Connection between the Green functions of the supersymmetric pair of Dirac Hamiltonians

The Sukumar theorem about the connection between the Green functions of the supersymmetric pair of the Schr\"odinger Hamiltonians is generalized to the case of the supersymmetric pair of the Dirac Hamiltonians.Comment: 12 pages,Latex, no figure

Supersymmetric transformations for coupled channels with threshold differences

The asymptotic behaviour of the superpotential of general SUSY transformations for a coupled-channel Hamiltonian with different thresholds is analyzed. It is shown that asymptotically the superpotential can tend to a diagonal matrix with an arbitrary number of positive and negative entries depending on the choice of the factorization solution. The transformation of the Jost matrix is generalized to "non-conservative" SUSY transformations introduced in Sparenberg et al (2006 J. Phys. A: Math. Gen. 39 L639). Applied to the zero initial potential the method permits to construct superpartners with a nontrivially coupled Jost-matrix. Illustrations are given for two- and three-channel cases.Comment: 17 pages, 3 explicit examples and figures adde

Darboux transformations of coherent states of the time-dependent singular oscillator

Darboux transformation of both Barut-Girardello and Perelomov coherent states for the time-dependent singular oscillator is studied. In both cases the measure that realizes the resolution of the identity operator in terms of coherent states is found and corresponding holomorphic representation is constructed. For the particular case of a free particle moving with a fixed value of the angular momentum equal to two it is shown that Barut-Giriardello coherent states are more localized at the initial time moment while the Perelomov coherent states are more stable with respect to time evolution. It is also illustrated that Darboux transformation may keep unchanged this different time behavior.Comment: 13 page

Twists in U(sl(3)) and their quantizations

The solution of the Drinfeld equation corresponding to the full set of different carrier subalgebras in sl(3) are explicitly constructed. The obtained Hopf structures are studied. It is demonstrated that the presented twist deformations can be considered as limits of the corresponding quantum analogues (q-twists) defined for the q-quantized algebras.Comment: 31 pages, Latex 2e, to be published in Journ. Phys. A: Math. Ge

Interaction between dust grains near a conducting wall

The effect of the conducting electrode on the interaction of dust grains in a an ion flow is discussed. It is shown that two grains levitating above the electrode at the same height may attract one another. This results in the instability of a dust layer in a plasma sheath.Comment: 9 pages. 3 figures. Submitted to Plasma Physics Report

Eigenphase preserving two-channel SUSY transformations

We propose a new kind of supersymmetric (SUSY) transformation in the case of the two-channel scattering problem with equal thresholds, for partial waves of the same parity. This two-fold transformation is based on two imaginary factorization energies with opposite signs and with mutually conjugated factorization solutions. We call it an eigenphase preserving SUSY transformation as it relates two Hamiltonians, the scattering matrices of which have identical eigenphase shifts. In contrast to known phase-equivalent transformations, the mixing parameter is modified by the eigenphase preserving transformation.Comment: 16 pages, 1 figur

Semi-classical twists for sl(3) and sl(4) boundary r-matrices of Cremmer-Gervais type

We obtain explicit formulas for the semi-classical twists deforming the coalgebraic structure of U(sl(3)) and U(sl(4)). In rank 2 and 3 the corresponding universal R-matrices quantize the boundary r-matrices of Cremmer-Gervais type defining Lie Frobenius structures on the maximal parabolic subalgebras in sl(n)

Electromagnetic Structure of the ρ\rho Meson in the Light-Front Quark Model

We investigate the elastic form factors of the rho meson in the light-front quark model(LFQM). With the phenomenologically accessible meson vertices including the one obtained by the Melosh transformation frequently used in the LFQM, we find that only the helicity $0\to 0$ matrix element of the plus current receives the zero-mode contribution. We quantify the zero-mode contribution in the helicity $0\to 0$ amplitude using the angular condition of spin-1 system. After taking care of the zero-mode issue, we obtain the magnetic($\mu$) and quadrupole($Q$) moments of the rho meson as $\mu=1.92$ and $Q=0.43$, respectively, in the LFQM consistent with the Melosh transformation and compare our results with other available theoretical predictions.Comment: 14pages, 5figure

Generalization of the Darboux transformation and generalized harmonic oscillators

The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and these formalisms are applied for a general quadratic system (a generalized harmonic oscillator) and a quadratic system with an inverse-square interaction up to N=2. Among the new features found, it is shown, for the general quadratic system, that the shape of potential difference between the original system and the transformed system could oscillate according to a classical solution, which is related to the existence of coherent states in the system