Nonlinear dynamics of a two-dimensional lattice

The dynamics of the nonlinear excitations in a two-dimensional (2D) φ⁴-diatomic lattice, with nonlinear on-site electron-phonon coupling at the polarizable ion site has been presented, without considering the self consistent phonon approximation. One of the major results obtained from our calculations is in the understanding of continuous structural phase transition, where we have obtained the minimum in soft mode frequency at a soft mode temperatureT _s (>T _c), not at critical temperatureT _c. This occurs due to the anisotropy of such 2D systems.     

Surface optical waves at the boundary with a nonlinear Kerr medium

A rigorous solution consistent with a plane wave approximation is given to the boundary problem for Maxwell’s equations for surface optical waves at the boundary with a nonlinear Kerr medium. Exact formulas for the flux intensity (J ₀) and energy density (W ₀) of these waves are derived depending on the parameters of the adjacent media and the propagation constant (ξ). It is shown that these variables as functions of ξ have minima. Thus, J ₀ and W ₀ increase sharply as the propagation constant deviates from the minimum value ξ_min. Their values are greater, the larger the difference between the dielectric constants of the linear and nonlinear media is. An expression for the propagation velocity of a nonlinear surface wave is also obtained.     

Topological solitons and zero modes in high-T c superconductivity

The realization of topological solitons, zero modes, and supersymmetry in theCP ₁ nonlinear sigma model, a theory of high-T _c superconductivity, is presented.     

电光效应的自相似性

通过对KNbO₃,LiNbO₃,BaTiO₃及几种半导体晶体的电光系数进行数值分析，发现电光系数在自由状态和受夹状态下对应的Miller-δ系数相同，与外加电场频率无关，进而提出用Miller-δ系数表征晶体非线性光学性质.在此基础上，提出一种全新的电光效应产生机制，认为电光效应源于非线性系统的自相似性，表现为对线性性质的一种“自我复制”，而Miller-δ系数是“自我复制”的比例因子. 关键词： 电光效应 非线性光学 自相似性     

Nonlinear and quantum origin of doubly infinite family of modified addition laws for fourmomenta

We show that infinite variety of Poincaré bialgebras with nontrivial classicalr-matrices generate nonsymmetric nonlinear composition laws for the fourmomenta. We also present the problem of lifting the Poincaré bialgebras to quantum Poincaré groups by using e.g. Drinfeld twist, what permits to provide the nonlinear composition law in any order of dimensionfull deformation parameterλ (from physical reasons we can putλ=λ _p whereλ _p is the Planck length). The second infinite variety of composition laws for fourmomentum is obtained by nonlinear change of basis in Poincaré algebra, which can be performed for any choice of coalgebraic sector, with classical or quantum coproduct. In last Section we propose some modification of Hopf algebra scheme with Casimir-dependent deformation parameter, which can help to resolve the problem of consistent passage to macroscopic classical limit. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. Supported by KBN grant 5PO3B05620     

Nonequilibrium thermodynamics of lasing and bistable optical systems

A simple model of nonlinear optical systems exhibiting instability—such as in laser action and in bistable absorption—is presented that provides a prototype of nonequilibrium thermodynamics on a statistical basis. The adiabatic reduction of the atomic degrees of freedom in a revised Langevin treatment establishes a fully consistent framework in which the active electromagnetic field mode is in contact with two thermal reservoirs (the cavity and the atoms) as well as being acted upon by an external field. The results are summarized by the first and second laws,dE=W+Q _c +Q _A anddS Q_c/¯T_c+Q_A/¯T_A, with the statistical mechanical representations of the entities therein exhibiting the nature of the mode; i.e., (a) a heat-engine structure operating between two reservoirs of temperatures¯T _c > 0 and¯T _A < 0 for the laser, and (b) a nonlinear response against external work balanced by a single reservoir (¯ T _c = ¯T _A ) for the absorptive bistability.Originally presented at the Taniguchi Symposium, October 1979.⁴⁴     

Barium doping-induced polar nanoregions in lead germanate single crystal

The results of measurement of the linear and nonlinear dielectric susceptibilities of pure and Ba-doped lead germanate, (Pb_{1? x} Ba _x )₅Ge₃O₁₁ with x = 0, 0.02 and 0.05, single crystals are presented. The change in the sign of the third-order dielectric susceptibility, χ ₃, as predicted by the thermodynamic theory of the continuous phase transitions, is observed in pure crystal. On the contrary, in the Ba-doped crystals, the third-order dielectric susceptibility is positive and shows a peak near the temperature, which corresponds to the position of the peak of the linear dielectric susceptibility, χ ₁. This result indicates that the Ba-doped lead germanate crystals do not show features typical of a continuous phase transition. In B-doped lead germanate crystal, the scaled nonlinear sucsebtibility, a ₃, shows ferroelectric relaxor-type behavior.     

