Partly occupied Wannier functions

We introduce a scheme for constructing partly occupied, maximally localized Wannier functions (WFs) for both molecular and periodic systems. Compared to the traditional occupied WFs the partly occupied WFs possess improved symmetry and localization properties achieved through a bonding-antibonding closing procedure. We demonstrate the equivalence between bonding-antibonding closure and the minimization of the average spread of the WFs in the case of a benzene molecule and a linear chain of Pt atoms. The general applicability of the method is demonstrated through the calculation of WFs for a metallic system with an impurity: a Pt wire with a hydrogen molecular bridge.     

基于小波特征的小麦白粉病与条锈病的定量识别

小麦白粉病和条锈病是小麦常发病害中为害较重的两种病害,在我国小麦产区均有发生,但它们由不同病原引起,需要采取不同的防治措施。因此,快速、准确的获取小麦病害类型信息对于病害的防治具有重要的指导意义。遥感数据具有快速、准确的获取空间上连续信息的特点,提出一种基于实测冠层高光谱数据信息的小麦病害定量识别方法。通过对标准化光谱进行连续小波变换,分析350～1 300 nm范围内各波段及其连续小波特征与小麦白粉病和条锈病之间的相关性,以及在不同病害间的差异性,筛选出对不同病害敏感的光谱波段(SBs)和小波特征(WFs),然后采用Fisher判别分析法分别基于SBs,WFs以及结合SBs和WFs建立小麦白粉病、条锈病及正常小麦识别模型,分别采用未参与建模的55个地面调查数据和留一法进行验证。结果显示： (1)基于WFs模型的总体识别精度(分别为92.7%和90.4%)明显高于基于SBs模型的总体识别精度(分别为65.5%和61.5%);(2)SBs和WFs结合模型的总体识别精度(分别为94.6%和91.1%)略高于基于WFs模型的总体识别精度,在Fisher80-55模型中白粉病和正常样本的生产者精度提高了10%以上。(3)条锈病样本能在基于WFs和SBs & WFs的模型中准确判别出来,用户精度和生产者精度均达到100%。结果表明采用作物光谱信息能够准确的识别健康作物和不同类型的作物病害,为采用遥感影像进行大范围作物病害识别提供了理论基础,对于指导作物病害防治具有实际应用价值。     

The spectrum of depolarized light scattered from critical mixtures

The temperature dependence of the spectrum of depolarized light scattering in a uniform phase of critical mixtures of n-dodecane-ββ' dichlorodiethyl ether and n-hexane-nitrobenzene is studied experimentally. The depolarized light scattering spectrum was found to narrow dozens of times in the temperature interval from 30 to 1°C from the critical temperature of exfoliation in both mixtures. The results obtained are discussed.     

Coupled Magnetoelastic Waves and the Effective Spin-Phonon Coupling Parameter in High-Temperature Superconductors

The present paper is devoted to finding the spectrum of spin-phonon interaction and elucidating the mechanism of critical temperature increase in high-temperature superconductors. The spin-wave dynamic equations and the spectrum of coupled spin-phonon oscillations are obtained. The dependence of the spin wave spectrum on the spin-phonon coupling parameter is investigated. It is demonstrated that the superconducting transition temperature is directly proportional to the spin-phonon interaction force.     

Superfluid phase transition in trapped atomic Fermi gas

Superfluid phase transition in an atomic Fermi gas confined to a harmonic trap is studied. The critical transition temperature and the temperature dependence and spatial shape of the order parameter are determined. The spectrum and wave functions of single-particle and collective excitations are obtained for a gas in the superfluid phase. The excitation eigenfrequencies exhibit a pronounced temperature dependence, allowing, e.g., identification of the superfluid phase.     

Frenkel-Kontorova model with toda interactions

We have studied the Frenkel-Kontorova (FK) model with Toda interactions. The phase diagram is found to be asymmetric due to the exponential form of the Toda interaction. The reflection symmetry observed in the standard FK model is broken here. The singularity spectrum and the generalized dimension are calculated and their dependence on the nonlinearity parameter is discussed. The critical exponents of the gap in the phonon spectrum, the correlation length, and the Peierls-Nabarro barrier are found to be the same as those in the standard FK model and are independent of the nonlinearity parameter.     

Dynamical dielectric susceptibility of ferroelectric thin films and multilayers

The thickness dependence of the real and imaginary parts of the dynamical dielectric susceptibility is investigated phenomenologically for a multilayer structure consisting of alternating ferroelectric and paraelectric layers. It is shown that the frequency dependence of the linear dielectric response can be closely approximated by that of a damped harmonic oscillator, with the static susceptibility, relaxation time, and soft-mode frequency depending on the layer thickness and temperature. When the layer thickness and temperature are equal to their critical values corresponding to the onset of a size-driven ferroelectric phase transition, the static susceptibility and the relaxation time become anomalously large and then decrease with further increasing layer thickness. A spectrum of natural polarization oscillations is predicted to exist with thickness-dependent frequencies. This spectrum includes a soft-mode frequency which vanishes at the critical thickness and at the critical temperature. The frequency spectrum lies below the soft-mode frequency of a thick film (in which the gradient of polarization is negligible). The calculations are compared with experimentally measured dispersion of the dielectric response of a PbTiO₃-Pb_0.72La_0.28TiO₃ multilayer structure. The agreement between the theory and experiment is found to be good.     

