共查询到20条相似文献,搜索用时 15 毫秒
1.
We develop a consistent mathematical theory of weakly nonlinear periodic dielectric media for the dimensions one, two and three. The theory is based on the Maxwell equations with classical quadratic and cubic constitutive relations. In particular, we give a complete classification of different nonlinear interactions between Floquet-Bloch modes based on indices which measure the strength of the interactions. The indices take on a small number of prescribed values which are collected in a table. The theory rests on the asymptotic analysis of oscillatory integrals describing the nonlinear interactions. 相似文献
2.
《Waves in Random and Complex Media》2013,23(4):R41-R69
Abstract Weakly nonlinear interactions between wavepackets in a lossless periodic dielectric medium are studied based on the classical Maxwell equations with a cubic nonlinearity. We consider nonlinear processes such that: (i) the amplitude of the wave component due to the nonlinearity does not exceed the amplitude of its linear component; (ii) the spatial range of a probing wavepacket is much smaller than the dimension of the medium sample, and it is not too small compared with the dimension of the primitive cell. These nonlinear processes are naturally described in terms of the cubic interaction phase function based on the dispersion relations of the underlying linear periodic medium. It turns out that only a few quadruplets of modes have significant nonlinear interactions. They are singled out by a system of selection rules including the group velocity, frequency and phase matching conditions. It turns out that the intrinsic symmetries of the cubic interaction phase stemming from assumed inversion symmetry of the dispersion relations play a significant role in the cubic nonlinear interactions. We also study canonical forms of the cubic interaction phase leading to a complete quantitative classification of all possible significant cubic interactions. The classification is ultimately based on a universal system of indices reflecting the intensity of nonlinear interactions. 相似文献
3.
《Waves in Random and Complex Media》2013,23(4):R25-R52
Abstract Weakly nonlinear interactions between wavepackets in lossless periodic dielectric media are studied based on the classical nonlinear Maxwell equations. We consider nonlinear processes such that: (i) the amplitude of the wave component due to the nonlinearity does not exceed the amplitude of its linear component; (ii) the spatial range of a probing wavepacket is much smaller than the dimension of the medium sample, and it is not too small compared with the dimension of the primitive cell. These nonlinear processes are naturally described in terms of the Bloch modes and the dispersion relations of the underlying linear periodic medium. It turns out that only a few triads of modes have significant nonlinear interactions. They are singled out by the frequency and phase matching conditions and, as we show, by an additional selection rule: the group velocity matching condition. The latter condition is the most important selection rule for the nonlinear regimes. We give a complete quantitative classification of all possible significant interactions for quadratic nonlinearities. The classification is based on a universal system of indices reflecting the intensity of nonlinear interactions. The obtained classification points to the second harmonic generation as being one of the stronger nonlinear interactions, and often the strongest one. 相似文献
4.
Alejandro J. Garza Osman Ibrahim Osman Nuha Ahmed Wazzan Sher Bahadar Khan Abdullah Mohamed Asiri Gustavo E. Scuseria 《Molecular physics》2014,112(24):3165-3172
The linear and nonlinear optical (NLO) properties of methoxybenzylidene (1) and thiophen-2-ylmethylidene (2) tetrahydronaphthalone derivatives are studied using long-range corrected density functional theory (LC-DFT). The calculated hyperpolarisabilities indicate that both compounds have measurable NLO properties (approximately one to two times the hyperpolarisability of p-nitroaniline). Charge-transfer indices and time-dependent DFT calculations suggest that the NLO properties are a result of a charge-transfer excitation, which is typical in conjugated donor–acceptor structures. The ultraviolet–visible spectra of 1 and 2 are also predicted using gap-fitting schemes, and these data are used to assess how accurately the hyperpolarisabilities of 1 and 2 could be estimated by the solvatochromic method. 相似文献
5.
A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions.
The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona,
J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowski’s equation for the time
evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids
in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential.
Rosenfeld’s fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on
the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations
which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic
interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected
hydrodynamic interactions. 相似文献
6.
