213 research outputs found
Accelerator dynamics of a fractional kicked rotor
It is shown that the Weyl fractional derivative can quantize an open system.
A fractional kicked rotor is studied in the framework of the fractional
Schrodinger equation. The system is described by the non-Hermitian Hamiltonian
by virtue of the Weyl fractional derivative. Violation of space symmetry leads
to acceleration of the orbital momentum. Quantum localization saturates this
acceleration, such that the average value of the orbital momentum can be a
direct current and the system behaves like a ratchet. The classical counterpart
is a nonlinear kicked rotor with absorbing boundary conditions.Comment: Submitted for publication in Phys. Rev.
S-Matrix Poles Close to Thresholds in Confined Geometries
We have studied the behavior of the S-matrix poles near threshold for quantum
waveguides coupled to a cavity with a defect. We emphasize the occurrence of
both dominant and shadow poles on the various sheets of the energy Riemann
surface, and show that the changes of the total conductivity near threshold as
the cavity's width changes can be explained in terms of dominant to shadow pole
transitions.Comment: 10 pages, 5 figure
Epidemiology, Diagnosis and Treatment Outcomes of Skin Melanoma in the Republic of Belarus
The primary incidence of skin melanoma in the Republic of Belarus over 25 years (from 1991 through 2015) has increased 3.3-fold (from 2.6 to 9.0 per 100,000 population). A higher level of urban population incidence, a large proportion of people affected at the employable age. In 2015 the proportion of prognostically unfavourable pT3-pT4 neoplasms was 38.2%. Metastatic disease was detected in 12.4% of the patients.
Methodology: Material of the paper is based on the data of Belarusian Cancer Registry using the principles of data collection, monitoring and processing recommended by the IARC.
Results: The proportion of stage IB neoplasms made up almost one third of the cases assigned to stage I. Of the cases assigned to stage II, the proportion of neoplasms with a high prognostic index of metastatic spread (T3b-T4b) was more than 70%. The recurrence rate is 15.1% even at melanoma invasion depth of up to 1 mm (with ulceration), while it rises to 32.4% at pT2b. The cumulative 5-year disease-specific survival of all patients in 2005 was 54.1 ± 1.5%, and in 2015 it was 64.0±2.2%.
Conclusion: A strong correlation is observed between survival of patients and the extent of invasion and ulceration of the primary focus. For metastasis-free pT1a melanoma, the 5-year survival was 92.2%, for T1b – 79.9%, for pT2b – 72.5%, for pT3b – 55.1%, for pT4b – 49.1%. According to the Cancer Registry data, ulceration of the primary neoplasm is frequently observed: it amounts to 41.1% of the cases with melanoma invasion depth up to 2 mm (pT2), to 55.9% with 2-4 mm (pT3) and to 76.3% with the tumor thickness of more than 4 mm (pT4)
Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices
A direct and exact method for calculating the density of states for systems
with localized potentials is presented. The method is based on explicit
inversion of the operator . The operator is written in the discrete
variable representation of the Hamiltonian, and the Toeplitz property of the
asymptotic part of the obtained {\it infinite} matrix is used. Thus, the
problem is reduced to the inversion of a {\it finite} matrix
Resonance Lifetimes from Complex Densities
The ab-initio calculation of resonance lifetimes of metastable anions
challenges modern quantum-chemical methods. The exact lifetime of the
lowest-energy resonance is encoded into a complex "density" that can be
obtained via complex-coordinate scaling. We illustrate this with one-electron
examples and show how the lifetime can be extracted from the complex density in
much the same way as the ground-state energy of bound systems is extracted from
its ground-state density
Non-Hermitian Rayleigh-Schroedinger Perturbation Theory
We devise a non-Hermitian Rayleigh-Schroedinger perturbation theory for the
single- and the multireference case to tackle both the many-body problem and
the decay problem encountered, for example, in the study of electronic
resonances in molecules. A complex absorbing potential (CAP) is employed to
facilitate a treatment of resonance states that is similar to the
well-established bound-state techniques. For the perturbative approach, the
full CAP-Schroedinger Hamiltonian, in suitable representation, is partitioned
