Far infrared and millimeter wave studies of impurity scattering within electron-hole liquid in semiconductors

Despite the experimental evidence in far-infrared that impurities are ionized within the electron-hole liquid in silicon and germanium, combination of luminescence data with millimeter wave cyclotron resonance and far-infrared magneto-optics tells us that the impurity-assisted intervalley electron scattering within EHL in silicon can apparently be interpreted on the basis of neutral impurity scattering. Justification of simulating the impurity center within EHL as neutral is grounded for the electron scattering problem, making use of the atomic scattering theory in contrast with a simple ionized impurity model calculation with proper screening.     

Some aspects of image processing using foams

We have explored some concepts of chaotic dynamics and wave light transport in foams. Using some experiments, we have obtained the main features of light intensity distribution through foams. We are proposing a model for this phenomenon, based on the combination of two processes: a diffusive process and another one derived from chaotic dynamics. We have presented a short outline of the chaotic dynamics involving light scattering in foams. We also have studied the existence of caustics from scattering of light from foams, with typical patterns observed in the light diffraction in transparent films. The nonlinear geometry of the foam structure was explored in order to create optical elements, such as hyperbolic prisms and filters.     

Solvability of linear kinetic equations with multi-energetic inelastic scattering

In this paper we shall analyse the linear Boltzmann equation describing the motion of test particles through a background of heavy field particles that can appear in several energy states. The inelastic scattering process consists in the exchange of quanta of energy between the field and test particles. The well-posedness of the problem is investigated by means of the substochastic semigroup theory and the conditions on the scattering collision frequencies are given for the evolution to keep the collision rate finite and to preserve the total number of particles.     

Scattering Theory for Jacobi Operators with Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators which are short range perturbations of quasi-periodic finite-gap operators. We show existence of transformation operators, investigate their properties, derive the corresponding Gel'fand-Levitan-Marchenko equation, and find minimal scattering data which determine the perturbed operator uniquely. Work supported by the Austrian Science Fund (FWF) under Grant No. P17762, the Austrian Academy of Sciences under DOC-21388, and INTAS Research Network NeCCA 03-51-6637.     

Scattering theory relevant to the linear transport of particle swarms

The long-time behavior of the velocity distribution of a spatially uniform diluted guest population of charged particles moving within a host medium under the influence of a D.C. electric field is studied within the framework of scattering theory. We prove the existence of wave and scattering operators for a simplified one-dimensional model of the linearized Boltzmann equation. The theory is applied to the study of the long-term behavior of electrons and the occurrence of traveling waves in runaway processes.     

Scattering theory of the linear Boltzmann operator

In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schrödinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Møller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space.     

Wave-packet continuum discretization for quantum scattering

A general approach to a solution of few- and many-body scattering problems based on a continuum-discretization procedure is described in detail. The complete discretization of continuous spectrum is realized using stationary wave packets which are the normalized states constructed from exact non-normalized continuum states. Projecting the wave functions and all scattering operators like t$t$-matrix, resolvent, etc. on such a wave-packet basis results in a formulation of quantum scattering problem entirely in terms of discrete elements and linear equations with regular matrices. It is demonstrated that there is a close relation between the above stationary wave packets and pseudostates which are employed often to approximate the scattering states with a finite L₂$L_2$ basis. Such a fully discrete treatment of complicated few- and many-body scattering problems leads to significant simplification of their practical solution. Also we get finite-dimensional approximations for complicated operators like effective interactions between composite particles constructed via the Feshbach-type projection formalism. As illustrations to this general approach we consider several important particular problems including multichannel scattering and scattering in the three-nucleon system within the Faddeev framework.     

Marangoni instability of a liquid layer with insoluble surfactant under heat flux modulation

We investigate the parametric excitation of Marangoni convection by a periodic flux modulation in a liquid layer with insoluble surfactant absorbed on the nondeformable free surface. The stability analysis of the convective system is performed for arbitrary wave numbers of the disturbances. An interesting feature of the onset of convection is the existence of bifurcating neutral curves with double minima, one of which corresponds to a quasi-periodic solution, and the other one corresponds to a subharmonic solution. The evolution of the subharmonic instability region depending on the amplitude of the external heat flux modulation and the frequency of the modulation is studied. The quasi-periodic neutral curve is close to the oscillatory neutral curve of the nonmodulated problem.     

Correlations of a single atom and a resonance mode and their manifestation in some physical phenomena

A kinetic equation governing relaxation of a single two-level atom and a high-Q cavity mode in an entangled thermostat exhibiting quantum correlations is presented. Based on two kinds of collective operators, we demonstrate the possibility of the existence of dual squeezed states in this system. One kind of generator of collective operators corresponds to algebra obtained by polynomial deformation of the angular-momentum algebra, while the other kind corresponds to the Heisenberg-Weyl algebra. Squeezed states of the collective system are defined in terms of commutative relations for operators of the corresponding generator algebras. It is shown that quantum correlations in the system manifest themselves in two physical phenomena. The first one is the known entanglement-swapping protocol and is based on the projection measurement. In the other case, quantum correlations reveal themselves in the coherent scattering dynamics of an atom in the field of a standing light wave.     

Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model

Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure point spectrum outside its thresholds. We study the asymptotic fields and the existence of the wave operators. Finally we show asymptotic completeness for the Nelson Hamiltonian.     

