Faculty & Staff

Dr. William Hodge

Director of Introductory Physics
  • Profile

    William Hodge is a theoretical solid-state physicist. He uses both analytical and numerical methods to calculate geometric phases in quantum systems.

    It is well established that when a quantum system undergoes an adiabatic process, the energy eigenfunctions of the system can acquire two phases: (1) a dynamic phase and (2) a geometric phase. Although the acquired phase is not measurable, when the system undergoes an adiabatic loop (that is, a closed cycle) the resulting geometric phase is not arbitrary. There are profound physical implications to this and the study of geometric phases has become a productive area of research in a wide variety of disciplines including nuclear physics, molecular physics, and spin-wave dynamics. For example, the modern theory of macroscopic polarization was established by expressing the polarization of a crystalline dielectric as a geometric phase.

  • Selected Publications
    Journal Articles

    W. B. Hodge, E. D. Welchman and M. J. Rave. “Non-trivial Berry phase for an asymmetric one-dimensional potential in the free electron limit.” Eur. Phys. J. B. 84, 351 (2011). https://doi.org/10.1140/epjb/e2011-20576-0

    W. B. Hodge, S. V. Migirditch and W. C. Kerr. “Electron spin and probability current density in quantum mechanics.” Am. J. Phys. 82, 681 (2014). https://doi.org/10.1119/1.4868094

    W. B. Hodge, N. P. Cassera and M. J. Rave. “Berry phase oscillations in a simple model.” Eur. J. Phys. 40, 015401 (2019). https://doi.org/10.1088/1361-6404/aae7aa