Ultrashort pulse propagation under manipulated resonance conditions

The propagation of a polarized ultrashort laser pulse is analyzed by the inverse scattering method under initial conditions including a spatial pulse profile, a state of the medium, and a “switched-on” resonant atom-field interaction. Magnetic degeneracy of atomic levels is taken into account. The Maxwell-Bloch equations are rewritten in Hamiltonian form without redefining the spatial and temporal variables. The inverse scattering method is based on an analysis of a new spectral problem. Gelfand-Levitan-Marchenko-type equations are derived, a soliton solution is obtained, and the changes in parameters of two solitons after their collision are calculated. A possible experimental setup for implementing the system under analysis is discussed.     

Effects of collisions on linear and non-linear spectroscopic line shapes

A fundamental physical problem is the determination of atom-atom, atom-molecule and molecule-molecule differential and total scattering cross sections. In this work, a technique for studying atomic and molecular collisions using spectroscopic line shape analysis is discussed. Collisions occuring within an atomic or molecular sample influence the sample's absorptive or emissive properties. Consequently the line shapes associated with the linear or non-linear absorption of external fields by an atomic system reflect the collisional processes occuring in the gas. Explicit line shape expressions are derived characterizing linear or saturated absorption by two- or three-level “active” atoms which are undergoing collisions with perturber atoms. The line shapes may be broadened, shifted, narrowed, or distorted as a result of collisions which may be “phase-interrupting” or “velocity-changing” in nature. Systematic line shape studies can be used to obtain information on both the differential and total active atom-perturber scattering cross sections.     

Nonlinear transport and dynamics of fluctuations

The time evolution of the macroscopic variables of a system initially in a state far from thermal equilibrium is studied from a statistical mechanical point of view. Exact nonlinear transport equations for the mean values and linear nonstationary Langevin equations for the fluctuations around the mean path are derived. Connections between the dynamics of fluctuations and the transport equations are discussed. The Langevin random forces depend on the macroscopic state and they are related to the transport kernels by a fluctuation-dissipation formula.     

Response functions for crystals and surfaces,with applications to surface scattering

A general solution of the equations of forced motion of a harmonic crystal or other vibrating system with arbitrary time-dependent forces acting on the atoms is given. The solution is given in terms of dynamical “response functions”, for which expressions in terms of the normal mode frequencies and eigenvectors (polarization vectors) are given. Numerical calculations of the response functions are described for (111) and (100) surfaces of face-centered cubic crystals interacting with Lennard-Jones 6–12 potentials, and the qualitative features of the surface and bulk response functions are discussed. The use of these functions in problems of atomic scattering from surfaces is outline, and conveneint parameterized forms for this application are given.     

Ionization and stabilization of a three-dimensional system with a short-range potential in a strong laser field

The interaction of a three-dimensional atomic system in a short-range potential with intense laser radiation is investigated by the direct numerical integration of the nonstationary Schrödinger equation. The calculations helped to discover a stabilization regime, which is interpreted as a result of forming a Kramers-Henneberger atom “dressed” in a field. Dynamics of the energy spectrum of photoelectrons depending on the increase of the laser field intensity is investigated, and conditions of a photodetachment of an electron from a bound state of the Kramers-Henneberger potential are analyzed. These results reveal specific features of the stabilization process of the three-dimensional system with a short-range potential compared to the similar process in a system with a long-range (Coulomb) potential.     

Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

Multiple Rayleigh-Gans-Debye scattering in colloidal systems-dynamic light scattering

Equations for (depolarized) intensity auto-correlation functions including second order scattering contributions are derived. The equations obtained are quite similar to those for static light scattering¹). The geometry of the scattering system plays an important role here.An iterative procedure to correct correlation functions for double scattering is presented.Experiments on colloidal solutions containing latex and silica particles are performed, testing the theory and the iterative correction procedure for double scattering. We use cylindrical cuvettes with cylindrical incident and detected beams of radiation. The agreement between experiment and theory is found to be quite good, yielding a routine correction procedure for double scattering.     

Thermal decomposition of bogolyubov “Chains” in the quasiharmonic approximation for the case of an ionic crystal

The problem of Bogolyubov “chains” for binary distribution functions of a two-component system is solved in the first approximation of the thermal decomposition process. The corresponding equations of state are derived for the case of an ionic crystal.     

The variational method in atomic scattering

This paper reviews the application of the variational method to the scattering (both elastic and inelastic) of electrons and positrons by atoms. The coupled equations of scattering theory are formulated using a pseudostate expansion. The Kohn variational procedure for multichannel scattering is derived. Many variants are considered, including the inverse Kohn procedure, the “optimized minimum norm”, the “optimized anomaly free”, and the “variational least squares”. Applications to both model and realistic problems are described. Results obtained for scattering by hydrogen, and by complex atoms are discussed.     

Nonstationary two-flux model of radiation transport for optical tomography of scattering media

A nonstationary two-flux model is formulated for the transport of radiation in an inhomogeneous scattering medium and is applied to the situation where such a medium is irradiated by the narrow beam of a pulsed laser. It is shown that when the time distribution of the transmitted photons is measured it is possible simultaneously to reconstruct the two spatial functions (the coefficients of absorption coefficient and of scattering of the radiation by the medium) by means of an inverse Radon transformation and the solution of a system of nonlinear differential equations on the projection lines. An analytic solution is obtained in quadratures for these differential equations. The results constitute a method of solving problems in optical tomography in an inhomogeneous scattering medium Zh. Tekh. Fiz. 67, 61–65 (May 1997)     

A source of nonclassical radiations exhibiting photon antibunching

We show that coherent spontaneous emission by a two-level atomic system in a Dicke state placed in a resonant cavity gives a non-classical radiation exhibiting photon-antibunching. It is assumed that the “effective” population of the ground state atoms is initially large compared to unity.     

