William Rainey Harper

Norm Estimates of Harper Operators

n denotes the canonical orthonormal basis in l2. The study of the spectral properties of this class of operators has attracted a significant amount of interest in the past couple of decades (see [5], [3], [8], [1], [10], [14], [12], [7] for some of the most important developments). Most of this work has focused on the “Ten Martini problem” of M. Kac, concerning the possible values of the labels...

Quantum diffusion in the generalized Harper equation

We study numerically the dynamic and spectral properties of a one-dimensional quasi-periodic system, where site energies are given by k = V cos 2πf xk with xk denoting the kth quasiperiodic lattice site. When 2πf is given by the reciprocal lattice vector G(m, n) with n and m being successive Fibonacci numbers, the variance of the wavepacket is found to grow quadratically in time, regardless of ...

Harper skirts transparency on foreign aid.

Polymorphic Type Assignment and CPSConversionRobert Harper

Meyer and Wand established that the type of a term in the simply typed -calculus may be related in a straightforward manner to the type of its call-by-value CPS transform. This typing property may be extended to Scheme-like continuation-passing primitives, from which the soundness of these extensions follows. We study the extension of these results to the Damas-Milner polymorphic type assignmen...

trange nonchaotic attractors in Harper maps

n the last two decades there has been an enormous inerest in the so-called strange nonchaotic attractors SNA). These attracting invariant objects of dynamical ystems capture the evolution of a large subset of the hase space and are very relevant for their description. n particular, SNA are geometrically complicated (they re strange) and their dynamics is regular (in most of the xamples, quasipe...