Monday, October 20, 2008, Joint Physics Colloquium, 4:30 PM, 104 Thaw Hall, PITT

Dr. Cosmas Zachos

Argonne National Laboratory

"Deformation Quantization: Quantum Mechanics Lives & Works in Phase-Space"

Abstract:

Wigner's 1932 quasi-probability Distribution Function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum flows in: semi-classical limits; quantum optics; nuclear physics; decoherence (e.g., quantum computing); quantum chaos. It is also of importance in signal processing (time-frequency analysis).

Nevertheless, a remarkable aspect of its internal logic, pioneered by the late J Moyal, has only emerged in the last quarter-century: It furnishes a third, alternate, formulation of Quantum Mechanics, independent of the conventional Hilbert-space, or path-integral formulations, and perhaps more intuitive---since it shares language with classical mechanics.

It is logically complete and self-standing, and accommodates the uncertainty principle in an unexpected manner. Simple illustrations of this fact will be detailed.