The University of Queensland

Centre for Mathematical Physics

SEMINARS

Thursday 1^st November, 2007

Priestley Building, room 641

An exactly solvable asymmetric rotor Hamiltonian

Luke Yates

11.00am

Abstract:

The rigid rotor Hamiltonian is the textbook model used for the determination of rotational spectra in applications of molecular spectroscopy. In the symmetric (prolate-oblate) limits the model is trivially handled in the quantum case using the angular momentum algebra. However the asymmetric case, in particular for large total angular momentum, solutions are surprisingly difficult.

Using Schwinger’s oscillator model of the angular momentum algebra we show that the rigid rotor Hamiltonian becomes a specific combination of generators of the dynamical su(1,1) symmetry algebra and look to the methods of exactly solvable models, via Yang-Baxter algebras and the Bethe Ansatz, for solutions.

We show that the symmetric case belongs the class of exactly solvable Hamiltonians associated with the rational R-matrix and Yang-Baxter algebra Y(gl(2)) whilst the trigonometric extension to Y(sl_q(2)), with realisations in terms of q-deformed algebras, yields at best the special case of the most anisotropic rotor.

Continuous Variable EPR States

Sol Jacobsen

11.30am

Abstract:

In 1994 Fan Hong-yi and John Klauder gave explicit forms of the common eigenvectors of relative position and total momentum of the two particles considered by Einstein, Podolsky and Rosen (EPR) in 1935. EPR posited that either quantum mechanics is incomplete, or spatiotemporal locality is violated. Numerous experiments have been performed to test Bell’s assertion that hidden variables could not explain the discrepancy if we want to keep the probabilities predicted by quantum mechanics, and the discrete case is now well documented. Hong-yi and Klauder’s result provides a new way to consider the extension of this work to continuous variables. This short presentation will explain the context of the EPR experiment, outline the development of CHSH inequalities and Wigner functions for continuous variables and compare the work with current quantum optics implementations.