准孤子对在色散缓变光纤中传输特性的数值研究

用分步富里叶变换法求解色散缓变光纤的光孤子NLS方程，在一定条件下孤子对在该光纤中演变为准孤子，其幅值和宽度发生周期性变化，没有出现通常情况下的周期性离合现象。     

On the modulation instability development in optical fiber systems

Extensive numerical simulations were performed to investigate all stages of modulation instability development from the initial pulse of pico-second duration in photonic crystal fiber: quasi-solitons and dispersive waves formation, their interaction stage and the further propagation. Comparison between 4 different NLS-like systems was made: the classical NLS equation, NLS system plus higher dispersion terms, NLS plus higher dispersion and self-steepening and also fully generalized NLS equation with Raman scattering taken into account. For the latter case a mechanism of energy transfer from smaller quasi-solitons to the bigger ones is proposed to explain the dramatical increase of rogue waves appearance frequency in comparison to the systems when the Raman scattering is not taken into account.     

随机共振问题Fokker-Planck方程的数值研究

本文用有限差分方法对一随机共振的Fokker-Planck方程的主要性质进行了广泛的数值研究。结果表明,当绝热近似条件ω?D△V和小信号近似条件A?1得到满足时,以往的解析近似理论结果与数值结果符合;当驱动强度增加时,则系统表现出明显的决定性非线性振动行为。然而,就随机共振问题本身而言,绝热近似解析理论概括了在双稳系统中发生的随机共振的主要性质。 关键词：     

Quasi-solitons of magnetostatic waves in a two-layer structure under single-mode excitation

We investigate the quasi-solitons of the envelope of forward body magnetostatic waves in a structure that consists of two magnetically coupled films separated by a nonmagnetic interlayer under the initial excitation of a pulse in one of them. We have found that as the pulse propagates, its energy is transferred from one film to the other through intermode coupling; as a result, “pulsating” quasi-solitons of the coupled modes of the two films emerge. We show that the amplitude of each of the mode pulses at the exit from the waveguide can be regulated over a wide range by varying the magnetizing field.     

Theoretical studies of inelastic atomic collisions in a two-state model problem

A two-state scattering problem in which two non-crossing Morse curves are coupled by an exponential potential is discussed theoretically in both the diabatic and adiabatic approximations. Inelastic cross sections are estimated by various approximate analytical formulas, which are expressed in terms of the distorted wave matrix elements. The Landau (steepest descent) method is applied to estimate the distorted wave matrix element. The previously proposed separable potential approximation in the adiabatic method is found to be best among others by comparing with the exact numerical results. Transition probability as a function of l (angular momentum of relative motion) is well reproduced by this approximation. A glory effect in the velocity dependence of the cross section is found in the low energy region, and the adiabatic approximation reproduces this undulation phenomenon well.     

Analytical control of molecular excitations including strong field polarization effects

An analytical scheme is presented for designing a laser pulse to excite H2 from one specified vibrational-rotational state to another. The scheme is based on an adiabatic two-state approximation in a Floquet picture. By continuously and smoothly changing the laser frequency, we explicitly harness the dynamic Stark shifts and maintain resonance between the dressed diabatic states during laser-molecule interaction. The explicit time-dependent solution of the Schr?dinger equation confirms the validity and efficacy of the analytically designed laser pulses. The scheme depends on the molecular polarizability to achieve its control objectives.     

Mass-Imbalanced Three-Body Systems in 2D: Bound States and the Analytical Approach to the Adiabatic Potential

Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schrödinger equation is used to study universal properties of such systems with respect to the bound-state energies. The number of universal bound states is represented in a form of boundaries in a mass-mass diagram. The number of bound states is strongly mass dependent and increases as one particle becomes much lighter than the other ones. This behavior is understood through an accurate analytical approximation to the adiabatic potential for one light particle and two heavy ones.     

非对称双稳耦合网络系统的尺度随机共振研究

研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象. 关键词： 尺度随机共振 非对称双稳耦合网络系统 余弦信号 矩形信号     

Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback

Based on adiabatic approximation theory, in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise. The analytical expressions of the mean first-passage time(MFPT) and output signal-to-noise ratio(SNR) are derived by using a path integral approach, unified colored-noise approximation(UCNA), and small delay approximation. The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed. Moreover, three types of asymmetric potential function characteristics are thoroughly discussed. And they are well-depth asymmetry(DASR), well-width asymmetry(WASR), and synchronous action of welldepth and well-width asymmetry(DWASR), respectively. The conclusion of this paper is that the time-delayed feedback can suppress SR, however, the non-Gaussian noise deviation parameter has the opposite effect. Moreover, the correlation time plays a significant role in improving SNR, and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance. Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance, in which no matter whether these signals have low frequency or high frequency, accompanied by strong or weak noise.     

