Quantization of Thought

Franco Gallone, Antonio Sparzani

Segal quantization, usually thought of and used as a tool for quantizing kinematical frameworks, is extended to (finite-dimensional) dynamical systems, i.e., to kinematical frameworks plus dynamical motions applied to them. Such a procedure allows us to classify quantum dynamical systems, and to understand how physical inequivalence appears in spite of von Neumann unitary equivalence, for the former is also grounded on the evolution operators of the systems being different functions of the labeled observables of the systems. Second quantization is also examined and is shown to be just one possible procedure of quantization, which can only be used in a particular class of cases.

Ray LaPierre

Maurice A. de Gosson, Franz Luef

The usual Poisson bracket { A , B } can be identified with the so-called Moyal bracket { A , B } M for larger classes of symbols than was previously thought, provided that one uses the Born–Jordan quantization rule instead of the better known Weyl correspondence. We apply our results to a generalized version of Ehrenfest’s theorem on the time evolution of averages of operators.

Enrico Fonda, David P. Meichle, Nicholas T. Ouellette +2 more

Quantized vortices are key features of quantum fluids such as superfluid helium and Bose-Einstein condensates. The reconnection of quantized vortices and subsequent emission of Kelvin waves along the vortices are thought to be central to dissipation in such systems. By visualizing the motion of submicron particles dispersed in superfluid (4)He, we have directly observed the emission of Kelvin waves from quantized vortex reconnection. We characterize one event in detail, using dimensionless similarity coordinates, and compare it with several theories. Finally, we give evidence for other examples of wavelike behavior in our system.

Ray LaPierre