Staggered Ladder Spectra

Arvedson, E.; Wilkinson, M.; Mehlig, B. and Nakamura, K. (2006). Staggered Ladder Spectra. Physical Review Letters, 96(3) 030601.

DOI: https://doi.org/10.1103/PhysRevLett.96.030601

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. The ladders are staggered: the odd-even separation differs from even-odd. The Fokker-Planck equation corresponds, in the limit of weak damping, to a generalized Ornstein-Uhlenbeck process where the random force depends upon position as well as time. The process describes damped stochastic acceleration, and exhibits anomalous diffusion at short times and a stationary non-Maxwellian momentum distribution.

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