One-dimensional harmonic lattice caricature of hydrodynamics

We derive the hydrodynamic (Euler) approximation for the harmonic time evolution of infinite classical oscillator system on one-dimensional lattice ¹ It is known that equilibrium (i.e., time-invariant attractive) states for this model are translationally invariant Gaussian ones, with the mean 0, which satisfy some linear relations involving the interaction quadratic form. The natural parameter characterizing equilibrium states is the spectral density matrix function (SDMF)F(), [– , ). Time evolution of a space profile of local equilibrium parameters is described by a space-time SDMFF(t;x, ) t, xR ¹. The hydrodynamic equation forF(t; x, ) which we derive in this paper means that the normal mode profiles indexed by are moving according to linear laws and are mutually independent. The procedure of deriving the hydrodynamic equation is the following: We fix an initial SDMF profileF(x, ) and a familyP ,>0 of mean 0 states which satisfy the two conditions imposed on the covariance of spins at various lattice points: (a) the covariance at points close to the value ^–1 x in the stateP is approximately described by the SDMFF(x, ); (b) The covariance (on large distances) decreases with distance quickly enough and uniformly in. Given nonzerotR ¹, we consider the states P _–1 ,>0, describing the system at the time moments ^–1 t during its harmonic time evolution. We check that the covariance at lattice points close to ^–1 x in the state P _–1 is approximately described by a SDMFF(t;x, ) and establish the connection betweenF(t; x, ) andF(x,).     

One-dimensional harmonic lattice caricature of hydrodynamics: A higher correction

Corrections to the hydrodynamic limit for an infinite chain of coupled harmonic oscillators are obtained. This makes more precise the asymptotic picture for this type of evolution of a system with infinitely many degrees of freedom.     

One-dimensional hard rod caricature of hydrodynamics

We give here a rigorous deduction of the “hydrodynamic” equation which holds in the hydrodynamic limit, for a model system of one-dimensional identical hard rods interacting through elastic collisions. The equation should be considered as the analog of the Euler equation of real hydrodynamics. Owing to the degeneracy of the model, it is written in terms of a functiong(q, v, t) expressing the density of particles with velocityv at the pointq at timet. For this equation we prove an existence and uniqueness theorem in some natural class of functions. Our main result is the proof that if {^∈, ∈ >0} is a class of initial states which are homogeneous on a scale much less than ε^?1, and if the corresponding particle densities tend, asε→0, in the proper scale, to the initial hydrodynamic densityg _o (q,v), then, under some general assumptions on the states ∈^? and ong ₀, the particle densities of the evolved states at timeε ^?1 t, tend asε→0 to the unique solution of the hydrodynamic equation with initial conditiong ₀. The proof is completed by exhibiting a large class of initial families {^∈, ∈ >0} which possess the required properties.     

One-dimensional caricature of phase transition

In the limit as the volume grows and the temperature vanishes, it is shown that the one-dimensional nearest neighbor ferromagnetic Ising model presents a sharp transition between two different regimes. Fluctuations are studied in one of these regimes and also in the critical case.     

A new formula to calculate Franck-Condon factors for displaced and distorted harmonic oscillators

A new formula has been derived to calculate Franck-Condon factors for two harmonic oscillators with different equilibrium positions and different vibrational frequencies. The derivation is simple and straightforward, and a new expression for calculating the matrix element 〈v|xⁿ|v′〉 has also been derived.     

Mapping quantum many-body system to decoupled harmonic oscillators: General discussions and examples

We present a class of quantum systems that can be mapped to decoupled harmonic oscillators through appropriate similarity transformations. We will take advantage of these similarity transformations to discover hidden ladder operators, such that the eigenstates of the system can be constructed like those of harmonic oscillator. We also provide five systems belonging to this family as examples.     

A new lattice approximation forthe Høegh-Krohn quantum field model

The lattice approximation for the exponential interaction model (Høbegh-Krohn quantum field model) with different lattice cutoffs a, a′ in the free and interacting parts is discussed. It is shown that the continuum limit exists under certain conditions on the dependence a′(a).     

One-dimensional approximation to stochastic lattice system with strong coupling

One-dimensional approximation to stochastic lattice system with strong coupling is derived. For a special periodic coupling, the existence of a rotation number is proved, which yields the frequency locking of the system. And by the one-dimensional approximation system, an approximation to the rotation number is also derived.     

