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Staggered Ladder Spectra

E. Arvedson·M. Wilkinson·B. Mehlig·K. Nakamura
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Abstract

We exactly solve a Fokker-Planck equation by determining its eigenvalues and eigenfunctions: we construct nonlinear second-order differential operators which act as raising and lowering operators, generating ladder spectra for the odd and even parity states. These are staggered: the odd-even separation differs from even-odd. The Fokker-Planck equation describes, in the limit of weak damping, a generalised Ornstein-Uhlenbeck process where the random force depends upon position as well as time. Our exact solution exhibits anomalous diffusion at short times and a stationary non-Maxwellian momentum distribution.

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E. Arvedson, M. Wilkinson, B. Mehlig, K. Nakamura. 2005-10-05. Staggered Ladder Spectra. https://doi.org/10.1103/physrevlett.96.030601

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