according to the Epstein-Nesbet scheme. The equations we derive in the
framework of the single-reference perturbation theory turn out to be identical
to those obtained by a time-dependent treatment in Wigner-Weisskopf theory. The
multireference perturbation theory is studied for a model problem and is shown
to be an efficient and accurate method. Algorithmic aspects of the integration
of the perturbation theories into existing ab initio programs are discussed,
and the simplicity of their implementation is elucidated.Comment: 10 pages, 1 figure, RevTeX4, submitted to Physical Review
Multiple bound states in scissor-shaped waveguides
We study bound states of the two-dimensional Helmholtz equations with
Dirichlet boundary conditions in an open geometry given by two straight leads
of the same width which cross at an angle . Such a four-terminal
junction with a tunable can realized experimentally if a right-angle
structure is filled by a ferrite. It is known that for there is
one proper bound state and one eigenvalue embedded in the continuum. We show
that the number of eigenvalues becomes larger with increasing asymmetry and the
bound-state energies are increasing as functions of in the interval
. Moreover, states which are sufficiently strongly bent exist in
pairs with a small energy difference and opposite parities. Finally, we discuss
how with increasing the bound states transform into the quasi-bound
states with a complex wave vector.Comment: 6 pages, 6 figure
Structure, Time Propagation and Dissipative Terms for Resonances
For odd anharmonic oscillators, it is well known that complex scaling can be
used to determine resonance energy eigenvalues and the corresponding
eigenvectors in complex rotated space. We briefly review and discuss various
methods for the numerical determination of such eigenvalues, and also discuss
the connection to the case of purely imaginary coupling, which is PT-symmetric.
Moreover, we show that a suitable generalization of the complex scaling method
leads to an algorithm for the time propagation of wave packets in potentials
which give rise to unstable resonances. This leads to a certain unification of
the structure and the dynamics. Our time propagation results agree with known
quantum dynamics solvers and allow for a natural incorporation of structural
perturbations (e.g., due to dissipative processes) into the quantum dynamics.Comment: 14 pages; LaTeX; minor change
Theory of x-ray absorption by laser-dressed atoms
An ab initio theory is devised for the x-ray photoabsorption cross section of
atoms in the field of a moderately intense optical laser (800nm, 10^13 W/cm^2).
The laser dresses the core-excited atomic states, which introduces a dependence
of the cross section on the angle between the polarization vectors of the two
linearly polarized radiation sources. We use the Hartree-Fock-Slater
approximation to describe the atomic many-particle problem in conjunction with
a nonrelativistic quantum-electrodynamic approach to treat the photon-electron
interaction. The continuum wave functions of ejected electrons are treated with
a complex absorbing potential that is derived from smooth exterior complex
scaling. The solution to the two-color (x-ray plus laser) problem is discussed
in terms of a direct diagonalization of the complex symmetric matrix
representation of the Hamiltonian. Alternative treatments with time-independent
and time-dependent non-Hermitian perturbation theories are presented that
exploit the weak interaction strength between x rays and atoms. We apply the
theory to study the photoabsorption cross section of krypton atoms near the K
edge. A pronounced modification of the cross section is found in the presence
of the optical laser.Comment: 13 pages, 3 figures, 1 table, RevTeX4, corrected typoe
Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers
Free energies and other thermodynamical quantities are investigated in
canonical and grand canonical ensembles of statistical mechanics involving
unstable states which are described by the generalized eigenstates with complex
energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is
applied to the systems containing parabolic potential barriers (PPB's). The
entropy and energy productions from PPB systems are studied. An equilibrium for
a chemical process described by reactions is also
discussed.Comment: 14 pages, AmS-LaTeX, no figur
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