Inversion in an extended three-level medium produced by adiabatic population transfer

Features of the adiabatic population transfer are studied with the spatial evolution of interacting pulses propagating in an optically dense medium of three-level Λ-atoms taken into account. A self-consistent analytical solution describing the spatial-temporal dynamics of interacting short pulses under the conditions of adiabatic population transfer is constructed in the adiabatic approximation with consideration for the first nonadiabatic correction. Practically complete inversion on a forbidden transition determined by coherent (adiabatic) population transfer is shown to take place over a length of the medium, which may exceed the absorption length of a weak probing pulse in the absence of control radiation on the adjacent transition by several orders of magnitude.     

Adiabatic Soliton Compresion in an Exponentially Dispersion-Decreasing Fiber Amplifier

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Adiabatic approximation in the ultrastrong-coupling regime of an oscillator and two qubits

We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyze the system by the adiabatic approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Relative energy-level spectrum of the system in the adiabatic displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution.     

Excitation of a two-level system by a chirped laser pulse

The excitation of a two-level system by a chirped laser pulse is analyzed using an analytical approach (in the perturbation-theory limit) that involves the modified rotating-wave approximation and the numerical solution to the Bloch equation. The dependence of the population of the upper energy level on the chirp is studied for various radiation intensities and pulse durations. An exact solution is compared with the result obtained using the modified rotating-wave approximation and the perturbation theory. It is demonstrated that, for a certain range of parameters, the excitation probability of a two-level system can be effectively controlled via a variation in the chirp.     

Fast-ion energy-flux enhancement from ultrathin foils irradiated by intense and high-contrast short laser pulses

Recent significant improvements of the contrast ratio of chirped pulse amplified pulses allows us to extend the applicability domain of laser accelerated protons to very thin targets. In this framework, we propose an analytical model particularly suitable to reproducing ion laser acceleration experiments using high intensity and ultrahigh contrast pulses. The model is based on a self-consistent solution of the Poisson equation using an adiabatic approximation for laser generated fast electrons which allows one to find the target thickness maximizing the maximum proton (and ion) energies and population as a function of the laser parameters. Model furnished values show a good agreement with experimental data and 2D particle-in-cell simulation results.     

Efficient population transfer by delayed pulses despite coupling ambiguity

In traditional schemes of multilevel multilaser excitation, each laser pulse interacts with only one pair of states, and the rotating wave approximation (RWA) is applicable. Here we study the population transfer process in a three-state system when each of the two lasers interacts with each of the pair of states and when the Rabi frequencies characterizing the interaction strengths of the system are comparable to or larger than the difference of the transition frequencies. We show that complete and robust population transfer is possible under conditions more general than those hitherto considered necessary for stimulated Raman adiabatic passage (STIRAP) or for successive π pulses. Using adiabatic Floquet theory we show that successful population transfer can be interpreted as adiabatic passage by means of a transfer state which connects the initial and final states. The Floquet picture offers a convenient interpretation of the population transfer as accompanied by multiple absorption of photons from or emission into the laser fields.     

Soliton Light Pulse Transport in a Quantum Wire of Nonlinear Ionic Crystal

We discuss theoretically the transport of a light pulse along a quantum wire made of a nonlinear ionic crystal. Under the adiabatic approximation, the propagation of the axial component of the electric field along the quantum wire has soliton properties and its distribution in the cross section of the quantum wire still approximately satisfies the Bessel equation. The size effect of the quantum wire on the dispersion relation of the polaritons is also discussed.     

Spectral series of the Schrödinger operator in a thin waveguide with a periodic structure. 2. Closed three-dimensional waveguide in a magnetic field

In the paper, which is the second part of the paper by J. Brüning, S. Dobrokhotov, S. Sekerzh-Zenkovich, T. Tudorovskiy, “Spectral series of the Schrödinger operator in thin waveguides with a periodic structure. 1,” Russ. J. Math. Phys. 13 (4), 401–420 (2006), using the adiabatic approximation, diverse quantum states of the stationary Schrödinger equation for a particle in a thin waveguide in a magnetic field are constructed. The problems of “destruction” of the adiabatic approximation as the value of energy increases and of replacing this approximation by the approximation of V. P. Maslov’s theory of complex germ (the complex WKB method) are studied.     

Short Vector Envelope Solitons

We find a class of short vector soliton solutions of the coupled third-order nonlinear Schrödinger equation (CNSE-3) and analyze the stability of such solitons in the adiabatic approximation. The analytical results are confirmed by numerical simulations of the dynamics of perturbed short vector solitons corresponding to the CNSE-3.