Introduction to Research
My research is in the branch of theoretical physics, known as "condensed matter", that seeks to understand the properties of materials from a fundamental microscopic basis. The last two decades have been a time of much progress in this area, driven primarily by the experimental discovery of a number of new, technologically important materials. A well-known example is the class of materials known as high-temperature superconductors: these are crystals of oxygen, copper, and two or more transition metals which conduct electricity without resistance at relatively high temperatures. Also siginificant are the artificial materials created by deposition of atoms on a surface, one layer at a time--these are found in the semiconductor lasers in CD players and disk drives.
When atoms form crystals, they only partially retain their identity. While electrons in the inner-most shells remain tightly bound to their respective atomic nuclei, the outer-most electrons are often liberated from their nuclei, and move throughtout the entire crystal. The interesting properties of all of the materials noted above are associated with the motion of these electrons in a variety of crystalline environments.
We now know a great deal about the properties of single electrons under such conditions. Each electron is a point-like particle which obeys the principles of quantum mechanics: both its position and its velocity cannot be simultaneously determined at any one time (the Heisenberg uncertainty principle), but rather its dynamics must be described using a "wave-function" which obeys Schroedinger's equation---this is the generalization of Newton's Laws of motion to the wavelike motion of quantum particles. In addition to moving through the crystal, each electron also spins on its own axis: this "spin" can be either in a clockwise or anti-clockwise direction, and is the property underlying the phenomenon of magnetism.
The interesting properties of the new materials are not those of single electrons, but arise from the collective dynamics of a very large number of electrons--on the order of Avogadro's number or about a trillion trillion electrons. Each electron repels every other by the Coulomb electrostatic force, and this tendency of electrons to stay apart from each other leads to many surprising new physical phenomena. The study of the emergent, collective properties of a fluid of mutually repelling quantum electrons is a significant part of modern theoretical physics, and the primary area of my research.
A key new idea that becomes necessary upon considering more than one electron is that of quantum entanglement. This is a non-local superposition of distinct states of two electrons, such that observation of one electron instantaneously determines the state of the other electron: often referred to as " spooky action-at-a-distance". The remarkable fact is that quantum entanglement can also be non-trivial for very large numbers of electrons, and can then determine their physical properties on a macroscopic scale, and so be easily observable in a laboratory. The subject of quantum matter is a central focus of my research, and its aim is to describe the connection between physical properties of numerous modern materials and the nature of quantum entanglement in the many-particle wavefunction.