David K. Hoffman
Physical Chemistry
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Research Interests
Work in our group is in two related areas, quantum dynamics and statistical mechanics (particularly kinetic theory). The two are closely coupled in that statistical mechanics seeks to explain the bulk, or macroscopic, properties of systems in terms of the properties and interactions of their constituent atoms and molecules. On the other hand the essential molecular information required for this purpose often requires a microscopic description of dynamical processes.
Presently we are developing new computational methods to treat inelastic and reactive molecular scattering. The basic approaches we are using derive from time-dependent quantum scattering theory wherein the colliding atoms and molecules are represented as wave packets. Scattering information that characterizes the collision process can be extracted from an analysis of the scattered wave after the encounter is complete. We have developed a new formalism to describe quantum dynamics, which we call the time-independent wavepacket approach, that can be thought of as a kind of hybrid between existing time-dependent and time-independent methods. Much of our effort is devoted to pioneering new computational schemes based on this approach. We are also very interested in developing new numerical methods well suited to the time-independent wavepacket approach. This includes devising accurate and efficient methods for representing functions and their derivatives on a grid and, in conjunction, developing polynomic expansions for operator functions of the Hamiltonian (e.g., the quantum propagator) on a grid. The ultimate goal is to extend the range of systems that can be rigorously treated by fully quantal methods. This goal requires a synthesis of theory and computation, and our efforts in quantum dynamics are divided between developing formal quantum dynamic theories, devising new computational algorithms and using these new methods in practical applications. With regard to the latter, we are very interested in developing computational schemes that are efficient for use on massively parallel computers. The dynamical methods used to treat molecular scattering systems can also be employed to investigate the quantum dynamics of other physical systems. One such application that we are presently exploring is the problem of electron transmission in so-called nanostructure devices. These are electronic devices that are so small that they are essentially quantal in nature and cannot be adequately described by classical theories.
We are also interested in problems in non-equilibrium statistical mechanics and kinetic theory that require dynamical data, such as discussed above, as input.