《Comptes Rendus Physique》2007,8(2):180-198
The use of microstructured crystals in quasi-phasematched (QPM) nonlinear interactions has enabled operation of nonlinear devices in regimes inaccessible to conventional birefringently phasematched media. This review addresses basic aspects of the theory of QPM interactions, microstructured ferroelectrics and semiconductors for QPM, devices based on QPM media, and a series of techniques based on engineering of QPM gratings to tailor spatial and spectral response of QPM interactions. Because it is not possible in a brief review to do justice to the large body of results that have been obtained with QPM media over the past twenty years, the emphasis in this review will be on aspects of QPM interactions beyond their use simply as highly nonlinear alternatives to conventional birefringent media. To cite this article: D.S. Hum, M.M. Fejer, C. R. Physique 8 (2007). 相似文献
7.
8.
Zoi Rapti 《Physics letters. A》2013,377(23-24):1543-1553
We present results on multibreather stability in one-dimensional nonlinear Klein–Gordon chains. Our analysis is based on Aubry?s band theory and perturbation theory. First, we provide an alternative proof of the stability of multibreathers in a chain with nearest neighbor interactions only. Then, we extend our analysis to the case of interactions with up to three neighbors. For next-nearest neighbor and third-nearest neighbor interactions we also extend the theory to study the stability properties of recently found multibreathers that have nonstandard phase shifts (not equal to 0 or π). 相似文献
9.
We study a quantum chain of oscillators with nonlinear quartic interactions, under the “narrow packet” approximation. We analyse the dynamics of quantum corrections and the conditions at which the quantum solution for average complex amplitude converges to the corresponding classical unstable solution which describes the four-wave decay processes of phonons. We develop an asymptotic theory by using a small quasiclassical parameter, and determine the characteristic time scale for which the evolution of decay processes is essentially specified by quantum effects.
AMS Subject classification: Primary: 35F10 Secondary: 35Q40, 35B40 相似文献
10.
D. Jovanović R. Fedele 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(3):363-368
Two-dimensional stability of a controlled Bose-Einstein
condensation state, in the form of a nonlinear Schr?dinger soliton
[JETP Lett. 80 535 (2004)], is studied
for the condensations with both repulsive and attractive inter-atom
interactions. The Gross-Pitaevski equation is solved numerically,
taking initialy a controlled soliton whose “effective mass” is
several times bigger than the critical value for a weak collapse in
the absence of a potential well, and allowing for reasonably large
errors in the experimental realization of the trapping potential
required by the theory. For repulsive and sufficiently weak
attractive interactions, the controlled state is shown to remain
stable inside a breathing potential well, for a time that is an
order of magnitude longer than the characteristic periods of the
forced and eigenoscillations of the soliton. The collapse is
observed only for attractive interactions, when the nonlinear
attraction exceeded the appropriate threshold.
Electronic supplementary material Supplementary Online Material 相似文献
11.
A theory of the dynamic response of the turbulent plasma against the externally-controlled perturbations is reported. Based on Mori’s method [Prog. Theor. Phys. 33 423 (1965)], the nonlinear force is assumed to be separated into the memory function and the nonlinear fluctuating force. The former corresponds to the damping term, and the latter is categorized into the noise term. The response of the turbulent plasma against the externally-controlled source is formulated. The response kernel, which connects the externally-controlled source and the response of the turbulent field, is shown to have both the nonlocal property (in space) and the non-Markovian response (in time). A discussion is made on the nonlocal and non-Markovian response, including the case of disparate-scale interactions. A new method is proposed to observe experimentally the nonlocal interaction in the drift wave turbulence via the zonal flows. 相似文献
12.
Traditionally, the moment method has been used in kinetic theory to calculate transport coefficients. Its application to the
solution of more complicated problems runs into enormous difficulties associated with calculating the matrix elements of the
collision operator. The corresponding formulas for large values of the indices are either lacking or are very cumbersome.
In this paper relations between matrix elements are derived from very general principles, and these can be employed as simple
recurrence relations for calculating all the nonlinear and linear anisotropic matrix elements from assigned linear isotropic
matrix elements. Efficient programs which implement this algorithm are developed. The possibility of calculating the distribution
function out to 8–10 thermal velocities is demonstrated. The results obtained open up prospects for solving many topical problems
in kinetic theory.
Zh. Tekh. Fiz. 69, 6–9 (September 1999) 相似文献
13.
P. M. Lushnikov 《Journal of Experimental and Theoretical Physics》1998,86(3):614-627
A nonlinear theory is presented for the formation of hexagonal optical structures in a photorefractive medium equipped with
a feedback mirror. Oppositely directed beams in photorefractive crystals are unstable against the excitation of sideband waves.
