fields. Our main result shows that the maximal group velocity…
Sharp Polynomial Velocity Decay Bounds for Multidimensional Periodic Schrödinger Operators
Houssam Abdul-Rahman, Jake Fillman, Christoph Fischbacher +1
We investigate periodic Schrödinger operators in arbitrary dimensions in the large coupling regime. Our results establish that both the Lieb--Robinson velocity and the asymptotic…
Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems
Houssam Abdul-Rahman, Robert Sims, Günter Stolz
We provide an analytic method for estimating the entanglement of the non-gaussian energy eigenstates of disordered harmonic oscillator systems. We invoke the explicit formulas of t…
Slow propagation velocities in Schrödinger operators with large periodic potential
Houssam Abdul-Rahman, Mohammed Darras, Christoph Fischbacher +1
Schrödinger operators with periodic potential have generally been shown to exhibit ballistic transport. In this work, we investigate if the propagation velocity, while positive, c…