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 DyScO3_3

We report the low temperature magnetic properties of the DyScO$_3$ perovskite, which were characterized by means of single crystal and powder neutron scattering, and by magnetization measurements. Below $T_{\mathrm{N}}=3.15$ K, Dy$^{3+}$ moments form an antiferromagnetic structure with an easy axis of magnetization lying in the $ab$-plane. The magnetic moments are inclined at an angle of $\sim\pm{28}^{\circ}$ to the $b$-axis. We show that the ground state Kramers doublet of Dy$^{3+}$ is made up of primarily $|\pm 15/2\rangle$ eigenvectors and well separated by crystal field from the first excited state at $E_1=24.9$ meV. This leads to an extreme Ising single-ion anisotropy, $M_{\perp}/M_{\|}\sim{0.05}$. The transverse magnetic fluctuations, which are proportional to $M^{2}_{\perp}/M^{2}_{\|}$, 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 $c$-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 $\nu$) of the Fresnel equation is also performed and, in detail, some specific cases, like $\nu=1/2$, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process $F(t)$, $t>0$ 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 $C_R$ is investigated by applying the methods of planar orthogonally reflecting Brownian motion within $C_R$. The composition of F with reflecting Brownian motion $B$ yields the law of biquadratic heat equation while the composition of $F$ with the first passage time $T_t$ of $B$ 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