## Seminarium ZTOC## Równanie dyfuzji i rozkłady Wignera## R. Wojnar (IPPT) |

1. It is considered a nonlinear diffusion equation in which the diffusion coefficient has the form D = a(t)f^n, where a = a(t) is an external time modulation, n is a positive constant, and f = f(x,t) is a solution to the nonlinear equation. It is shown that the Zeldovich-Kompaneets solution satisfies the equation if a = a(t) is replaced by the mean value of a. It is shown also that for n = 2 the Wigner semicircle distribution is obtained. 2. For an interpretation of nuclear energy spectra E. P. Wigner considered succession of spacings between adjacent energy levels, and demonstrated that the Gauss distribution multiplied by a linear function describes well the frequency of these spacings. It is shown that this Wigner distribution can be derived from a Smoluchowski diffusion equation under assumption of a special form of drift force.