2,894 research outputs found
SUSY transformations with complex factorization constants. Application to spectral singularities
Supersymmetric (SUSY) transformation operators corresponding to complex
factorization constants are analyzed as operators acting in the Hilbert space
of functions square integrable on the positive semiaxis. Obtained results are
applied to Hamiltonians possessing spectral singularities which are
non-Hermitian SUSY partners of selfadjoint operators. A new regularization
procedure for the resolution of the identity operator in terms of continuous
biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed.
It is also shown that the continuous spectrum eigenfunction has zero binorm (in
the sense of distributions) at the singular point.Comment: Thanks to A. Sokolov a number of inaccuracies are correcte
Initial-state nuclear effects in proton-nucleus collisions
Two important initial-state nuclear effects in hadron-nucleus collisions are
considered. The ratios of inclusive differential cross sections for Drell-Yan
dimuon production are calculated. The calculated results are compared to the
E866 data. It is shown that consideration of multiple soft rescatterings of
incident quarks in nuclei and initial-state quark energy loss effects allow to
get a good agreement between the calculated results and the experimental data.Comment: 6 pages, 6 figure
Three-dimensional structure of Mach cones in monolayer complex plasma
Structure of Mach cones in a crystalline complex plasma has been studied
experimentally using an intensity sensitive imaging, which resolved particle
motion in three dimensions. This revealed a previously unknown out-of-plane
cone structure, which appeared due to excitation of the vertical wave mode. The
complex plasma consisted of micron sized particles forming a monolayer in a
plasma sheath of a gas discharge. Fast particles, spontaneously moving under
the monolayer, created Mach cones with multiple structures. The in-plane cone
structure was due to compressional and shear lattice waves.Comment: Accepted for publication in Physical Review Letter
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
On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization
We study classical twists of Lie bialgebra structures on the polynomial
current algebra , where is a simple complex
finite-dimensional Lie algebra. We focus on the structures induced by the
so-called quasi-trigonometric solutions of the classical Yang-Baxter equation.
It turns out that quasi-trigonometric -matrices fall into classes labelled
by the vertices of the extended Dynkin diagram of . We give
complete classification of quasi-trigonometric -matrices belonging to
multiplicity free simple roots (which have coefficient 1 in the decomposition
of the maximal root). We quantize solutions corresponding to the first root of
.Comment: 41 pages, LATE
Phase shift effective range expansion from supersymmetric quantum mechanics
Supersymmetric or Darboux transformations are used to construct local phase
equivalent deep and shallow potentials for partial waves. We
associate the value of the orbital angular momentum with the asymptotic form of
the potential at infinity which allows us to introduce adequate long-distance
transformations. The approach is shown to be effective in getting the correct
phase shift effective range expansion. Applications are considered for the
and partial waves of the neutron-proton scattering.Comment: 6 pages, 3 figures, Revtex4, version to be publised in Physical
Review
Intertwining technique for a system of difference Schroedinger equations and new exactly solvable multichannel potentials
The intertwining operator technique is applied to difference Schroedinger
equations with operator-valued coefficients. It is shown that these equations
appear naturally when a discrete basis is used for solving a multichannel
Schroedinger equation. New families of exactly solvable multichannel
Hamiltonians are found
Opacity of relativistically underdense plasmas for extremely intense laser pulses
It is generally believed that relativistically underdense plasma is
transparent for intense laser radiation. However, particle-in-cell simulations
reveal abnormal laser field absorption above the intensity threshold about~ for the wavelength of . Above the threshold, the further increase of the laser intensity
doesn't lead to the increase of the propagation distance. The simulations take
into account emission of hard photons and subsequent pair photoproduction in
the laser field. These effects lead to onset of a self-sustained
electromagnetic cascade and to formation of dense electron-positron ()
plasma right inside the laser field. The plasma absorbs the field efficiently,
that ensures the plasma opacity. The role of a weak longitudinal electron-ion
electric field in the cascade growth is discussed.Comment: 8 pages, 3 figure
Darboux transformations for quasi-exactly solvable Hamiltonians
We construct new quasi-exactly solvable one-dimensional potentials through
Darboux transformations. Three directions are investigated:
Reducible and two types of irreducible second-order transformations. The
irreducible transformations of the first type give singular intermediate
potentials and the ones of the second type give complex-valued intermediate
potentials while final potentials are meaningful in all cases.
These developments are illustrated on the so-called radial sextic oscillator.Comment: 11 pages, Late
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