A Kind of Four-Mode Nonlinear Entangled State Representation in Quantum Optics

Based on the technique of integration within an ordered product of nonlinear bosonic operators, we construct a new four-mode nonlinear entangled state | α,β,γ〉 _λ,μ in 4-mode Fock space, which can make up a complete set. Its properties and applications are discussed. A possible scheme to generate this state is also presented.     

On generalized Lax equations of the Lax triple of the BKP and CKP hierarchies

Based on the Lax triple (B_m, B_n, L) of the BKP and CKP hierarchies, we derive the nonlinear evolution equations from the generalized Lax equation. The solutions of some evolution equations are presented, such as soliton and rational solutions.     

Possible transformation of YBa2Cu3O7 under pressure

Crystal structure measurements on the high-T _c material YBa₂Cu₃O₇ were carried out under pressure. Several X-ray reflections do not reveal a uniform shift with increasing pressure. Two models are presented, which show the experimental data to be consistent with an extensivec-axis orb-axis decrease, respectively.     

Optical surface <Emphasis Type="Italic">TM</Emphasis>-waves at the boundary of a nonlinear Kerr-type medium

Solutions for a nonlinear system of Maxwell’s equations and for a corresponding boundary problem describing the propagation of a surface TM-wave (p-polarization) along an interface with an optically nonlinear Kerr-type medium are presented. An analytical expression for the intensity of an integrated flux J₀ carried by such a wave along the interface between two media has been derived as a function of both the wave propagation constant ξ and the optical characteristics of the adjacent media. It is shown that flux intensities corresponding to the same values of the propagation constant ξ are much smaller for p-polarization than for s-polarization.     

非线性柱形涂层复合介质有效的直流-交流电响应

利用摄动展开方法, 研究了由圆柱形带涂层杂质随机嵌入基质所形成的非线性复合介质在外加 的带有不同频率和振幅的混合电场E₀ + E₁ sinωt+E₃ sin3ωt作用下有效的直流-交流电响应, 分别推导了复合介质在杂质核、涂层及基质区域的电势分布, 并在低杂质浓度下给出了复合介质有效的非线性响应及它们之间的关系. 关键词： 非线性柱形涂层复合介质 有效的非线性响应 外加交直流电场     

Dual formulation of classicalW-algebras

By extending the concept of Maurer-Cartan equations, a dual formulation of (classical) nonlinear extensions of the Virasoro algebra is introduced. This dual formulation is closely related to three-dimensional actions which are analogous to a Chern-Simons action. An explicit construction in terms of superfields of theN = 2 superW ₄-algebra is presented.     

Theory for nonlinear magnetooptics in metals

The electronic theory for nonlinear magnetooptics in metals is presented. Characteristic results are given for the enhancement of the Kerr rotation, its dependence on light polarization and direction of the magnetization, on surface and film structure and on material-specific properties. The nonlinear susceptibility tensor χ_ijl(2ω) is calculated and analyzed. We discuss also how second harmonic generation is used to investigate magnetic domain structure and nonequilibrium magnetic behavior as analyzed by pump-probe spectroscopy. Finally, the theory is extended to describe generally the time-dependent nonlinear response to external fields.     

Nonlinear dynamics of vortices pinned to unidirectional twins

The nonlinear resistive properties of superconductors in the mixed state in the presence of a system of unidirectional planar defects (twins) have been investigated theoretically within the framework of the two-dimensional stochastic model of anisotropic pinning based on the Fokker-Planck equations with a concrete form of the pinning potential. These equations allow one to obtain an exact analytical solution of the problem. Formulas are obtained for experimentally observable even and odd (relative to reversal of the direction of the external magnetic field) nonlinear longitudinal and transverse magnetoresistivities ρ _‖,⊥ ^± ( j,t,α,ε) as functions of the transport current density j, temperature t, the angle α between the directions of the current and the twins, and the relative volume fraction ε occupied by the twins. In light of the great variety of types of nonlinear resistive dependences contained in these expressions for ρ _‖,⊥ ^± the most characteristic of them are presented in the form of graphs with commentary. The desired nonlinear dependences ρ _‖,⊥ ^± are linear combinations of the even and odd parts of the function v(j,t, α,ε), which has the sense of the probability of overcoming the potential barrier of the twins; this makes it possible to give a simple physical treatment of the nonlinear regimes. New scaling relations for the Hall conductivity are obtained and investigated which differ from the previously known relations for isotropic pinning. The interaction of vortex motion directed along the twins and the Hall effect is considered for Hall constants which are arbitrary in magnitude and sign, and it is shown that in the case of small Hall viscosity vortex motion directed along the twins has an effect on the odd magnetoresistivities ρ _‖ ⁻ and ρ _⊥ ⁻ , whereas the reverse effect can be neglected. It is shown that pinning anisotropy is sufficient to manifest the new nonlinear (in the current) magnetoresistivities ρ _⊥ ⁺ and ρ _‖ ⁻ . Zh. éksp. Teor. Fiz. 116, 2103–2129 (December 1999)     

