Supersymmetry in Jahn-Teller systems

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Abstract
Supersymmetric Hamiltonians are constructed for E(X) epsilon and T(X) tau Jahn-Teller systems in octahedral symmetry. These represent a new class of Jahn-Teller Hamiltonians with a higher continuous symmetry, since they necessarily include anharmonic couplings among the vibrational modes. In such applications, supersymmetry has the physical consequences of relating Jahn-Teller energies to purely anharmonic energy shifts of pure vibrational states, and of relating Ham reduction factors to anharmonic dressing or renormalisation of the matrix elements of a vibrational operator. In each of the above systems a supergroup classification scheme is used to assign levels, and perturbation calculations are made of Ham reduction factors and the associated anharmonic renormalisation effects.

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