A relation between the positive and negative spectra of elliptic operators

We study the spectral properties of pairs of operators \(-\Delta \pm V\) and show that if their negative spectra are discrete, then their essential spectra fill the positive semi-axis. Analogous statements are proved for more general operators of the form \(m(i\nabla )\pm V\) as well as for operators on the lattice \(\mathbb {Z}^d\).     

Explicit approximate relation between reduced two- and one-particle density matrices

A class of approximation of the two-particle density matrix d₂ resembling the Hartree-Fock dependence on the one-particle density matrix d₁ is suggested. The integral relation between d₂ and d₁ is exactly maintained. An optimal choice is performed by means of the Pauli principle. The smallness of the error when applied to Coulomb systems, is qualitatively discussed. Extended Thomas-Fermi theory, as recently introduced by the authors is shortly outlined for the case of Coulomb interaction.     

Gaps and eigenfrequencies in the spectrum of a periodic acoustic waveguide

Sufficient conditions are found for the existence of eigenfrequencies within the spectral gaps which occur as a result of local regular perturbation of the hard walls of a periodic acoustic waveguide. Asymptotic formulas are derived and error estimates shown.     

Furi–Martelli–Vignoli spectrum and Feng spectrum of nonlinear block operator matrices

We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the Feng spectrum)of the whole operator matrix and that of its entries.In addition,the connection between the Furi-Martelli-Vignoli spectrum of the whole operator matrix and that of its Schur complement is presented by means of Schur decomposition.     

Influence of short-range correlations on the phonon spectra of f.c.c. helium and neon

The influence of short-range correlations on the phonon spectra of helium at high pressures and of neon is investigated. It is found that a simple cutoff procedure is insufficient. A more appropriate treatment of the hard core might also be necessary for the heavier rare-gas solids at higher temperatures.     

On the relation between plasma rotation induced by low-frequency resonant magnetic perturbations and transport in ergodic magnetic fields

The penetration of low-frequency resonant magnetic perturbations into a tokamak plasma and their influence on the plasma rotation are analyzed in linear and quaslisinear kinetic approaches. There are two explanations of experimentally observed acceleration of plasma rotation in the direction of the plasma current. First, it is a result of the resonant absorption of the momentum of the perturbation field by the plasma. Second, it is a result of a change in the radial electric field due to the ergodization of the magnetic field and the corresponding increase in the radial electron transport. It is shown that there is no contradiction between these two explanations. These are just two different interpretations of the same phenomenon. Published in Russian in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 6, pp. 420–423. The article was translated by the authors.     

On the spectrum of narrow periodic waveguides

This is a continuation of [1] and [2]. We consider the spectrum of the Dirichlet Laplacian on the domain {(x, y) : 0 < y < εh(x)}, where h(x) is a positive periodic function. The main assumption is that h(x) has one point of global maximum on the period interval. We study the location of bands and prove that the band lengths decay exponentially as ε → 0. To the memory of Leonid Romanovich Volevich     

Curvilinear coordinates and the dushenskii relation in the theory of molecular spectra. A general approach

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 1, pp. 69–73, July, 1991.     

矩形弹子球中的量子谱和经典周期轨道

利用SU(2)相干态的表示,我们构造了二维矩形弹子球中与经典周期轨道对应的波函数.经典周期轨道和量子波函数之间的关系可以通过物理图像清晰的表示出来.另外,利用周期轨道理论,我们计算了二维矩形弹子球体系的量子谱的傅立叶变换ρ(L).变换谱|ρN(L)|2对L图像中的峰可以和粒子在二维矩形腔中运动的经典轨迹的长度相比较.量子谱中的每一条峰正好对应一条经典周期轨道的长度,表明量子力学和经典力学的对应关系.     

Study on the relation between fraction cover and mixed spectra in karst environment

Karst rocky desertification is one of the most serious eco-environmental problems of land degradation in karst regions, southwest China. The fractional cover of vegetation and exposed bedrock are the main land surface symptoms and essential assessing indicators of karst rocky desertification. To assess the extent of rocky desertification in complex karst environments, the information of multiple land cover types fraction is needed. Based on in situ spectral reflectance data, this study proposed several spectral indices and explored the relationship between spectral features of main land cover types and their responding fractional cover. The results showed that spectral indices have much higher correlation coefficients with fractional cover than does spectral reflectance. Vegetation indices have good linear relation with fractional cover of photosynthetic vegetation (PV). The proposed spectral indices have high correlation coefficients with fractional cover of non-photosynthetic vegetation (NPV) and bare soil, with R2 0.70 and 0.73, respectively. Lower correlation coefficients (R2 = 0.55) with the factional cover of exposed bedrock, were observed. The absorption depth of four forms of the proposed indices has the highest correlation coefficient with the fractional cover of NPV, bare soil, and exposed rock. This study indicates that hyperspectral remote sensing has the potential for the extraction of karst rocky desertification information.     

