Problem of a quantum particle in a random potential on a line revisited

The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the spectral variables and the parameters of isospectral transformations of the potential. These transformations are given explicitly by the flows of the Korteweg-de Vries hierarchy which deform the potential leaving all its spectral properties invariant. Making use of conservation laws reduces the initial Feynman integral to a combination of quadratures which can be readily calculated. Different formulations of the problem are analyzed.Comment: 11 pages, RevTex, preprint ANU-RSPhySE-20994 (comment added

B(H) Constitutive Relations Near H_c1 in Disordered Superconductors

We provide a self-contained account of the B vs. H constitutive relation near H_c1 in Type II superconductors with various types of quenched random disorder. The traditional Abrikosov result B ~ [ln (H - H_c1)]^{-2}, valid in the absence of disorder and thermal fluctuations, changes significantly in the presence of disorder. Moreover, the constitutive relations will depend strongly on the type of disorder. In the presence of point disorder, B ~ (H - H_c1)^{3/2} in three-dimensional (thick) superconductors, as shown by Nattermann and Lipowsky. In two-dimensional (thin film) superconductors with point disorder, B ~ (H - H_c1). In the presence of parallel columnar disorder, we find that B ~ exp[-C / (H - H_c1)] in three dimensions, while B ~ exp[-K / (H - H_c1)^{1/2}] in two dimensions. In the presence of nearly isotropically splayed disorder, we find that B ~ (H - H_c1)^{3/2} in both two and three dimensions.Comment: 37 pages, 12 figures included in text; submitted to Physica