Staggered Ladder Spectra
E. ArvedsonDepartment of Physics, Göteborg University, 41296 Gothenburg, SwedenMichael WilkinsonFaculty of Mathematics and Computing, The Open University, Walton Hall, Milton Keynes, MK7 6AA, United KingdomB. MehligDepartment of Physics, Göteborg University, 41296 Gothenburg, SwedenKatsuhiro NakamuraDepartment of Applied Physics, Osaka City University, Sumiyoshi-ku, Osaka 558-8585, Japan
2006en
ABI
Annotatsiya
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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