Semiclassical expansion of quantum characteristics for many‐body potential scattering problem

In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star‐product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many‐body potential scattering problem simplifies to a statistical‐mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ?. We present semiclassical expansion of quantum characteristics for many‐body scattering problem and provide tools for calculation of average values of time‐dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non‐locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum‐mechanical extensions of the Liouville theorem on conservation of the phase‐space volume and the Poincaré theorem on conservation of 2p‐forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior.     

On scattering of diffusion process generators

If a selfadjoint generator of a diffusion process is perturbed by nonnegative potentials different on a compact region of non-zero measure the corresponding wave operators exist and are asymptotically complete even if one potential is singular on the region considered. That includes the hardcore potential scattering problem for second-order elliptic differential operators with variable coefficients.     

Travelling wave solutions for a singularly perturbed Burgers-KdV equation

This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers-KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for kink-type waves.     

Radar studies of ionospheric dusty plasma phenomena

We discuss the influence of charged dust on radar observations in the Earth ionosphere. This region in the upper Earth atmosphere can be described as a partially ionized, low‐temperature plasma. Plasma parameters vary by orders of magnitude spatially and in time. Dust particles influence the charge balance, in some cases dusty plasma condition is met. The polar mesospheric echoes are an example of dust plasma interactions observed with radar. The mesosphere is a region where atmospheric temperature decreases with altitude and can reach frost point temperature. The formation of the polar mesospheric radar echoes involves neutral atmosphere dynamics, which is latitude dependent and it involves charged dust particles, especially icy dust that forms in the polar summer mesosphere. Charged dust can also influence incoherent scatter that results from electromagnetic waves scattering off electrons, where the electrons are coupled to other charged components. Observers rarely report charged dust signatures in the incoherent scatter spectra; we show that there is a good chance for doing so with improved observations. The incoherent scatter can possibly also be used to estimate the amount of charged dust in the direct vicinity of a meteor, as we show based on the order of magnitude considerations. This prospect of new observational results makes theoretical investigations of radio‐wave scattering in the presence of charged dust with size distributions worthwhile.     

Thomson scattering off a pair （electron-positron） plasma

Thomson scattering off a pair (electron--positron) plasma is theoretically investigated in the collisionless and collisional limits respectively. Our calculations show that the power spectrum of the Thomson scattering off a collisionless pair plasma is just proportional to the velocity distribution function of the particles in the plasma. Collective modes in the plasma do not have any effects on the Thomson scattering spectrum because of the correlation between the negatively- and positively-charged particles. In the collisional limit, the power spectrum of the Thomson scattering presents three spikes: two peaks correspond to two contra-propagating sound waves and one peak corresponds to an entropy wave.     

Eigenvalues of one-dimensional non-self-adjoint Dirac operators and applications

We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials. In the general non-self-adjoint setting, we establish the existence and asymptotics of weakly coupled eigenvalues and Lieb–Thirring inequalities. As physical applications, we investigate the damped wave equation and armchair graphene nanoribbons.     

On Odd Perturbations of Free Fermion Fields

We study the scattering theory of fermion systems subject to a smooth local perturbation with a non-vanishing odd part. We introduce a modified free fermion fields which have an appropriate commutation relations with the free Fock fermion fields. We construct the wave operators using the modified field and prove asymptotic completeness. Our work extends former results on Hilbert space asymptotic completeness.     

太赫兹波在雾中的多重散射特性

太赫兹(THz)波作为微波和毫米波的延伸,它所提供的通信带宽和容量远大于毫米波。在随机介质中传播时,不但会发生时域和空域的形变,介质中的粒子还会对入射波发生散射,这些都会使得脉冲信号发生衰减。根据Mie理论与随机离散分布粒子的波传播与散射理论,计算了THz波信号入射下雾滴粒子的消光系数。结合雾滴粒子谱分布,得到了雾媒质的平均体系散射特性,采用蒙特卡罗法得到了平流雾对THz信号的多重散射特性,计算了THz波段信号对平流雾的透过率与反射率,分析了THz波段信号的前向、后向散射特性随散射角的分布。结果表明,低能见度大气环境中,雾对THz波产生的吸收和衰减不容忽视。相关研究结果对THz在大气传输、通信等方面的应用具有重要意义。     

雷达波段内磁性吸波颗粒光散射特性分析

针对目前在微波雷达隐身技术中广泛运用的吸波材料颗粒,根据米氏(Mie)散射理论对磁性吸波颗粒在雷达波段内的光散射特性进行了数值模拟和计算分析.在Mie系数中引入磁导率变量,分别计算了磁导率、折射率及颗粒粒径等参数对吸波颗粒光散射特性的影响;同时对比分析了磁性与非磁性吸波颗粒的散射光强、散射系数、吸收系数等散射特性规律.数值计算结果表明,颗粒磁特性的变化对其散射性能造成影响,磁导率的增大将使颗粒的吸收性能增强而后向散射强度减弱,有利于吸波颗粒雷达散射截面的减小,同时磁导率变化对颗粒散射特性的影响受到复折射率的制约.     

用蒙特卡罗方法计算光通过薄层随机分布粒子的散射

本文利用蒙特卡罗方法计算准直光束通过薄层随机分布粒子散射的透射和反射光强,并和输运理论的扩散近似结果做了比较。当散射接近各向同性时两者符合良好。当散射明显地成为各向异性时,蒙特卡罗方法的结果是合理的,而输运理论的扩散近似失效。