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

Stability of condensate in superconductors

According to the BCS theory the superconducting condensate develops in a single quantum mode and no Cooper pairs out of the condensate are assumed. Here we discuss a mechanism by which the successful mode inhibits condensation in neighboring modes and suppresses a creation of noncondensed Cooper pairs. It is shown that condensed and noncondensed Cooper pairs are separated by an energy gap which is smaller than the superconducting gap but large enough to prevent nucleation in all other modes and to eliminate effects of noncondensed Cooper pairs on properties of superconductors. Our result thus justifies basic assumptions of the BCS theory and confirms that the BCS condensate is stable with respect to two-particle excitations

Unbound states in quantum heterostructures

We report in this review on the electronic continuum states of semiconductor Quantum Wells and Quantum Dots and highlight the decisive part played by the virtual bound states in the optical properties of these structures. The two particles continuum states of Quantum Dots control the decoherence of the excited electron – hole states. The part played by Auger scattering in Quantum Dots is also discussed