4,321 research outputs found
Analytic calculation of nonadiabatic transition probabilities from monodromy of differential equations
The nonadiabatic transition probabilities in the two-level systems are
calculated analytically by using the monodromy matrix determining the global
feature of the underlying differential equation. We study the time-dependent
2x2 Hamiltonian with the tanh-type plus sech-type energy difference and with
constant off-diagonal elements as an example to show the efficiency of the
monodromy approach. The application of this method to multi-level systems is
also discussed.Comment: 13 pages, 2 figure
Optimal processing of noisy images in a photodetector with limited dynamic range
A study aimed at optimizing noisy image processing under conditions of strong additive noise has been performed. An algorithm of optimal signal processing was developed and a possibility of improving image quality due to the subtraction of excess additive noise (which limits the photodetector dynamic range) was substantiated. The possibility of technical implementation of noise subtraction due to forced recombination of charge carriers in the photodetector is experimentally confirmed. The proposed approach to design processing systems makes it possible to improve the quality of recorded images under noisy conditions without any changes in the photodetector desig
Magnetic ground state of the Ising-like antiferromagnet DyScO
We report the low temperature magnetic properties of the DyScO
perovskite, which were characterized by means of single crystal and powder
neutron scattering, and by magnetization measurements. Below
K, Dy moments form an antiferromagnetic structure
with an easy axis of magnetization lying in the -plane. The magnetic
moments are inclined at an angle of to the -axis. We
show that the ground state Kramers doublet of Dy is made up of primarily
eigenvectors and well separated by crystal field from the
first excited state at meV. This leads to an extreme Ising
single-ion anisotropy, . The transverse magnetic
fluctuations, which are proportional to , are
suppressed and only moment fluctuations along the local Ising direction are
allowed. We also found that the Dy-Dy dipolar interactions along the
crystallographic -axis are 2-4 times larger than in-plane interactions.Comment: 9 pages and 6 figures; to be published in Phys. Rev.
Vibrations and fractional vibrations of rods, plates and Fresnel pseudo-processes
Different initial and boundary value problems for the equation of vibrations
of rods (also called Fresnel equation) are solved by exploiting the connection
with Brownian motion and the heat equation. The analysis of the fractional
version (of order ) of the Fresnel equation is also performed and, in
detail, some specific cases, like , 1/3, 2/3, are analyzed. By means
of the fundamental solution of the Fresnel equation, a pseudo-process ,
with real sign-varying density is constructed and some of its properties
examined. The equation of vibrations of plates is considered and the case of
circular vibrating disks is investigated by applying the methods of
planar orthogonally reflecting Brownian motion within . The composition of
F with reflecting Brownian motion yields the law of biquadratic heat
equation while the composition of with the first passage time of
produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure
Strong-coupling limit in cold-molecule formation via photoassociation or Feshbach resonance through Nikitin exponential resonance crossing
The strong-coupling limit of molecule formation in an atomic Bose-Einstein
condensate via two-mode one-color photoassociation or sweep across a Feshbach
resonance is examined using a basic nonlinear time-dependent two-state model.
For the general class of term-crossing models with constant coupling, a common
strategy for attacking the problem is developed based on the reduction of the
initial system of semiclassical equations for atom-molecule amplitudes to a
third order nonlinear differential equation for the molecular state
probability. This equation provides deriving exact solution for a class of
periodic level-crossing models. These models reveal much in common with the
Rabi problem. Discussing the strong-coupling limit for the general case of
variable detuning, the equation is further truncated to a limit first-order
nonlinear equation. Using this equation, the strong nonlinearity regime for the
first Nikitin exponential-crossing model is analyzed and accurate asymptotic
expressions for the nonlinear transition probability to the molecular state are
derived. It is shown that, because of a finite final detuning involved, this
model displays essential deviations from the Landau-Zener behavior. In
particular, it is shown that in the limit of strong coupling the final
conversion probability tends to 1/6. Thus, in this case the strong interaction
limit is not optimal for molecule formation. We have found that if optimal
field intensity is applied the molecular probability is increased up to 1/4
(i.e., the half of the initial atomic population)
Coherent Excitation of a Two-Level Atom driven by a far off-resonant Classical Field: Analytical Solutions
We present an analytical treatment of coherent excitation of a Two-Level Atom
driven by a far-off resonant classical field. A class of pulse envelope is
obtained for which this problem is exactly solvable. The solutions are given in
terms of Heun function which is a generalization of the Hypergeometric
function. The degeneracy of Heun to Hypergeometric equation can give all the
exactly solvable pulse shapes of Gauss Hypergeometric form, from the
generalized pulse shape obtained here. We discuss the application of the
results obtained to the generation of XUV.Comment: 9 Pages, 8 Figures. Accepted for Physical Review A as a regular
articl
Shapes of leading tunnelling trajectories for single-electron molecular ionization
Based on the geometrical approach to tunnelling by P.D. Hislop and I.M. Sigal
[Memoir. AMS 78, No. 399 (1989)], we introduce the concept of a leading
tunnelling trajectory. It is then proven that leading tunnelling trajectories
for single-active-electron models of molecular tunnelling ionization (i.e.,
theories where a molecular potential is modelled by a single-electron
multi-centre potential) are linear in the case of short range interactions and
"almost" linear in the case of long range interactions. The results are
presented on both the formal and physically intuitive levels. Physical
implications of the obtained results are discussed.Comment: 14 pages, 5 figure
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