142 research outputs found
Inverse eigenvalue problem for discrete three-diagonal Sturm-Liouville operator and the continuum limit
In present article the self-contained derivation of eigenvalue inverse
problem results is given by using a discrete approximation of the Schroedinger
operator on a bounded interval as a finite three-diagonal symmetric Jacobi
matrix. This derivation is more correct in comparison with previous works which
used only single-diagonal matrix. It is demonstrated that inverse problem
procedure is nothing else than well known Gram-Schmidt orthonormalization in
Euclidean space for special vectors numbered by the space coordinate index. All
the results of usual inverse problem with continuous coordinate are reobtained
by employing a limiting procedure, including the Goursat problem -- equation in
partial derivatives for the solutions of the inversion integral equation.Comment: 19 pages There were made some additions (and reformulations) to the
text making the derivation of the results more precise and understandabl
Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line
The matrix Schroedinger equation with a selfadjoint matrix potential is
considered on the half line with the most general selfadjoint boundary
condition at the origin. When the matrix potential is integrable and has a
first moment, it is shown that the corresponding scattering matrix is
continuous at zero energy. An explicit formula is provided for the scattering
matrix at zero energy. The small-energy asymptotics are established also for
the corresponding Jost matrix, its inverse, and various other quantities
relevant to the corresponding direct and inverse scattering problems.Comment: This published version has been edited to improve the presentation of
the result
Reconstruction of the optical potential from scattering data
We propose a method for reconstruction of the optical potential from
scattering data. The algorithm is a two-step procedure. In the first step the
real part of the potential is determined analytically via solution of the
Marchenko equation. At this point we use a diagonal Pad\'{e} approximant of the
corresponding unitary -matrix. In the second step the imaginary part of the
potential is determined via the phase equation of the variable phase approach.
We assume that the real and the imaginary parts of the optical potential are
proportional. We use the phase equation to calculate the proportionality
coefficient. A numerical algorithm is developed for a single and for coupled
partial waves. The developed procedure is applied to analysis of
, , and data.Comment: 26 pages, 8 figures, results of nucl-th/0410092 are refined, some new
results are presente
Negative-Index Metamaterials: Second-Harmonic Generation, Manley-Rowe Relations and Parametric Amplification
Second harmonic generation and optical parametric amplification in
negative-index metamaterials (NIMs) are studied. The opposite directions of the
wave vector and the Poynting vector in NIMs results in a "backward"
phase-matching condition, causing significant changes in the Manley-Rowe
relations and spatial distributions of the coupled field intensities. It is
shown that absorption in NIMs can be compensated by backward optical parametric
amplification. The possibility of distributed-feedback parametric oscillation
with no cavity has been demonstrated. The feasibility of the generation of
entangled pairs of left- and right-handed counter-propagating photons is
discussed.Comment: 7 pages, 6 figure
In-medium nucleon-nucleon potentials in configuration space
Based on the thermodynamic Green function approach two-nucleon correlations
in nuclear matter at finite temperatures are revisited. To this end, we derive
phase equivalent effective -space potentials that include the effect of the
Pauli blocking at a given temperature and density. These potentials enter into
a Schr\"odinger equation that is the -space representation of the
Galitskii-Feynman equation for two nucleons. We explore the analytical
structure of the equation in the complex -plane by means of Jost functions.
We find that despite the Mott effect the correlation with deuteron quantum
numbers are manifested as antibound states, i.e., as zeros of the Jost function
on the negative imaginary axis of the complex momentum space. The analysis
presented here is also suited for Coulombic systems.Comment: 6 pages, 1 table, 4 figure
The Response to a Perturbation in the Reflection Amplitude
We apply inverse scattering theory to calculate the functional derivative of
the potential and wave function of a one-dimensional
Schr\"odinger operator with respect to the reflection amplitude .Comment: 16 pages, no figure
Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials
We give a complete description of the set of spectral data (eigenvalues and
specially introduced norming constants) for Sturm--Liouville operators on the
interval with matrix-valued potentials in the Sobolev space
and suggest an algorithm reconstructing the potential from the spectral data
that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO
Ab-Initio Calculation of Molecular Aggregation Effects: a Coumarin-343 Case Study
We present time-dependent density functional theory (TDDFT) calculations for
single and dimerized Coumarin-343 molecules in order to investigate the quantum
mechanical effects of chromophore aggregation in extended systems designed to
function as a new generation of sensors and light-harvesting devices. Using the
single-chromophore results, we describe the construction of effective
Hamiltonians to predict the excitonic properties of aggregate systems. We
compare the electronic coupling properties predicted by such effective
Hamiltonians to those obtained from TDDFT calculations of dimers, and to the
coupling predicted by the transition density cube (TDC) method. We determine
the accuracy of the dipole-dipole approximation and TDC with respect to the
separation distance and orientation of the dimers. In particular, we
investigate the effects of including Coulomb coupling terms ignored in the
typical tight-binding effective Hamiltonian. We also examine effects of orbital
relaxation which cannot be captured by either of these models
Model Calculations for the Two-Fragment Electro-Disintegration of He
Differential cross sections for the electro-disintegration process are calculated, using a model in which
the final state interaction is included by means of a nucleon-nucleus (3+1)
potential constructed via Marchenko inversion. The required bound-state wave
functions are calculated within the integrodifferential equation approach
(IDEA). In our model the important condition that the initial bound state and
the final scattering state are orthogonal is fulfilled. The sensitivity of the
cross section to the input interaction in certain kinematical regions
is investigated. The approach adopted could be useful in reactions involving
few cluster systems where effective interactions are not well known and exact
methods are presently unavailable. Although, our Plane-Wave Impulse
Approximation results exhibit, similarly to other calculations, a dip in the
five-fold differential cross-section around a missing momentum of , it is argued that this is an artifact of the omission of re-scattering
four-nucleon processes.Comment: 16 pages, 6 figures, accepted for publication by Phys.Rev.
Superradiance from an ultrathin film of three-level V-type atoms: Interplay between splitting, quantum coherence and local-field effects
We carry out a theoretical study of the collective spontaneous emission
(superradiance) from an ultrathin film comprised of three-level atoms with
-configuration of the operating transitions. As the thickness of the system
is small compared to the emission wavelength inside the film, the local-field
correction to the averaged Maxwell field is relevant. We show that the
interplay between the low-frequency quantum coherence within the subspace of
the upper doublet states and the local-field correction may drastically affect
the branching ratio of the operating transitions. This effect may be used for
controlling the emission process by varying the doublet splitting and the
amount of low-frequency coherence.Comment: 15 pages, 5 figure
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