3,027 research outputs found
Spectral singularities in PT-symmetric periodic finite-gap systems
The origin of spectral singularities in finite-gap singly periodic
PT-symmetric quantum systems is investigated. We show that they emerge from a
limit of band-edge states in a doubly periodic finite gap system when the
imaginary period tends to infinity. In this limit, the energy gaps are
contracted and disappear, every pair of band states of the same periodicity at
the edges of a gap coalesces and transforms into a singlet state in the
continuum. As a result, these spectral singularities turn out to be analogous
to those in the non-periodic systems, where they appear as zero-width
resonances. Under the change of topology from a non-compact into a compact one,
spectral singularities in the class of periodic systems we study are
transformed into exceptional points. The specific degeneration related to the
presence of finite number of spectral singularities and exceptional points is
shown to be coherently reflected by a hidden, bosonized nonlinear
supersymmetry.Comment: 16 pages, 3 figures; a difference between spectral singularities and
exceptional points specified, the version to appear in PR
Supersymmetric Jaynes-Cummings model and its exact solutions
The super-algebraic structure of a generalized version of the Jaynes-Cummings
model is investigated. We find that a Z2 graded extension of the so(2,1) Lie
algebra is the underlying symmetry of this model. It is isomorphic to the
four-dimensional super-algebra u(1/1) with two odd and two even elements.
Differential matrix operators are taken as realization of the elements of the
superalgebra to which the model Hamiltonian belongs. Several examples with
various choices of superpotentials are presented. The energy spectrum and
corresponding wavefunctions are obtained analytically.Comment: 12 pages, no figure
Semi-classical Laguerre polynomials and a third order discrete integrable equation
A semi-discrete Lax pair formed from the differential system and recurrence
relation for semi-classical orthogonal polynomials, leads to a discrete
integrable equation for a specific semi-classical orthogonal polynomial weight.
The main example we use is a semi-classical Laguerre weight to derive a third
order difference equation with a corresponding Lax pair.Comment: 11 page
Constraining ^(26)Al+p resonances using ^(26)Al(^3He,d)^(27)Si
The ^(26)Al(^3He,d)^(27)Si reaction was measured from 0°≤θ_(c.m.)≤35° at E(^3He)=20 MeV using a quadrupole-dipole-dipole-dipole magnetic spectrometer. States in ^(27)Si were observed above the background at 7652 and 7741 keV and upper limits were set for the state at 7592 keV. Implications for the ^(26)Al(p,γ)^(27)Si stellar reaction rate are discussed
Whittaker-Hill equation and semifinite-gap Schroedinger operators
A periodic one-dimensional Schroedinger operator is called semifinite-gap if
every second gap in its spectrum is eventually closed. We construct explicit
examples of semifinite-gap Schroedinger operators in trigonometric functions by
applying Darboux transformations to the Whittaker-Hill equation. We give a
criterion of the regularity of the corresponding potentials and investigate the
spectral properties of the new operators.Comment: Revised versio
Quantum Transport in a Nanosize Silicon-on-Insulator Metal-Oxide-Semiconductor
An approach is developed for the determination of the current flowing through
a nanosize silicon-on-insulator (SOI) metal-oxide-semiconductor field-effect
transistors (MOSFET). The quantum mechanical features of the electron transport
are extracted from the numerical solution of the quantum Liouville equation in
the Wigner function representation. Accounting for electron scattering due to
ionized impurities, acoustic phonons and surface roughness at the Si/SiO2
interface, device characteristics are obtained as a function of a channel
length. From the Wigner function distributions, the coexistence of the
diffusive and the ballistic transport naturally emerges. It is shown that the
scattering mechanisms tend to reduce the ballistic component of the transport.
The ballistic component increases with decreasing the channel length.Comment: 21 pages, 8 figures, E-mail addresses: [email protected]
On the Plants Leaves Boundary, "Jupe \`a Godets" and Conformal Embeddings
The stable profile of the boundary of a plant's leaf fluctuating in the
direction transversal to the leaf's surface is described in the framework of a
model called a "surface \`a godets". It is shown that the information on the
profile is encoded in the Jacobian of a conformal mapping (the coefficient of
deformation) corresponding to an isometric embedding of a uniform Cayley tree
into the 3D Euclidean space. The geometric characteristics of the leaf's
boundary (like the perimeter and the height) are calculated. In addition a
symbolic language allowing to investigate statistical properties of a "surface
\`a godets" with annealed random defects of curvature of density is
developed. It is found that at the surface exhibits a phase transition
with critical exponent from the exponentially growing to the flat
structure.Comment: 17 pages (revtex), 8 eps-figures, to appear in Journal of Physics
Second Order Darboux Displacements
The potentials for a one dimensional Schroedinger equation that are displaced
along the x axis under second order Darboux transformations, called 2-SUSY
invariant, are characterized in terms of a differential-difference equation.
The solutions of the Schroedinger equation with such potentials are given
analytically for any value of the energy. The method is illustrated by a
two-soliton potential. It is proven that a particular case of the periodic
Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the
corresponding Schroedinger equation equation are found for any value of the
energy. A simple analytic expression for a family of two-gap potentials is
derived
The exponential law: Monopole detectors, Bogoliubov transformations, and the thermal nature of the Euclidean vacuum in RP^3 de Sitter spacetime
We consider scalar field theory on the RP^3 de Sitter spacetime (RP3dS),
which is locally isometric to de Sitter space (dS) but has spatial topology
RP^3. We compare the Euclidean vacua on RP3dS and dS in terms of three
quantities that are relevant for an inertial observer: (i) the stress-energy
tensor; (ii) the response of an inertial monopole particle detector; (iii) the
expansion of the Euclidean vacuum in terms of many-particle states associated
with static coordinates centered at an inertial world line. In all these
quantities, the differences between RP3dS and dS turn out to fall off
exponentially at early and late proper times along the inertial trajectory. In
particular, (ii) and (iii) yield at early and late proper times in RP3dS the
usual thermal result in the de Sitter Hawking temperature. This conforms to
what one might call an exponential law: in expanding locally de Sitter
spacetimes, differences due to global topology should fall off exponentially in
the proper time.Comment: 22 pages, REVTex v3.1 with amsfonts and epsf, includes 2 eps figures.
(v2: Minor typos corrected, references updated.
Solution of the relativistic Dirac-Hulthen problem
The one-particle three-dimensional Dirac equation with spherical symmetry is
solved for the Hulthen potential. The s-wave relativistic energy spectrum and
two-component spinor wavefunctions are obtained analytically. Conforming to the
standard feature of the relativistic problem, the solution space splits into
two distinct subspaces depending on the sign of a fundamental parameter in the
problem. Unique and interesting properties of the energy spectrum are pointed
out and illustrated graphically for several values of the physical parameters.
The square integrable two-component wavefunctions are written in terms of the
Jacobi polynomials. The nonrelativistic limit reproduces the well-known
nonrelativistic energy spectrum and results in Schrodinger equation with a
"generalized" three-parameter Hulthen potential, which is the sum of the
original Hulthen potential and its square.Comment: 13 pages, 3 color figure
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