We use scattering theoretic methods to prove strong dynamical and exponential local-ization for one-dimensional, continuum, Anderson-type models with singular distributions ; in particular, the case of a Bernoulli distribution is covered. The operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms. Our main… (More)
We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics.
We consider the Laplacian on a rooted metric tree graph with branching number K ≥ 2 and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission… (More)
We use scattering theoretic methods to prove exponential local-ization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reeection and transmission coeecients for compactly supported single site perturbations. We show that randomly displaced, non-reeectionless… (More)
Human gene expression patterns are controlled and coordinated by the activity of a diverse array of epigenetic regulators, including histone methyltransferases, acetyltransferases, and chromatin remodelers. Deregulation of these epigenetic pathways can lead to genome-wide changes in gene expression, with serious disease consequences. In recent years,… (More)
We construct a W *-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb-Robinson bounds for such systems on finite lattices .
For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, of arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C log L)/L. This… (More)
We summarize recent works on the stability under disorder of the absolutely continuous spectra of random operators on tree graphs. The cases covered include: Schrödinger operators with random potential, quantum graph operators for trees with randomized edge lengths, and radial quasi-periodic operators perturbed by random potentials.
We study one-dimensional, continuum Bernoulli-Anderson models with general single-site potentials and prove positivity of the Lyapunov exponent away from a discrete set of critical energies. The proof is based on Fürstenberg's Theorem. The set of critical energies is described explicitly in terms of the transmission and reflection coefficients for… (More)
In this study, the author explores the relationship between conflicting ethical expectations for lying behavior and employee attitudes. In a sample of 140 full-time employees, the findings indicated that as the difference between formal codes of ethics and supervisor expectations for lying behavior increases, intentions to turnover and expressed feelings of… (More)