152 research outputs found
Resonance regimes of scattering by small bodies with impedance boundary conditions
The paper concerns scattering of plane waves by a bounded obstacle with
complex valued impedance boundary conditions. We study the spectrum of the
Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic
behavior of the solutions of the scattering problem. The study includes the
case when is an eigenvalue or a resonance. The transformation from the
impedance to the Dirichlet boundary condition as impedance grows is described.
A relation between poles and zeroes of the scattering matrix in the non-self
adjoint case is established. The results are applied to a problem of scattering
by an obstacle with a springy coating. The paper describes the dependence of
the impedance on the properties of the material, that is on forces due to the
deviation of the boundary of the obstacle from the equilibrium position
Localized basis sets for unbound electrons in nanoelectronics
It is shown how unbound electron wave functions can be expanded in a suitably
chosen localized basis sets for any desired range of energies. In particular,
we focus on the use of gaussian basis sets, commonly used in first-principles
codes. The possible usefulness of these basis sets in a first-principles
description of field emission or scanning tunneling microscopy at large bias is
illustrated by studying a simpler related phenomenon: The lifetime of an
electron in a H atom subjected to a strong electric field.Comment: 6 pages, 5 figures, accepted by J. Chem. Phys. (http://jcp.aip.org/
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators
The article is devoted to the following question. Consider a periodic
self-adjoint difference (differential) operator on a graph (quantum graph) G
with a co-compact free action of the integer lattice Z^n. It is known that a
local perturbation of the operator might embed an eigenvalue into the
continuous spectrum (a feature uncommon for periodic elliptic operators of
second order). In all known constructions of such examples, the corresponding
eigenfunction is compactly supported. One wonders whether this must always be
the case. The paper answers this question affirmatively. What is more
surprising, one can estimate that the eigenmode must be localized not far away
from the perturbation (in a neighborhood of the perturbation's support, the
width of the neighborhood determined by the unperturbed operator only).
The validity of this result requires the condition of irreducibility of the
Fermi (Floquet) surface of the periodic operator, which is expected to be
satisfied for instance for periodic Schroedinger operators.Comment: Submitted for publicatio
High orders of the perturbation theory for hydrogen atom in magnetic field
The states of hydrogen atom with principal quantum number and zero
magnetic quantum number in constant homogeneous magnetic field are
considered. The coefficients of energy eigenvalues expansion up to 75th order
in powers of are obtained for these states. The series for energy
eigenvalues and wave functions are summed up to values of the order
of atomic magnetic field. The calculations are based on generalization of the
moment method, which may be used in other cases of the hydrogen atom
perturbation by a polynomial in coordinates potential.Comment: 16 pages, LaTeX, 6 figures (ps, eps
Replica analysis of the generalized p-spin interaction glass model
We investigate stability of replica symmetry breaking solutions in
generalized -spin models. It is shown that the kind of the transition to the
one-step replica symmetry breaking state depends not only on the presence or
absence of the reflection symmetry of the generalized "spin"-operators
but on the number of interacting operators and their individual
characteristics.Comment: 14 pages, 1 figur
Time reversal in thermoacoustic tomography - an error estimate
The time reversal method in thermoacoustic tomography is used for
approximating the initial pressure inside a biological object using
measurements of the pressure wave made on a surface surrounding the object.
This article presents error estimates for the time reversal method in the cases
of variable, non-trapping sound speeds.Comment: 16 pages, 6 figures, expanded "Remarks and Conclusions" section,
added one figure, added reference
Stimulation of the fluctuation superconductivity by the PT-symmetry
We discuss fluctuations near the second order phase transition where the free
energy has an additional non-Hermitian term. The spectrum of the fluctuations
changes when the odd-parity potential amplitude exceeds the critical value
corresponding to the PT-symmetry breakdown in the topological structure of the
Hilbert space of the effective non-Hermitian Hamiltonian. We calculate the
fluctuation contribution to the differential resistance of a superconducting
weak link and find the manifestation of the PT-symmetry breaking in its
temperature evolution. We successfully validate our theory by carrying out
measurements of far from equilibrium transport in mesoscale-patterned
superconducting wires.Comment: Phys. Rev. Lett 201
Dynamical Systems Gradient method for solving nonlinear equations with monotone operators
A version of the Dynamical Systems Gradient Method for solving ill-posed
nonlinear monotone operator equations is studied in this paper. A discrepancy
principle is proposed and justified. A numerical experiment was carried out
with the new stopping rule. Numerical experiments show that the proposed
stopping rule is efficient. Equations with monotone operators are of interest
in many applications.Comment: 2 figure
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography
The paper contains a simple approach to reconstruction in Thermoacoustic and
Photoacoustic Tomography. The technique works for any geometry of point
detectors placement and for variable sound speed satisfying a non-trapping
condition. A uniqueness of reconstruction result is also obtained
Lyapunov exponent of the random Schr\"{o}dinger operator with short-range correlated noise potential
We study the influence of disorder on propagation of waves in one-dimensional
structures. Transmission properties of the process governed by the
Schr\"{o}dinger equation with the white noise potential can be expressed
through the Lyapunov exponent which we determine explicitly as a
function of the noise intensity \sigma and the frequency \omega. We find
uniform two-parameter asymptotic expressions for which allow us to
evaluate for different relations between \sigma and \omega. The value
of the Lyapunov exponent is also obtained in the case of a short-range
correlated noise, which is shown to be less than its white noise counterpart.Comment: 20 pages, 4 figure
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