The spatial statistical properties of wave functions in a disordered finite one-dimensional sample

For a given wave function one can define a quantity $\mu_E$ having a meaning of its inverse spatial size. The Laplace transform of the distribution function $P(\mu_E)$ is calculated analytically for a 1D disordered sample with a finite length $L$.Comment: LaTEX, 7 pages, Preprint IFUM-456/FT, Milano, Jan.199

Passive scalar convection in 2D long-range delta-correlated velocity field: Exact results

The letter presents new field-theoretical approach to 2D passive scalar problem. The Gaussian form of the distribution for the Lyapunov exponent is derived and its parameters are found explicitly.Comment: 11 pages, RevTex 3.0, IFUM-94/455/January-F

Mean Field Approach to the Giant Wormhole Problem

We introduce a gaussian probability density for the space-time distribution of wormholes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic ``large'' universe.Comment: 10 pages, Late