长周期光纤光栅结构参数与透射谱关系的仿真研究

利用光纤3层模型理论,通过仿真研究发现长周期光纤光栅结构参数与透射谱的变化有规律性关系,给出了一阶低次包层模与导模耦合时透射谱的变化规律。当长周期光纤光栅的纤芯、包层的半径和折射率增大时,谐振波向短波方向漂移;当长周期光纤光栅周期增大时,谐振波向长波方向漂移;当长周期光纤光栅长度增加时,谐振波没有漂移现象,但是其深度减小。通过综合分析发现:谐振波漂移方向比较明确,但是损耗峰深度的变化并没有明显的规律。     

Empirical formulas for the fermion spectra and Yukawa matrices

We present empirical relations that connect the dimensionless ratios of low energy fermion masses for the charged lepton, up-type quark and down-type quark sectors and the CKM elements: and . Explaining these relations from first principles imposes strong constraints on the search for the theory of flavor. We present a simple set of normalized Yukawa matrices, with only two real parameters and one complex phase, which accounts with precision for these mass relations and for the CKM matrix elements and also suggests a simpler parametrization of the CKM matrix. The proposed Yukawa matrices accommodate the measured CP-violation, giving a particular relation between standard model CP-violating phases, . According to this relation the measured value of is close to the maximum value that can be reached, for . Finally, the particular mass relations between the quark and charged lepton sectors find their simplest explanation in the context of grand unified models through the use of the Georgi-Jarlskog factor.Received: 31 July 2004, Revised: 22 September 2004, Published online: 9 November 2004     

The Lyapunov spectrum of a continuous product of random matrices

We present a functional integration method for the averaging of continuous productsP _t ofN×N random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum ofP _t . This problem is relevant to the study of the statistical properties of various disordered physical systems, and specifically to the computation of the multipoint correlators of a passive scalar advected by a random velocity field. Apart from these applications, our method provides a general setting for computing statistical properties of linear evolutionary systems subjected to a white-noise force field.     

Highly resolved electronic absorption and luminescence spectra of some phenanthrolines in Shpolskii matrices part I. Phosphorescence spectra

In n-hexane matrices, at 77 K, the phosphorescence spectra of 1,9-, 1,8-, 1,7- and 4,7- phenanthrolines show quasi-linear structure (Shpolskii effect). Highly resolved spectra of isometric phenanthrolines allow measuring slight differences between 0-0 wave numbers of respective isomers and detecting characteristic features of the vibronic structure of the spectrum of each isomer. Vibrational analysis of the spectra show that in T₁ → S₀ electronic transitions of the phenanthrolines examined there participates, besides the totally symmetric ones, at least one out-of-plane vibration (a₂ or a″). The presence of this vibration and its combination with the totally symmetric ones seem to explain the shape of phosphorescence polarization spectra of phenanthrolines in polar glasses, described in the literature.     

Theory of the vibrational spectra of transition h.c.p. metals

Summary A semi-first principle (SFM) model using the concept of a rigid-shell moving relative to its nucleus to simulate the response of thed-electrons has been proposed for studying lattice dynamics of transition metals which belong to the h.c.p. structure. The long-range interaction between ion-ion as well as shell-shell via conduction electrons is described using the screened potential and the short-range interaction is described using two-body and three-body unpaired forces between cores as well as shells. Elastic constants, phonon dispersion curves and thermal properties,e.g. lattice specific heat, Debye characteristic temperature of three prominent transition metals (Zr, Hf, Ti) have been calculated and compared with the experimental results.

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Riassunto Un modello a principio semiprimo (SFM) che usa il concetto di uno strato rigido con movimento relativo al suo nucleo per simulare la risposta degli elettronid è stato proposto per studiare la dinamica reticolare dei metalli di transizione che appartengono alla struttura h.c.p. Si descrive l’interazione a lungo raggio tra ione-ione e strato-strato via elettroni di conduzione usando il potenziale schermato e l’interazione a corto raggio è descritta usando forze spaiate a due e tre corpi tra i nuclei e gli strati. Sono state calcolate e confrontate con i risultati sperimentali le curve di dispersione dei fononi con costanti elastiche e le proprietà termiche, cioè calore specifico del fononi con costanti elastiche e le proprietà termiche, cioè calore specifico del reticolo, la temperatura caratteristica di Debye di tre importanti metalli di transizione (Zr, Hf, Ti).

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Резюме Для исследования динамики решетки переходных металлов, которые имеют гексагональную с плотной упаковкой структуру, предлагается модель, использующая концепцию жесткой оболочки, движущейся относительно ее ядра, чтобы смоделировать откликd-электронов. Описывается длиннодействующее взаимодействие между ионами, а также между оболочками через электроны проводимости, используя экранированный потенциал. Короткодействующее взаимодействие описывается с помощью двух-частичных и трех-частичных неспаренных сил между остовами и оболочками. Вычисляются упругие постоянные, фононные дисперсионные кривые и тепловые свойства, т.е. удельная теплоемкость решетки, характеристическая температура Дебая для трех переходных металлов решетки, характеристическая температура Дебая для трех переходных металлов (Zr, Hf, Ti). Полученные результаты сравниваются с экспериментальными данными.

     

Asymptotic correlations at the spectrum edge of random matrices

Edge correlation functions among the eigenvalues are evaluated for Laguerre and Jacobi ensembles of real-symmetric and self-dual quaternion random matrices of infinite dimension. Universal and non-universal behavior of the eigenvalue correlations is found.     

A relation between cumulants of a thermodynamic variable and the state equation

A general relation between the cumulant of any order of a thermal variable and the thermal equilibrium state equation is pointed out. This relation has particular importance near the critical point of a phase transtion. This is discussed for standard examples.