70 research outputs found
Generalized Eigenvectors for Resonances in the Friedrichs Model and Their Associated Gamov Vectors
A Gelfand triplet for the Hamiltonian H of the Friedrichs model on R with
finite-dimensional multiplicity space K, is constructed such that exactly the
resonances (poles of the inverse of the Livsic-matrix) are (generalized)
eigenvalues of H. The corresponding eigen-antilinearforms are calculated
explicitly. Using the wave matrices for the wave (Moller) operators the
corresponding eigen-antilinearforms on the Schwartz space S for the unperturbed
Hamiltonian are also calculated. It turns out that they are of pure Dirac type
and can be characterized by their corresponding Gamov vector, which is uniquely
determined by restriction of S to the intersection of S with the Hardy space of
the upper half plane. Simultaneously this restriction yields a truncation of
the generalized evolution to the well-known decay semigroup of the Toeplitz
type for the positive half line on the Hardy space. That is: exactly those
pre-Gamov vectors (eigenvectors of the decay semigroup) have an extension to a
generalized eigenvector of H if the eigenvalue is a resonance and if the
multiplicity parameter k is from that subspace of K which is uniquely
determined by its corresponding Dirac type antilinearform.Comment: 16 page
Fingerprints of carbon defects in vibrational spectra of gallium nitride (GaN) consider-ing the isotope effect
This work examines the carbon defects associated with recently reported and
novel peaks of infrared (IR) absorption and Raman scattering appearing in GaN
crystals at carbon () doping in the range of concentrations from
to . 14 unique vibrational modes of defects
are observed in GaN samples grown by hydride vapor phase epitaxy (HVPE) and
then compared with defect properties predicted from first-principles
calculations. The vibrational frequency shift in two enriched samples
related to the effect of the isotope mass indicates six distinct configurations
of the carbon-containing point defects. The effect of the isotope replacement
is well reproduced by the density functional theory (DFT) calculations.
Specific attention is paid to the most pronounced defects, namely tri-carbon
complexes() and carbon substituting for nitrogen . The position
of the transition level (+/0) in the bandgap found for defects by
DFT at 1.1 eV above the valence band maximum, suggest that
provides compensation of . defects are observed to be
prominent, yet have high formation energies in DFT calculations. Regarding
defects, it is shown that the host Ga and N atoms are involved in the
defect's delocalized vibrations and significantly affect the isotopic frequency
shift. Much more faint vibrational modes are found from di-atomic carbon-carbon
and carbon-hydrogen (C-H) complexes. Also, we note changes of vibrational mode
intensities of , , C-H, and defects in the IR
absorption spectra upon irradiation in the defect-related UV/visible absorption
range. Finally, it is demonstrated that the resonant enhancement of the Raman
process in the range of defect absorption above 2.5 eV enables the detection of
defects at carbon doping concentrations as low as
Continuum corrections to the level density and its dependence on excitation energy, n-p asymmetry, and deformation
In the independent-particle model, the nuclear level density is determined
from the neutron and proton single-particle level densities. The
single-particle level density for the positive-energy continuum levels is
important at high excitation energies for stable nuclei and at all excitation
energies for nuclei near the drip lines. This single-particle level density is
subdivided into compound-nucleus and gas components. Two methods were
considered for this subdivision. First in the subtraction method, the
single-particle level density is determined from the scattering phase shifts.
In the Gamov method, only the narrow Gamov states or resonances are included.
The level densities calculated with these two methods are similar, both can be
approximated by the backshifted Fermi-gas expression with level-density
parameters that are dependent on A, but with very little dependence on the
neutron or proton richness of the nucleus. However, a small decrease in the
level-density parameter was predicted for some nuclei very close to the drip
lines. The largest difference between the calculations using the two methods
was the deformation dependence on the level density. The Gamov method predicts
a very strong peaking of the level density at sphericity for high excitation
energies. This leads to a suppression of deformed configurations and,
consequently, the fission rate predicted by the statistical model is reduced in
the Gamov method.Comment: 18 pages 24 figure
Concave and Convex photonic Barriers in Gradient Optics
Propagation and tunneling of light through photonic barriers formed by thin
dielectric films with continuous curvilinear distributions of dielectric
susceptibility across the film, are considered. Giant heterogeneity-induced
dispersion of these films, both convex and concave, and its influence on their
reflectivity and transmittivity are visualized by means of exact analytical
solutions of Maxwell equations. Depending on the cut-off frequency of the film,
governed by the spatial profile of its refractive index, propagation or
tunneling of light through such barriers are examined. Subject to the shape of
refractive index profile the group velocities of EM waves in these films are
shown to be either increased or deccreased as compared with the homogeneous
layers; however, these velocities for both propagation and tunneling regimes
remain subluminal. The decisive influence of gradient and curvature of photonic
barriers on the efficiency of tunneling is examined by means of generalized
Fresnel formulae. Saturation of the phase of the wave tunneling through a stack
of such films (Hartman effect), is demonstrated. The evanescent modes in lossy
barriers and violation of Hartman effect in this case is discussed
Trialogue on the number of fundamental constants
This paper consists of three separate articles on the number of fundamental
dimensionful constants in physics. We started our debate in summer 1992 on the
terrace of the famous CERN cafeteria. In the summer of 2001 we returned to the
subject to find that our views still diverged and decided to explain our
current positions. LBO develops the traditional approach with three constants,
GV argues in favor of at most two (within superstring theory), while MJD
advocates zero.Comment: Version appearing in JHEP; 31 pages late
Adiabatic decaying vacuum model for the universe
We study a model that the entropy per particle in the universe is constant.
