Full transmission within a wide energy range and super-criticality in relativistic barrier scattering

For potential barriers with scalar and vector coupling, we show that a Dirac particle could experience nearly full transmission within a wide sub-barrier energy band. Moreover, for certain potential configurations, including pseudo-spin symmetry where the scalar potential is the negative of the vector, full transmission occurs for arbitrarily small momentum.Comment: 10 pages, 4 figures, 1 table, 1 video animatio

Supersymmetric Jaynes-Cummings model and its exact solutions

The super-algebraic structure of a generalized version of the Jaynes-Cummings model is investigated. We find that a Z2 graded extension of the so(2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional super-algebra u(1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.Comment: 12 pages, no figure

Taming the Yukawa potential singularity: improved evaluation of bound states and resonance energies

Using the tools of the J-matrix method, we absorb the 1/r singularity of the Yukawa potential in the reference Hamiltonian, which is handled analytically. The remaining part, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. Analysis of resonance energies and bound states spectrum is performed using the complex scaling method, where we show their trajectories in the complex energy plane and demonstrate the remarkable fact that bound states cross over into resonance states by varying the potential parameters.Comment: 8 pages, 2 tables, 1 figure. 2 mpg videos and 1 pdf table file are available upon request from the corresponding Autho

Solution of One-dimensional Dirac Equation via Poincare Map

We solve the general one-dimensional Dirac equation using a "Poincare Map" approach which avoids any approximation to the spacial derivatives and reduces the problem to a simple recursive relation which is very practical from the numerical implementation point of view. To test the efficiency and rapid convergence of this approach we apply it to a vector coupling Woods--Saxon potential, which is exactly solvable. Comparison with available analytical results is impressive and hence validates the accuracy and efficiency of this method.Comment: 8 pages, 6 figures. Version to appear in EP

The rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation: I. Bound states

This is the first in a series of articles in which we study the rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation. Here, we compute the bound states energy spectrum by diagonalizing the finite dimensional Hamiltonian matrix of H2, LiH, HCl and CO molecules for arbitrary angular momentum. The calculation was performed using the J-matrix basis that supports a tridiagonal matrix representation for the reference Hamiltonian. Our results for these diatomic molecules have been compared with available numerical data satisfactorily. The proposed method is handy, very efficient, and it enhances accuracy by combining analytic power with a convergent and stable numerical technique.Comment: 18 Pages, 6 Tables, 4 Figure

Response of a dx2−y2d_{x^2-y^2} Superconductor to a Zeeman Magnetic Field

We study the response of a two dimensional $d_{x^2-y^2}$ superconductor to a magnetic field that couples only to the spins of the electrons. In contrast to the s-wave case, the $d_{x^2-y^2}$ state is modified even at small magnetic fields, with the gap nodes widening into normal, spin polarized, pockets. We discuss the promising prospects for observing this in the cuprate superconductors in fields parallel to the Cu-O planes. We also discuss the phase diagram, inclusive of a finite momentum pairing state with a novel linkage between the momentum of the pairs and the nodes of the relative wave function.Comment: An error in the calculation of the phase boundary separating the normal state and FFLO state corrected; Figure 2 modified. No change has been made to the part on weak field response. Final version to appear in PR

Coulomb Blockade of Tunneling Through a Double Quantum Dot

We study the Coulomb blockade of tunneling through a double quantum dot. The temperature dependence of the linear conductance is strongly affected by the inter-dot tunneling. As the tunneling grows, a crossover from temperature-independent peak conductance to a power-law suppression of conductance at low temperatures is predicted. This suppression is a manifestation of the Anderson orthogonality catastrophe associated with the charge re-distribution between the dots, which accompanies the tunneling of an electron into a dot. We find analytically the shapes of the Coulomb blockade peaks in conductance as a function of gate voltage.Comment: 11 pages, revtex3.0 and multicols.sty, 4 figures uuencode

Charged particle in the field an electric quadrupole in two dimensions

We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support a tridiagonal matrix representation for the angular and radial components of the wave operator. This solution is for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The expansion coefficients of the wavefunction are written in terms of orthogonal polynomials satisfying three-term recursion relations. The charged particle could become bound to the quadrupole only if its moment exceeds a certain critical value.Comment: 16 pages, 2 Tables, 4 Figure

Relativistic scattering with spatially-dependent effective mass in the Dirac equation

We formulate an algebraic relativistic method of scattering for systems with spatially dependent mass based on the J-matrix method. The reference Hamiltonian is the three-dimensional Dirac Hamiltonian but with a mass that is position-dependent and having a constant asymptotic limit. Additionally, this effective mass distribution is locally represented in a finite dimensional function subspace. The spinor couples to spherically symmetric vector and pseudo scalar potentials that are short-range such that they are accurately represented by their matrix elements in the same finite dimensional subspace. We calculate the relativistic phase shift as a function of energy for a given configuration and study the effect of spatial variation of the mass on the energy resonance structure.Comment: 24 pages, 5 figure

Nonmonotonous Magnetic Field Dependence and Scaling of the Thermal Conductivity for Superconductors with Nodes of the Order Parameter

We show that there is a new mechanism for nonmonotonous behavior of magnetic field dependence of the electronic thermal conductivity of clean superconductors with nodes of the order parameter on the Fermi surface. In particular, for unitary scatterers the nonmonotony of relaxation time takes place. Contribution from the intervortex space turns out to be essential for this effect even at low temperatures. Our results are in a qualitative agreement with recent experimental data for superconducting UPt_3. For E_{2u}-type of pairing we find approximately the scaling of the thermal conductivity in clean limit with a single parameter x=T/T_c\sqrt{B_{c2}/B} at low fields and low temperatures, as well as weak low-temperature dependence of the anisotropy ratio K_{zz}/K_{yy} in zero field. For E_{1g}-type of pairing deviations from the scaling are more noticeable and the anisotropy ratio is essentially temperature dependent.Comment: 37 pages, 8 Postscript figures, REVTE