Staggered Ladder Spectra

Details Staggered Ladder Spectra Staggered Ladder Spectra

2005-10-05

arxiv.org/abs/cond-mat/0510113v1

Phys. Rev. Lett. 96, 030601 (2006)

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.96.030601

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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