The sources for the entropy are the particle creation and a lambda decaying
term. We find exact solutions for the Einstein field equations and show the
compatibilty of the model with respect to the age and the acceleration of the
universe.Comment: 10 pages, 2 figure
Alpha decay and proton-neutron correlations
We study the influence of proton-neutron (p-n) correlations on alpha-decay
width. It is shown from the analysis of alpha Q values that the p-n
correlations increase the penetration of the alpha particle through the Coulomb
barrier in the treatment following Gamow's formalism, and enlarges the total
alpha-decay width significantly.
In particular, the isoscalar p-n interactions play an essential role in
enlarging the alpha-decay width.
The so-called "alpha-condensate" in Z > 84 isotopes are related to the strong
p-n correlations.Comment: 5 pages, 6 figures, accepted for publication in Phys. Rev. C (R.C.
Accretion Disc Theory: From the Standard Model Until Advection
Accretion disc theory was first developed as a theory with the local heat
balance, where the whole energy produced by a viscous heating was emitted to
the sides of the disc. One of the most important new invention of this theory
was a phenomenological treatment of the turbulent viscosity, known as ''alpha''
prescription, when the (r) component of the stress tensor was
approximated by ( P) with a unknown constant . This
prescription played the role in the accretion disc theory as well important as
the mixing-length theory of convection for stellar evolution. Sources of
turbulence in the accretion disc are discussed, including nonlinear
hydrodynamical turbulence, convection and magnetic field role. In parallel to
the optically thick geometrically thin accretion disc models, a new branch of
the optically thin accretion disc models was discovered, with a larger
thickness for the same total luminosity. The choice between these solutions
should be done of the base of a stability analysis. The ideas underlying the
necessity to include advection into the accretion disc theory are presented and
first models with advection are reviewed. The present status of the solution
for a low-luminous optically thin accretion disc model with advection is
discussed and the limits for an advection dominated accretion flows (ADAF)
imposed by the presence of magnetic field are analysed.Comment: Roceeding of the Int. Workshop "Observational Evidence for Black
Holes in the Universe". Calcutta, 11-17 January 1998. Kluwer Acad. Pu
Quantum-Classical Transition of the Escape Rate of a Uniaxial Spin System in an Arbitrarily Directed Field
The escape rate \Gamma of the large-spin model described by the Hamiltonian H
= -DS_z^2 - H_zS_z - H_xS_x is investigated with the help of the mapping onto a
particle moving in a double-well potential U(x). The transition-state method
yields in the moderate-damping case as a Boltzmann average of the
quantum transition probabilities. We have shown that the transition from the
classical to quantum regimes with lowering temperature is of the first order
(d\Gamma/dT discontinuous at the transition temperature T_0) for h_x below the
phase boundary line h_x=h_{xc}(h_z), where h_{x,z}\equiv H_{x,z}/(2SD), and of
the second order above this line. In the unbiased case (H_z=0) the result is
h_{xc}(0)=1/4, i.e., one fourth of the metastability boundary h_{xm}=1, at
which the barrier disappears. In the strongly biased limit \delta\equiv 1-h_z
<< 1, one has h_{xc} \cong (2/3)^{3/4}(\sqrt{3}-\sqrt{2})\delta^{3/2}\cong
0.2345 \delta^{3/2}, which is about one half of the boundary value h_{xm} \cong
(2\delta/3)^{3/2} \cong 0.5443 \delta^{3/2}.The latter case is relevant for
experiments on small magnetic particles, where the barrier should be lowered to
achieve measurable quantum escape rates.Comment: 17 PR pages, 16 figures; published versio
Dynamics of the Universe with global rotation
We analyze dynamics of the FRW models with global rotation in terms of
dynamical system methods. We reduce dynamics of these models to the FRW models
with some fictitious fluid which scales like radiation matter. This fluid
mimics dynamically effects of global rotation. The significance of the global
rotation of the Universe for the resolution of the acceleration and horizon
problems in cosmology is investigated. It is found that dynamics of the
Universe can be reduced to the two-dimensional Hamiltonian dynamical system.
Then the construction of the Hamiltonian allows for full classification of
evolution paths. On the phase portraits we find the domains of cosmic
acceleration for the globally rotating universe as well as the trajectories for
which the horizon problem is solved. We show that the FRW models with global
rotation are structurally stable. This proves that the universe acceleration is
due to the global rotation. It is also shown how global rotation gives a
natural explanation of the empirical relation between angular momentum for
clusters and superclusters of galaxies. The relation is obtained
as a consequence of self similarity invariance of the dynamics of the FRW model
with global rotation. In derivation of this relation we use the Lie group of
symmetry analysis of differential equation.Comment: Revtex4, 22 pages, 5 figure
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