It is shown here that as this instability evolves to its nonlinear stage, the three-wave interaction between weak sideband
beams does not stabilize it, but rather leads to explosive growth of the amplitudes of beams whose transverse wave vectors
form angles that are multiples of π/3. As a result, sideband beams at these angles are found to be correlated. A range of parameters is found in which four-wave
interactions saturate the explosive instability, which explains the appearance of stable hexagons in the experiment. Outside
this region, nonlinearities of higher order saturate the explosive instability, and the process of hexagon generation must
be studied numerically. Matrix elements are obtained for the three-and four-wave interactions as functions of the distance
to the feedback mirror, and an equation for the time evolution of the sideband wave amplitudes is derived that describes the
hexagon generation. A comparison is made with experimental results for the photorefractive crystals KNbO3 and BaTiO3.
Zh. éksp. Teor. Fiz. 113, 1122–1146 (March 1998) 相似文献
14.
Two-dimensional discrete models are used to describe nonlinear interactions of 'atoms' within interface regions. An evolution algorithm is presented for a distribution of dislocations on a plane. Results of numerical simulations illustrate motion of a dislocation kink. A finite-thickness nonlinear interface is studied in two dimensions; it gives a further extension of the mathematical model to the analysis of contact problems with frictional interfaces. 相似文献
15.
Planar oscillations of a chain of dumbbell-shaped particles possessing three degrees of freedom are studied. This system models
the dynamics of quasi-one-dimensional crystals consisting of elongated anisotropic molecules. A system of nonlinear differential
equations describing the anharmonic interaction of the elastic and orientational waves in the lattice, corresponding to different
degrees of freedom of the particles, is constructed assuming a cubic interparticle interaction potential. It is shown that
in the low-frequency approximation the system obtained is equivalent to the equations of the moment theory of elasticity,
widely employed for describing nonlinear and dispersion properties of layered crystals and phase transformations in alloys.
Some types of three-wave collinear interactions are investigated, suggesting the possibility of exciting orientational waves
in organic crystals because of their nonlinear interaction with acoustic waves.
Fiz. Tverd. Tela (St. Petersburg) 39, 137–144 (January 1997) 相似文献
16.
Using the -mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross-Pitaevskii theory in (3+1)-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the δ function indicates that the vortices can only be generated from the zero points of Φ and are quantized in terms of the Hopf indices and Brouwer degrees. The -mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory. 相似文献
17.
The aim of our studies is to investigate the nature of intermolecular interactions in crystals based on aromatic molecules. For this purpose we carry out angle dispersive (ADXD) as well as energy dispersive (EDXD) X-ray diffraction experiments under pressure in combination with Rietveld refinement. The other approach is density functional theory (DFT), where our calculations are based on the experimentally obtained lattice parameters. In the present work we focus on anthracene C 14 H 10 (monoclinic space group P2 1 /a) as a representative for the herringbone structure that is common for rigid rod-like molecules. We discuss its structural properties as a function of pressure and find very good agreement between experiment and theory. 相似文献
18.
S. A. Baruzdin 《Technical Physics》1999,44(12):1457-1461
Pulsed stochastic excitation of a two-level system described by Bloch equations is studied. An equation for the average powers
of the components of the state vector of the system is obtained on the basis of the theory of stochastic differential equations,
and solved. The dynamical and nonlinear properties of the response of a system under pulsed stochastic resonance conditions
are analyzed and the results are compared with the corresponding stationary state. The results obtained can be used in spectroscopy
and for analysis of nonlinear filters based on the saturation effect and intended for processing rf and light range signals.
Zh. Tekh. Fiz. 69, 65–69 (December 1999) 相似文献
19.
We develop a Luttinger liquid theory of the Coulomb drag of persistent currents flowing in concentric mesoscopic rings by incorporating nonlinear corrections to the electron dispersion relation. We demonstrate that at low temperatures, interactions between electrons in different rings generate an additional phase and thus alter the period of Aharonov–Bohm oscillations. The resulting nondissipative drag depends strongly on the relative parity of the electron numbers. We also show that interactions set a new temperature scale below which the linear response theory does not apply at certain values of external flux. 相似文献
20.
《Journal of Nonlinear Mathematical Physics》2013,20(3-4):372-378
Abstract A relativistic two-particle model with superposition of time-asymmetric scalar and vector interactions is proposed and its symmetries are considered. It is shown that first integrals of motion satisfy nonlinear Poisson-bracket relations which include the Poincaré algebra and one of the algebras so(1,3), so(4) or e(3). 相似文献