44 citations · 154 across the 14 of their papers we have counts for
16 papers
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 v…
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, ca…
Exponentially decaying velocity bounds of quantum walks in periodic fields
Houssam Abdul-Rahman, Günter Stolz
We consider a class of discrete-time one-dimensional quantum walks, associated with CMV unitary matrices, in the presence of a local field. This class is parametrized by a transmis…
Dynamical Evolution of Entanglement in Disordered Oscillator Systems
Houssam Abdul-Rahman
We study the non-equilibrium dynamics of a disordered quantum system consisting of harmonic oscillators in a -dimensional lattice. If the system is sufficiently localized, we sh…
Entanglement bounds in the XXZ quantum spin chain
Houssam Abdul-Rahman, Christoph Fischbacher, Günter Stolz
We consider the XXZ spin chain, characterized by an anisotropy parameter , and normalized such that the ground state energy is and the ground state given by the all spins…
A class of two-dimensional AKLT models with a gap
Houssam Abdul-Rahman, Marius Lemm, Angelo Lucia +2
The AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki also conjec…
On the Regime of Localized Excitations for Disordered Oscillator Systems
Houssam Abdul-Rahman, Robert Sims, Günter Stolz
We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle Hamiltonian. This le…
Entanglement of a class of non-Gaussian states in disordered harmonic oscillator systems
Houssam Abdul-Rahman
For disordered harmonic oscillator systems over the -dimensional lattice, we consider the problem of finding the bipartite entanglement of the uniform ensemble of the energy eig…
Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches
Houssam Abdul-Rahman, Robert Sims, Günter Stolz
We prove spatial decay estimates on disorder-averaged position-momentum correlations in a gapless class of random oscillator models. First, we prove a decay estimate on dynamic cor…
Localization Properties of the XY Spin Chain. A review of mathematical results with an eye toward Many-Body Localization
Houssam Abdul-Rahman, Bruno Nachtergaele, Robert Sims +1
We review several aspects of Many-Body Localization-like properties exhibited by the disordered XY chains: localization properties of the energy eigenstates and thermal states, pro…
Entanglement Dynamics of Disordered Quantum XY Chains
Houssam Abdul-Rahman, Bruno Nachtergaele, Robert Sims +1
We consider the dynamics of the quantum XY chain with disorder under the general assumption that the expectation of the eigenfunction correlator of the associated one-particle Hami…
Fast and numerically stable circle fit
Houssam Abdul-Rahman, Nikolai Chernov
We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoid…
A uniform area law for the entanglement of eigenstates in the disordered XY chain
Houssam Abdul-Rahman, Günter Stolz
We consider the isotropic or anisotropic XY spin chain in the presence of a transversal random magnetic field, with parameters given by random variables. It is shown that eigenfunc…