99 research outputs found
Invisibility and PT-symmetry
For a general complex scattering potential defined on a real line, we show
that the equations governing invisibility of the potential are invariant under
the combined action of parity and time-reversal (PT) transformation. We
determine the PT-symmetric an well as non-PT-symmetric invisible configurations
of an easily realizable exactly solvable model that consists of a two-layer
planar slab consisting of optically active material. Our analysis shows that
although PT-symmetry is neither necessary nor sufficient for the invisibility
of a scattering potential, it plays an important role in the characterization
of the invisible configurations. A byproduct of our investigation is the
discovery of certain configurations of our model that are effectively
reflectionless in a spectral range as wide as several hundred nanometers.Comment: 11 pages, 3 figures, revised version, accepted for publication in
Phys.Rev.
Analyticity and uniform stability in the inverse spectral problem for Dirac operators
We prove that the inverse spectral mapping reconstructing the square
integrable potentials on [0,1] of Dirac operators in the AKNS form from their
spectral data (two spectra or one spectrum and the corresponding norming
constants) is analytic and uniformly stable in a certain sense.Comment: 19 page
Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
Spectral singularities are spectral points that spoil the completeness of the
eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify
spectral singularities of complex scattering potentials with the real energies
at which the reflection and transmission coefficients tend to infinity, i.e.,
they correspond to resonances having a zero width. We show that a wave guide
modeled using such a potential operates like a resonator at the frequencies of
spectral singularities. As a concrete example, we explore the spectral
singularities of an imaginary PT-symmetric barrier potential and demonstrate
the above resonance phenomenon for a certain electromagnetic wave guide.Comment: Published versio
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
Multidimensional Borg-Levinson Theorem
We consider the inverse problem of the reconstruction of a Schr\"odinger
operator on a unknown Riemannian manifold or a domain of Euclidean space. The
data used is a part of the boundary and the eigenvalues corresponding
to a set of impedances in the Robin boundary condition which vary on .
The proof is based on the analysis of the behaviour of the eigenfunctions on
the boundary as well as in perturbation theory of eigenvalues. This reduces the
problem to an inverse boundary spectral problem solved by the boundary control
method
Inverse spectral problems for energy-dependent Sturm-Liouville equations
We study the inverse spectral problem of reconstructing energy-dependent
Sturm-Liouville equations from their Dirichlet spectra and sequences of the
norming constants. For the class of problems under consideration, we give a
complete description of the corresponding spectral data, suggest a
reconstruction algorithm, and establish uniqueness of reconstruction. The
approach is based on connection between spectral problems for energy-dependent
Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page
The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case
We present a technique for reconstructing a semi-infinite Jacobi operator in
the limit circle case from the spectra of two different self-adjoint
extensions. Moreover, we give necessary and sufficient conditions for two real
sequences to be the spectra of two different self-adjoint extensions of a
Jacobi operator in the limit circle case.Comment: 26 pages. Changes in the presentation of some result
Exceptional points in quantum and classical dynamics
We notice that, when a quantum system involves exceptional points, i.e. the
special values of parameters where the Hamiltonian loses its self-adjointness
and acquires the Jordan block structure, the corresponding classical system
also exhibits a singular behaviour associated with restructuring of classical
trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2
-igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies
with supersymmetric Yang-Mills dynamics are elucidated.Comment: References added. Final version to be published in J. Phys.
Incomplete inverse spectral and nodal problems for differential pencils
[[abstract]]We prove uniqueness theorems for so-called half inverse spectral problem (and also for some its modification) for second order differential pencils on a finite interval with Robin boundary conditions. Using the obtained result we show that for unique determination of the pencil it is sufficient to specify the nodal points only on a part of the interval slightly exceeding its half.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子
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Self-assembly and anti-amyloid cytotoxicity activity of amyloid beta peptide derivatives
The self-assembly of two derivatives of KLVFF, a fragment Abeta(16-20) of the amyloid beta (Abeta) peptide, is investigated and recovery of viability of neuroblastoma cells exposed to Abeta is observed at sub-stoichiometric peptide concentrations. Fluorescence assays show that NH2-KLVFF-CONH2 undergoes hydrophobic collapse and amyloid formation at the same critical aggregation concentration (cac). In contrast, NH2-K(Boc)LVFF-CONH2 undergoes hydrophobic collapse at a low concentration, followed by amyloid formation at a higher cac. These findings are supported by the beta-sheet features observed by FTIR. Electrospray ionization mass spectrometry indicates that NH2-K(Boc)LVFF-CONH2 forms a significant population of oligomeric species above the cac. Cryo-TEM, used together with SAXS to determine fibril dimensions, shows that the length and degree of twisting of peptide fibrils seem to be influenced by the net peptide charge. Grazing incidence X-ray scattering from thin peptide films shows features of beta-sheet ordering for both peptides, along with evidence for lamellar ordering of NH2-KLVFF-CONH2. This work provides a comprehensive picture of the aggregation properties of these two KLVFF derivatives and show their utility, in unaggregated form, in restoring the viability of neuroblastoma cells against Abeta-induced toxicity
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