Intertwining relations of non-stationary Schr\"odinger operators

General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in turn results in a $R$-separation of variables. The Fokker-Planck and diffusion equation are briefly considered. Second-order intertwining operators are also discussed within a general approach. However, due to its complicated structure only particular solutions are given in some detail.Comment: 18 pages, LaTeX20

Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility

In this paper, we continue to study factorization of supersymmetric (SUSY) transformations in one-dimensional Quantum Mechanics into chains of elementary Darboux transformations with nonsingular coefficients. We define the class of potentials that are invariant under the Darboux - Crum transformations and prove a number of lemmas and theorems substantiating the formulated formerly conjectures on reducibility of differential operators for spectral equivalence transformations. Analysis of the general case is performed with all the necessary proofs.Comment: 13 page

Vector meson decays from the Extended Chiral Quark Model

We derive the the effective lagrangian that describes the interactions among vector, axial-vector mesons and pseudoscalars starting from the extended chiral quark model (ECQM). The results for the low-energy constants of this effective lagrangian have a parametric resemblance with existing predictions based on the Nambu-Jona-Lasinio model (except for some overall signs that we correct), but are numerically different. Therefore a precise measurement of these decay constants can shed some light on the way chiral symmetry breaking is modelled in QCD. Although most of the constants are poorly measured, comparison with phenomenology allows us to determine one of the parameters of the ECQM that could not be fully determined in previous analyses.Comment: 7 pages, revtex

Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics. I: general classification of reducibility and analysis of the third-order algebra

We study possible factorizations of supersymmetric (SUSY) transformations in the one-dimensional quantum mechanics into chains of elementary Darboux transformations with nonsingular coefficients. A classification of irreducible (almost) isospectral transformations and of related SUSY algebras is presented. The detailed analysis of SUSY algebras and isospectral operators is performed for the third-order case.Comment: 16 page

Lorentz Symmetry Breaking in Abelian Vector-Field Models with Wess-Zumino Interaction

We consider the abelian vector-field models in the presence of the Wess-Zumino interaction with the pseudoscalar matter. The occurence of the dynamic breaking of Lorentz symmetry at classical and one-loop level is described for massless and massive vector fields. This phenomenon appears to be the non-perturbative counterpart of the perturbative renormalizability and/or unitarity breaking in the chiral gauge theories.Comment: 11 pages,LaTeX, Preprint DFUB/94 - 1

Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics

The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are investigated in detail. The particular case of diagonal initial Hamiltonian is considered, and the existence of solutions is demonstrated. Explicit examples illustrate the construction.Comment: 15

On two-dimensional superpotentials: from classical Hamilton-Jacobi theory to 2D supersymmetric quantum mechanics

Superpotentials in ${\cal N}=2$ supersymmetric classical mechanics are no more than the Hamilton characteristic function of the Hamilton-Jacobi theory for the associated purely bosonic dynamical system. Modulo a global sign, there are several superpotentials ruling Hamilton-Jacobi separable supersymmetric systems, with a number of degrees of freedom greater than one. Here, we explore how supersymmetry and separability are entangled in the quantum version of this kind of system. We also show that the planar anisotropic harmonic oscillator and the two-Newtonian centers of force problem admit two non-equivalent supersymmetric extensions with different ground states and Yukawa couplings.Comment: 14 pages, 2 figures, version to appear in J. Phys. A: Math. Ge

Negative Magnetoresistance in (In,Mn)As

The magnetotransport properties of an In0.95Mn0.05As thin film grown by metal-organic vapor phase epitaxy were measured. Resistivity was measured over the temperature range of 5 to 300 K. The resistivity decreased with increasing temperature from 90 ohm-cm to 0.05 ohm-cm. The field dependence of the low temperature magnetoresistance was measured. A negative magnetoresistance was observed below 17 K with a hysteresis in the magnetoresistance observed at 5 K. The magnetoresistance as a function of applied field was described by the Khosla-Fischer model for spin scattering of carriers in an impurity band.Comment: 8 pages, 4 figures, accepted to Physical Review

Asymptotic Analysis of Thin Interface in Composite Materials with Coated Boundary

This paper considers the problem of thin interface in a fibre reinforced composite material. Using the singular asymptotic procedure, the authors obtain simplified relations known as spring model. Phenomenon of edge effect is also studied using the Papkovich-Fadle approach. The singularities of the limit problem are analysed