Further analysis of the connected moments expansion

We apply the connected moments expansion to simple quantum--mechanical examples and show that under some conditions the main equations of the approach are no longer valid. In particular we consider two--level systems, the harmonic oscillator and the pure quartic oscillator.Comment: 19 pages; 2 tables; 4 figure

Universal conductance fluctuations in non-integer dimensions

We propose an Ansatz for Universal conductance fluctuations in continuous dimensions from 0 up to 4. The Ansatz agrees with known formulas for integer dimensions 1, 2 and 3, both for hard wall and periodic boundary conditions. The method is based solely on the knowledge of energy spectrum and standard assumptions. We also study numerically the conductance fluctuations in 4D Anderson model, depending on system size L and disorder W. We find a small plateau with a value diverging logarithmically with increasing L. Universality gets lost just in 4D.Comment: 4 pages, 4 figures submitted to Phys. Rev.