Research Projects in Theoretical Physics
For further information on any particular research topics, check with the individual faculty members:
This man studies cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient of a neutral gas. Here, we take another look at this approach, and discuss the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the 'pole' expansion and the physical significance of the 'higher' poles.
My current projects center on the theoretical and computational investigation of the properties and behaviors of neutron stars and black holes. I am especially interested in the gravitational and electromagnetic radiation that can be emitted by these compact objects either individually, in binary systems or through their interactions with their surroundings. This overarching theme results in many specific analytic and computational projects. Examples include the development of techniques for solving various partial differential equations, understanding the physics of relativistic fluid and magnetohydrodynamic flows, simulating complicated magnetic field topologies inside and around magnetars, evolving single and binary compact objects as sources of observable radiation, and understanding gravitational collapse and the properties of black holes in non-vacuum environments.
Neutron star collapse, supernovae, gamma-ray sources, etc., are some of the exciting topics in relativistic astrophysics, and the perfect fluid is the fundamental model for all of these. I study relativistic perfect fluids near black holes using computational methods. In particular, Eric Hirschmann, Steven Millward and I at BYU are studying a magnetized fluid around a black hole with computational Magneto-Hydrodynamics (MHD). Various computational projects are available in RFD and MHD, which require writing, testing and running computer programs to model relativistic fluids.
My group studies properties of mathematical modeling in variety of fields using information theory, differential geometry, and computational methods. There is a deep connection between models and geometry. In essence, a mathematical model is a mapping between parameters and data which means we can study mathematical models generally as abstract manifolds in data space. I am particularly interested how complex systems can be described by relatively simple models. Complicated systems often display emergent behaviors that are both remarkably simple and very different from the microscopic physics that make up the system (for example, biological behavior is very different from chemstry, which in turn is very different from particle physics). We consider a variety of models in order to discover the emergent physical laws that govern its behavior. More broadly, we look to understand the physical and mathematical origins of emergence. Potential projects include the study of specific physical systems (for example in biology, condensed matter physics, engineering, climate, and others), as well as the development of more general theoretical and computational tools for exploring model properties.
Jean-Francois Van Huele
Members of our group solve conceptual and technical problems in the area of quantum dynamics (QD), quantum information (QI), and the vast domain where the two overlap (QID). QD studies the evolution of systems that obey the quantum rules of microscopic physics, with applications in quantum optics, atomic physics, optomechanics, and material science. QD uses techniques of differential equations, operator calculus, and abstract algebra to answer questions such as: how do the characteristics of a quantum system change over time? How is energy transferred between different parts of a system? What is the likelihood that transitions will occur? How do we find the currents of probability or spin? What models are sufficiently simple to be soluble but complex enough to capture the relevant physics? QI deals with how we access, and process what we know about quantum systems. QI uses techniques of linear algebra, geometry, and probability to decide what we can know about systems through measurement, how correlated these systems may be, and to what extent we can control systems and use them for designing new quantum technologies such as cloning, teleportation, or disembodiment. QID describes measurement, entanglement, and control as a dynamical process of interacting quantum systems.