Mapping quantum-classical Liouville equation: projectors and trajectories

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.Comment: 4 figure

Fractionation of human immune γ-globulin

Equine and bovine serum proteins have recently been fractionated by means of a physical method utilizing an electrophoretic adaptation of the principles of the Clusius column (l-4), first described and tested by Kirkwood (5) and Nielsen (6). The method of electrophoresis-convection has now been applied to the fractionation of human γ-globulin. The γ-globulin was prepared by ethanol fractionation (7) from the plasma of individuals hyperimmunized to Hemophilus pertussis organisms. The resulting fractions of γ-globulin have been characterized electrophoretically, and the protective antibody activity and agglutinin titer have been measured

Chip-based microcavities coupled to NV centers in single crystal diamond

Optical coupling of nitrogen vacancy centers in single-crystal diamond to an on-chip microcavity is demonstrated. The microcavity is fabricated from a hybrid gallium phosphide and diamond material system, and supports whispering gallery mode resonances with spectrometer resolution limited Q > 25000

Reflective silicon binary diffraction grating for visible wavelengths

We introduce a new device based on sub-wavelength resonant gratings. We built a silicon-on-oxide reflective binary grating for visible light that mimics the functionality of a blazed diffraction grating in a flat geometry