Howland will investigate stability and chaos in quantum systems with Hamiltonians almost periodic in time; existence of scarred wave functions and resonant states corresponding to unstable periodic orbits of the classical system; perturbation theory of the multiphoton a.c. Stark effect; and existence of absolutely continuous spectra in random Schroedinger operators and other systems. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.
