Mathematical Physics

Our research in Mathematical Physics focuses on quantum information theory, nanotechnology and quantum gravity and cosmology.

The goal of quantum information theory is to study and utilize the profound way in which quantum effects can influence the physical propagation and processing of information. It is part of the world-wide effort to develop methods for controlling individual molecules, atoms and photons. One of the main goals is to utilize the quantum mechanical phenomenon of entanglement to achieve a quantum parallelization of computation. This can then provide an exponential speed-up of certain types of calculations. The same quantum phenomena can be used to protect information channels (for example, fibre optic channels) from eavesdropping, a proven technology which already has cryptographic applications. In this context, some of our faculty members are closely involved with University of Waterloo’s Institute for Quantum Computing (IQC).

Nanotechnology is a confluence of the global research efforts of teams of physicists, chemists, molecular biologists, and engineers towards creating nanometer-sized devices with new functionalities. An important role in those developments is played by carbon nano-structures, such as fullerenes, nanotubes, and graphene. Investigation of their properties involves a range of mathematical and computational methods relevant to both quantum and classical physics, and is naturally linked to the other areas of research in the department. In this context, some of our faculty members are closely involved with the Waterloo Institute for Nanotechnology (WIN).

At the present time cosmology is considered to be in its “golden age”, with key advances in its mathematical description driven by a wealth of data from satellite-based telescopes. Cosmology also provides an arena for developing and testing theories of quantum gravity, since it is expected that classical general relativity breaks down in the very early universe and that quantum effects will come into play. In this context, some faculty members are also closely involved with the Perimeter Institute for Theoretical Physics.

The regular faculty whose primary research interest is Mathematical Physics are:

• J. Emerson (quantum computing, foundations of quantum theory)
• A. Kempf (quantum information theory, quantum fluctuations of spacetime and the cosmic microwave background radiation, quantum gravity)
• F. Girelli (quantum gravity, noncommutative geometry)
• Z. Miskovic (nanoscale physics, carbon nanostructures)

• E. Martin-Martinez (relativistic quantum information, quantum theory, general relativity, information and the structure of spacetime)

• G. Geshnizjani (cosmology,physics of early universe, dark energy, cosmic microwave background, large scale structure of the universe)

• G. Smith (Quantum Information and Computing)

• J. Wallman (quantum computing, quantum characterization and the foundations of quantum theory)

 Cross-appointed faculty:

• A. Jagannath (equilibrium and non-equilibrium statistical mechanics, disordered media, spin glasses, statistical physics methods in high-dimensional statistics and non-convex optimization)

Retired faculty members who continue to be active in research in this field, and are involved in graduate supervision are: J. Paldus, R.G.McLenaghan, and J. Wainwright.