On the theory of superradiant Rayleigh Scattering from a Bose-Einstein condensate

A theory of the superradiant Rayleigh scattering by a Bose-Einstein condensate is suggested. The theory is based on a semiclassical approach. Atomic states with definite momenta are used as basis functions. The Maxwell-Bloch equations are derived and solved to describe the intensity of scattered radiation and the evolution of the population of coherent atomic states.     

Wave Resonance in Media with Modular,Quadratic and Quadratically-Cubic Nonlinearities Described by Inhomogeneous Burgers-Type Equations

The phenomenon of “wave resonance” which occurs at excitation of traveling waves in dissipative media possessing modular, quadratic and quadratically-cubic nonlinearities is studied. The mathematical model of this phenomenon is the inhomogeneous (or “forced”) equation of Burgers type. Such nonlinearities are of interest because the corresponding equations admit exact linearization and describe real physical objects. The presence of “accompanying sources” (traveling with the wave) on the right-hand side of the inhomogeneous equations ensures the inflow of energy into the wave, which thereafter spreads throughout the wave profile, flows to emerging shock fronts, and then dissipates due to linear and nonlinear losses. As an introduction, the phenomenon of wave resonance in ideal and dissipative media is described and physical examples are given. Exact expressions for nonlinear steady-state wave profiles are derived. Non-stationary processes of wave generation, spatial “beating” of amplitudes with different relationship between the speed of motion of the sources and the natural wave velocity in the medium are studied. Resonance curves are constructed that contain a nonlinear shift of the absolute maxima to the “supersonic” region. The features of the resonance in each of the three types of nonlinearity are discussed.     

压缩真空中梯形三能级原子的辐射压力

研究了压缩真空中梯形三能级原子在单色行波场中的辐射压力。从系统的哈密顿量出发,利用玻因-马尔可夫近似,推导出了原子的光学布洛赫方程。此时用数值方法求得布洛赫方程的稳态解,然后用图示法考察了原子的辐射压力随双光子失谐、拉比频率、自发发射率等参量的依赖关系。结果表明：单光子跃迁和双光子跃迁可导致辐射压力出现各自的多普勒位移共振峰;辐射压力表现出较宽的失谐范围且强烈依赖于压缩参量以及压缩真空和相干光之间的相位关系。当相位满足匹配条件时,辐射压力减小。     

Classical dynamical theory of heavy ion fusion and scattering

A classical dynamical model which includes dissipative forces is suggested for heavy ion reactions high above the Coulomb barrier. Internal degrees of freedom corresponding to rotation of the ions are included. The reactions divide into three parts: (1) quasi-elastic scattering, with relatively small energy loss, associated with higher angular momenta, (2) deep inelastic scattering, with larger energy loss and considerable transfer of mass, associated with intermediate angular momenta, and (3) complete fusion where a highly excited compound state is formed, generally associated with the lowest angular momenta. One can predict a fusion cross section for two values of the friction coefficient, “weak” and “strong” friction cases. Reasonable values for fusion can be obtained in the weak friction case, but scattering angular distributions are not consistent with available experimental data. In the strong friction case it is more difficult to fit all the fusion cross sections with a single friction parameter. But the predicted angular distributions and energy losses are in better agreement with experiment than for the weak friction case.     

Observation of latent coherent effects in randomized systems

Coherent interference effects of the following three types are experimentally discovered in disordered (randomized) systems: (i) Josephson behavior of the HTSC polycrystal BaKBiO in the phase-separated state; (ii) oscillations of bismuth film resistance, which are periodic in “direct” magnetic field; and (iii) mesoscopic oscillations of the resistance in the course of film growth. In the first case, the method for detecting the “latent” nonstationary Josephson effect is substantiated by the frequency modulation method for microwave radiation, while in the other two cases, simple models are proposed to explain the nature of coherent oscillations of the resistance. The analogy between the observed oscillations and the Josephson effect in randomized systems is discussed.     

Structure analysis of multiphase systems by anomalous small-angle X-ray scattering

The theory of small-angle scattering is reviewed with special attention paid to the anomalous scattering and multiphase systems. A general equation is derived that describes the scattering of a multiphase system as a sum of scattering functions of each of the phases, as if it scattered alone in a two-phase system, and interphase interference scattering functions. These scattering functions depend only on the spatial distribution of the phase boundaries, but not on the scattering density. Contrast variation techniques are most rewarding when the scattering density of only one phase can be varied. For anomalous small-angle X-ray scattering (ASAXS), this means the most favourable is the case in which resonant atoms are contained in one phase only. The general equation involves n(p ? 1) unknown partial atomic number density differences, where p is the number of phases and n the number of the different atom types in the sample. These partial atomic number density differences can be found if a suitable structure model is applied to calculate the phase scattering functions. Then, the phase compositions and densities can be calculated by solving a system of linear equations incorporating the atom number conservation law. The partial structure factors formalism is also reviewed. Corresponding equations for a system of n types of atoms and p phases are derived. The number of independent partial structure factors is p(p ? 1)/2 and depends on the number of phases, but not on the number of the types of the atoms in the sample, as in the case of wide-angle scattering.     

Structure of the superfluid ground state of an atomic Fermi gas near the Feshbach resonance

The ground state of an atomic Fermi gas near the Feshbach resonance for a negative scattering length is investigated using the variational method. The structure of the superfluid state is formed by two coherently coupled subsystems, viz., the quasimolecular subsystem in a closed channel and the subsystem of atomic pairs in an open channel. The derived system of equations makes it possible to describe the properties of the ground state for arbitrary values of the parameters (in particular, to find the gap in the single-particle Fermi excitation spectrum and the speed of sound characterizing the branch of collective Bose excitations).