A prominent theme of modern condensed matter physics is electronic transport – in particular the electrical conductivity – of disordered metallic systems at very low temperatures. From the Landau theory of weakly interacting Fermi liquids one expects the essential aspects of the situation to be captured by the single-electron approximation. Mathematical models that have been proposed and studie...

Using the irreducible representations of the group SO(d+1), we discuss the degeneracy symmetry of hydrogen atom in d-dimensions and calculate its energy spectrum as well as the correspouding degeneracy. We show that SO(d + 1) is the energy spectrum generating group. PACS : 03.65.Fd

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system – which we show is essentially ...

We propose a factorization scheme for ordinary differential equations with polynomial nonlinearities (reaction-diffusion in the traveling frame and dampedanharmonic-oscillator equations) which is different and more efficient than that given by L.M. Berkovich in Sov. Math. Dokl. 45, 162 (1992). We then invert the factorization brackets in the SUSYQM style to get ODE’s with a different polynomial...