44 citations · 74 across the 6 of their papers we have counts for
8 papers
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…
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…
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…
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…
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…