Linear and nonlinear intersubband optical absorption coefficients and refractive index changes in a quantum box with finite confining potential

In this work, both the intersubband optical absorption coefficients and the refractive index changes are calculated exactly in a quantum box. Analytical expressions for the linear and nonlinear intersubband absorption coefficients and refractive index changes are obtained by using the compact-density matrix approach. Numerical results are presented for typical GaAs/Al_xGa_1−x As quantum box system. The linear, third-order nonlinear and total absorption and refractive index changes are investigated as a function of the incident optical intensity and structure parameters such as box-edge length and stoichiometric ratio. Our results show that both the incident optical intensity and the structure parameters have a great effect on the total absorption and refractive index changes.     

Effective response in nonlinear spherical coated composites under external AC and DC electric field

By using the perturbation method, effective nonlinear direct current (DC) and alternating current (AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of external electric field E_a =E₀ +E₁ sin ωt+E₃ sin 3ωt with different amplitudes and frequencies. The local potentials of composites at all harmonics are given in the inclusion particles and the host regions. All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

Nonlinear kinematic response of premixed flames to harmonic velocity disturbances

This paper analyzes the nonlinear dynamics of premixed flames responding to harmonic velocity disturbances. These nonlinear dynamics were studied by solving a constant flame speed front tracking equation for the flame’s response to harmonically oscillating velocity disturbances. The solution to these equations is used to quantify the transfer function relating the ratio of the normalized flame area to velocity fluctuations, G = (A′/A_o)/(u′/u_o), upon the amplitude of velocity oscillations, ε = u′/u_o. Due to nonlinearities, the amplitude of this transfer function relative to its linear value decreases with increasing amplitude of velocity oscillation, u′/u_o. In contrast, the transfer function phase exhibits almost no amplitude dependence. The velocity amplitude where transfer function nonlinearities become significant depends strongly upon three parameters: a Strouhal number, St = ωL_f/u_o (where L_f is the flame length), the ratio of the flame length to width, β = L_f/R, and the flame shape in the absence of perturbations (i.e., conical, inverted wedge, etc.). In the linear case, the transfer function, G, depends only upon an algebraic combination of the first two parameters, given by St₂ = St (1 + β²)/β². In general, however, G exhibits a distinct dependence upon both parameters St and β. In particular, we show that the nonlinear response of G is an intrinsically dynamic phenomenon; i.e., its quasi-steady response (St 1) is purely linear. As such, nonlinearity is enhanced with increasing Strouhal numbers. In contrast, nonlinearity is suppressed at large β values; as such, the response of a long flame remains quite similar to its linear value, even at large ε values where the flame front exhibits substantial corrugation and cusping. Finally, we show that the response of conical flames remains much more linear at comparable disturbance amplitudes than for “V” or wedge-shaped flames. These predictions are shown to be consistent with available experimental data.     

Development of interatomic potentials appropriate for simulation of liquid and glass properties of NiZr2 alloy

A new interatomic potential for the Ni–Zr system is presented. This potential was developed specifically to match experimental scattering data from Ni, Zr and NiZr₂ liquids. Both ab initio and published thermodynamic data were used to optimise the potential to study the liquid and amorphous structure of the NiZr₂ alloy. This potential has the C ₁₆ phase, being more stable than C _11b phase in the NiZr₂ alloy, consistent with experiments. The potential leads to the correct glass structure in the molecular dynamics simulation and, therefore, can be used to study the liquid–glass transformation in the NiZr₂ alloy.     

Nonperturbative Operator Quantization of Strongly Nonlinear Fields

At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of a strongly nonlinear field can form a non-associative algebra. It is shown that such an algebra can be described as an algebra of some pairs. The comparison of presented techniques with the Green's functions method in superconductivity theory is made. A possible application to the QCD and High-T _c superconductivity theory is discussed.