Ph.D., 1970 - University of Chicago
Currently, I am exploring a general analytical technique for solving time-dependent operator equations through a succession of unitary integrations. The Bloch-Liouville equation for a (2j+1)-level system in time-dependent fields is of particular interest, along with current topics in nuclear magnetic resonance and quantum bits. The method extends to dissipation and decoherence which are of great interest in quantum information and quantum computing. Proceeding in analogy to the Bloch sphere construction for a single spin (two-level system), a geometrical construction describes higher dimensional spheres and other manifolds for two-spin and larger systems. A related investigation is to alter the evolution of entanglement between two spins in the presence of dissipation and decoherence. The so-called sudden death of entanglement can be delayed or averted by suitable local actions on the two spins.
Our recent interest is in the area of quantum information: studies of entanglement and other correlations such as quantum discord, their evolution under dissipative and decoherent processes and how they may be controlled, geometrical and symmetry studies of operators and states of N qubits and connections betweem the Lie and clifford algebras involved with topics in projective geometry and design theory.