A Discrete Version of the Inverse Scattering Problem and the J-matrix Method

The problem of the Hamiltonian matrix in the oscillator and Laguerre basis construction from the S-matrix is treated in the context of the algebraic analogue of the Marchenko method.Comment: 11 pages. The Laguerre basis case is adde

Local density of states at polygonal boundaries of d-wave superconductors

Besides the well-known existence of Andreev bound states, the zero-energy local density of states at the boundary of a d-wave superconductor strongly depends on the boundary geometry itself. In this work, we examine the influence of both a simple wedge-shaped boundary geometry and a more complicated polygonal or faceted boundary structure on the local density of states. For a wedge-shaped boundary geometry, we find oscillations of the zero-energy density of states in the corner of the wedge, depending on the opening angle of the wedge. Furthermore, we study the influence of a single Abrikosov vortex situated near a boundary, which is of either macroscopic or microscopic roughness.Comment: 10 pages, 11 figures; submitted to Phys. Rev.

NN potentials from inverse scattering in the J-matrix approach

An approximate inverse scattering method [7,8] has been used to construct separable potentials with the Laguerre form factors. As an application, we invert the phase shifts of proton-proton in the $^1S_0$ and $^3P_2-^3F_2$ channels and neutron-proton in the $^3S_1-^3D_1$ channel elastic scattering. In the latter case the deuteron wave function of a realistic $np$ potential was used as input.Comment: LaTex2e, 17 pages, 3 Postscript figures; corrected typo

Semiclassical theory of weak antilocalization and spin relaxation in ballistic quantum dots

We develop a semiclassical theory for spin-dependent quantum transport in ballistic quantum dots. The theory is based on the semiclassical Landauer formula, that we generalize to include spin-orbit and Zeeman interaction. Within this approach, the orbital degrees of freedom are treated semiclassically, while the spin dynamics is computed quantum mechanically. Employing this method, we calculate the quantum correction to the conductance in quantum dots with Rashba and Dresselhaus spin-orbit interaction. We find a strong sensitivity of the quantum correction to the underlying classical dynamics of the system. In particular, a suppression of weak antilocalization in integrable systems is observed. These results are attributed to the qualitatively different types of spin relaxation in integrable and chaotic quantum cavities.Comment: 20 page

Multiple Andreev Reflections in Weak Links of Superfluid 3He-B

We calculate the current-pressure characteristics of a ballistic pinhole aperture between two volumes of B-phase superfluid 3He. The most important mechanism contributing to dissipative currents in weak links of this type is the process of multiple Andreev reflections. At low biases this process is significantly affected by relaxation due to inelastic quasiparticle-quasiparticle collisions. In the numerical calculations, suppression of the superfluid order parameter at surfaces is taken into account self-consistently. When this effect is neglected, the theory may be developed analytically like in the case of s-wave superconductors. A comparison with experimental results is presented.Comment: 12 pages, 9 figures, RevTeX

Quasiparticle states of the Hubbard model near the Fermi level

The spectra of the t-U and t-t'-U Hubbard models are investigated in the one-loop approximation for different values of the electron filling. It is shown that the four-band structure which is inherent in the case of half-filling and low temperatures persists also for some excess or deficiency of electrons. Besides, with some departure from half-filling an additional narrow band of quasiparticle states arises near the Fermi level. The dispersion of the band, its bandwidth and the variation with filling are close to those of the spin-polaron band of the t-J model. For moderate doping spectral intensities in the new band and in one of the inner bands of the four-band structure decrease as the Fermi level is approached which leads to the appearance of a pseudogap in the spectrum.Comment: 8 pages, 7 figure