Second harmonic generation in deposited clusters

We analyse theoretically the generation of second and higher harmonics for sodium clusters deposited on an insulating surface. To this end, we use the time-dependent local-density approximation solved on a three-dimensional grid. We explore the impact of the various laser parameters (intensity, frequency, polarisation) on the efficiency of second harmonic generation. The success sensitively depends on a proper tuning of these parameters. We find optimum conditions for which the laser frequency is half the resonance frequency of the system, if the polarisation is directed orthogonal to the surface of the substrate, and if the intensity is large but safely below the critical value for destruction of the electron cloud. Received 22 October 1999 and Received in final form 14 December 1999     

One-dimensional multiple-well oscillators: A time-dependent quantum mechanical approach

Time-dependent Schrödinger equation (TDSE) is solved numerically to calculate the ground- and first three excited-state energies, expectation values 〈x ^2j 〉, j=1, 2 …, 6, and probability densities of quantum mechanical multiple-well oscillators. An imaginary-time evolution technique, coupled with the minimization of energy expectation value to reach a global minimum, subject to orthogonality constraint (for excited states) has been employed. Pseudodegeneracy in symmetric, deep multiple-well potentials, probability densities and the effect of an asymmetry parameter on pseudodegeneracy are discussed.     

Stationary states and hydrodynamics of FHP cellular automata

The large scale behavior of FHP-type cellular automata is investigated in the presence of some additional random effects. It is shown that every translationinvariant stationary state of the modified model is a superposition of product measures. By means of the entropy argument of Yau and of Olla, Varadhan, and Yau, the macroscopic (Euler-type) equations governing the hydrodynamic behavior of FHP automata are also derived.Dedicated to Oliver Penrose on the occasion of his 65th birthday.     

Second harmonic generation in inhomogeneous MgO:LiNbO3 waveguides

A fibre laser at 1111.6 nm is frequency doubled by two inhomogeneous MgO:LiNbO3 waveguides and the output powers of 85 mW and 49 mW at 555.8 nm have been generated with the conversion efficiencies of 47% and 27% respectively. By analysing the second harmonic generation temperature tuning curves, we investigate the influence of the optical inhomogeneities upon the conversion efficiency. The final result shows that the efficiency difference is mainly affected by the optical inhomogeneities in our case.     

Second harmonic generation of metal nanoparticles under tightly focused illumination

The near-field and far-field second harmonic(SH) responses of a metal spherical nanoparticle placed in the focal region of a highly focused beam are investigated by using the calculation model based on three-dimensional finite-difference time-domain(FDTD) method. The results show that off-axis backward-propagating SH response can be reinforced by tightly focusing, due to the increase of the relative magnitude of the longitudinal field component and the phase shift along the propagation direction.     

Strong-interaction approximation in the theory of second harmonic generation of intense short laser pulses

The method of strong interaction of nonlinear waves has been developed to analyse the second harmonic generation of intense laser radiation in the transient regime. Analytic solution for frequency conversion efficiency – taking into account the pump radiation depletion, influence of phase mismatch, dispersion of group velocities and higher nonlinearities – has been first obtained. A comparison of theoretically derived results and known experimental data has been conducted, and a general agreement of these results has been obtained. The optimal conditions of the second harmonic generation of neodymium laser radiation into femtosecond pulse duration range have been determined.     

Second harmonic generation from closed packed hexagonal structure of nano-nickel arrays

A closed packed hexagonal structure of nickel nanoparticles was fabricated by deposition of thin nickel films on self-assembled polystyrene micron spheres, which were made of nanospherical lithography in conjunction with left-off the micro spheres. The optical second harmonic generation from these periodically arrayed nickel nanoparticles reveals intensity with a value much larger than that generated from a uniform nickel-film of the same thickness. Quasi phase matching contributed from Bragg wave vectors of the periodic arrayed nickel nanoparticles can satisfactorily express this enhancement.     

Second harmonic generation in Ga nanoparticle monolayers

Ga nanoparticle monolayers formed by evaporation-condensation in ultrahigh vacuum and embedded in a transparent SiO_x matrix generate second harmonic (SH) signals in transmission and reflection when illuminated by a 150 fs, 800 nm laser pulses. The observed SH light exhibits a critical dependence on input and output polarizations, angle of incidence and azimuthal orientation of the samples. The results lead to a consistent picture of shape and orientation of the nanoparticles. Linear transmittance spectra in the visible range support these findings and the observed size dependence of the SH signal. Received 29 November 2000     

二维不可压缩流体Kelvin-Helmholtz不稳定性的二次谐波产生

推导了Kelvin-Helmholtz(KH)不稳定性二次谐波产生的理论公式,利用该公式得到的二次谐波增长的弱非线性结果与LARED-S程序的模拟结果符合.二维模拟定出了KH不稳定性单模非线性增长的阈值. 关键词： Kelvin-Helmholtz不稳定性 二次谐波产生 非线性阈值     

用激活性非线性介质Nd：MgO：LiNbO3产生二次谐波

以Nd:MgO:LiNbO_3同时兼作激活介质和非线性光学材料,研究自倍频激光器。用小型氙灯泵浦,在室温下获得二次谐波激光(0.547μm) 阈值小于4.8'J,最大输出400μJ/shot,工作温度范围大于20℃～45℃,无光损伤。