The Phase Space of Finite Systems

Details The Phase Space of Finite Systems The Phase Space of Finite Systems

Oct 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000hscm.conf..349w&link_type=abstract

HAMILTONIAN SYSTEMS AND CELESTIAL MECHANICS (HAMSYS-98). Proceedings of the III International Symposium. Held 7-11 December 1998

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Scientific paper

The Newton equation of a shallow optical waveguide (a harmonic oscillator) is compatible with the algebraic structure of SU(2). Wavefunctions satisfy orthogonality relations with respect to a discrete measure of 2ℓ + 1 points, of position, momentum, or mode number. The Wigner function for SU(2) in the representation ℓ devolves the classical 'c-number' variables of position, momentum, and energy, picturing the state -- a (2ℓ + 1)-dimensional vector of sensor data -- on the surface of a sphere of radius l + (1)/(2). The three coordinates are canonically conjugate in this SU(2) sense. Linear SU(2)-optical systems rotate the sphere rigidly, while others deform it nonlinearly.

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