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The second-order Born approximation (SBA) has been used to calculate the differential cross section for electron-hydrogen collisions in the presence of a linearly polarized laser field. We present a more precise treatment of the small-energy region of an incident electron by improving the calculation of the second Born term in this energy region. Detailed calculations of the scattering amplitudes are performed by using the Sturmian basis expansion. Our SBA results agree very well with those obtained in the first-order Born approximation at larger incident electron energies.

<p style='text-indent:20px;'>Pseudo almost automorphy (PAA) is a natural generalization of Bochner almost automorphy and Stepanov almost automorphy. Therefore, the results of the existence of PAA solutions of differential equations are few, and the results of the existence of pseudo almost automorphic solutions of difference equations are rare. In this work, we are concerned with a model of delayed cellular neural networks (CNNs). The delays are considered in varying-time form. By the Banach's fixed point theorem, Stepanov like PAA, and constructing a novel Lyapunov functional, we fixed a sufficient criteria that agreement the existence and the Stepanov-exponential stability of Stepanov-like PAA solution of this model of CNNs are obtained. In addition, a numerical example and simulations are performed to verify our theoretical results.</p>

Short title: Theoretical study of quantum dissipation and Laser noise effects PACS index number(s): 42.50. Lc, 42.50.Ct Submitted to: Phys. Rev A. Date: 14 September 1998 AbstractThe nonlinear dynamics of dissipative quantum systems in incoherent laser fields is studied in the framework of master equation with random telegraph model describing the laser noise and Markovian approximation for dealing with the system-bath couplings. Floquet theory and time-dependent perturbation methods are used to facilitate both analytical and numerical solutions. We develop a theoretical formalism that provides a powerful tool for the detailed analysis of the dissipative quantum dynamics of multilevel systems driven by intense stochastic laser fields. It is found that the system relaxes to a steady state by the effect of laser phase and frequency noises and the kinetic of this relaxation increases with the addition of dissipative terms, introduced by the coupling to the reservoir. The case of amplitude fluctuations shows a different behavior. Other results concerning the destruction of quantum coherence and the dynamical localization will be established and further relaxation mechanisms such spontaneous emission and ionization process will be also considered. I-INTRODUCTIONThe study of the time evolution of quantum systems, which are on the one hand driven by an external field and in contact with a heat bath (reservoir) on the other hand, has received a great deal of attention in recent years [1][2][3][4]. In quantum optics, such systems are investigated in the dressed-atom picture of resonance fluorescence [5], where a beam of atoms interacts with a coherent laser field and all the electromagnetic modes of the vacuum [6].Moreover, it is by now recognized that nearly all types of laser-atom interactions can be strongly affected by laser noise. Indeed one practical reason to this fact is the use, in experiments, of high powers which are obtained in pulsed operation, and thus at the expense of poorly stabilized laser beams. Furthermore, real atoms experience a fluctuating environment of many perturbing interactions and ideal lasers exist only in theoretical models, while the used laser sources are subjected to many types of fluctuations notably in phase, amplitude and frequency [7][8][9][10]. Other kinds of fluctuations due to collisional effects can affect the atomic transition frequencies [9,11]. Therefore, we cannot establish, without taking into account of the dissipative action of the environment and the statistical properties of the laser light, a rigorous comparison between theoretical predictions and experimental results. Different approaches to the dissipative dynamics of open quantum systems in strong external fields has been proposed and applied to the description of atoms under the influence of thermal noise [1][2][3][4]. While for the incoherence of laser field, a series of models, all based on so-called pre-Gaussian Markovian processes [7][8][9][10] has been used in order to describe the stochastic behavior of the...

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