Phase transitions in open quantum systems

We consider the behavior of open quantum systems through the dependence of the coupling to one decay channel by introducing the coupling parameter alpha, which is proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place that creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled, e.g., for a uniform picket-fence level distribution with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the case of an unfolded Gaussian orthogonal ensemble and of a spectrum bounded from below. In all these cases, the reorganization of the spectrum occurs at the critical value alpha(crit) of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.     

Parallel pump spin wave instability in thin ferromagnetic films

The spin wave instability generated by parallel pumping in a tangentially magnetized ferromagnetic film is considered, with simultaneous regard for both the dipole and exchange fields. A dispersion equation and some expressions for the critical microwave threshold of the spin wave parametric excitation have been obtained. The dependence of the critical field on the magnetizing field has an unusually oscillating character. This is connected both with the discreteness of spin wave spectrum and the peculiarities of spin wave polarization in a tangentially magnetized film.     

Spectrum and eigenfunctions of the Frobenius-Perron operator of the tent map

The spectrum and eigenfunctions of the Frobenius-Perron operator induced by the tent map are discussed in detail. Special attention is paid to the case where the critical point of the map lies on an aperiodic trajectory and the differences from maps with a periodic critical trajectory are stressed. It is shown that the relevant eigenvalues of the spectrum are not sensitive to the aperiodicity of the critical trajectory. All other parts of the spectrum and all eigenfunctions in particular are changed drastically if the critical trajectory becomes aperiodic. The intimate connection between the point spectrum and the kneading invariant is established and the critical slowing down as well as the band splitting are a consequence of its properties. The structure of the infinite sequence of null spaces and its implications on the spectrum of the operator are discussed. It is shown that any initial distributionP(0,x) of bounded variation can be projected uniquely onto the eigenfunctions of the relevant eigenvalues and that the time dependence ofP(n, x) is determined by this expansion up to an errorO( ⁿ). From this the stationary and the asymptotic behavior of the correlation function x(n) x can be derived exactly.     

A critical point analysis of multi-phonon structure in the far infrared dielectric response of CdTe

A determination by dispersive Fourier transform spectrometry of the frequency dependence of the imaginary part of the anharmonic self-energy of the q ? 0 transverse optic mode in CdTe at 293K is presented. More than 20 features in the spectrum are revealed for the first time and attributed to two- and three-phonon decay processes with the aid of a critical point analysis based on published data for the dispersion curves of CdTe.     

One-dimensional anisotropic Heisenberg model in the transverse magnetic field

The one-dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces a gap in the spectrum of the model with the easy-plane anisotropy. Using conformal invariance, the field dependence of the gap is found at small fields. The ground state phase diagram is obtained. It contains four phases with the long-range order of different types and a disordered phase. These phases are separated by critical lines, where the gap and the long-range order vanish. Using scaling estimates, the mean-field approach, and numerical calculations in the vicinity of all critical lines, we find the critical exponents of the gap and the long-range order. It is shown that the transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.     

Auditory analysis of the periodicity of sound and its envelope: A mathematical model

A mathematical model of the auditory analysis of periodicity of sound and its envelope is proposed. The model consists of a sequence of mathematical transformations that describe the signal processing stages. The following parameters and properties of the auditory system are taken into account: the crude analysis of the input acoustic signal accurate to the width of the aural critical band; the frequency dependence of the width of the aural critical band; the spectrum of the input signal analysis by a set of 3500 filters closely spaced in frequency; the absolute audibility thresholds at a given frequency; the time-domain analysis of both the output signals of each filter and the envelope profile with the help of the periodicity function; the pulsed activity of auditory neurons; the ability of the auditory system to memorize the spectral-time images of the signal and its individual parameters; the ability of the auditory system to form the perception of the loudness of sound, to memorize and compare the loudness of sound at different time moments, and to conclude which of them is higher or lower or whether they are equal accurate to a certain threshold; the dependence of the critical modulation bandwidth on the modulation frequency; and the dependence of the audibility thresholds of amplitude modulation on the modulation frequency. By an example of processing amplitude-modulated signals with various carrier-to-envelope frequency ratios, the model is shown to give a satisfactory explanation of their pitch and auditory estimate of the envelope period.     

Green’s function approach to the low temperature properties of Cs<Subscript>2</Subscript>CuCl<Subscript>4</Subscript>: anisotropy effects

We have studied the effect of both axial and transverse anisotropy on the critical field and thermodynamic properties of the field induced three dimensional antiferromagnetic Heisenberg model on the frustrated hexagonal lattice for Cs₂CuCl₄ compound. The spin model is mapped to a bosonic one with the hard core repulsion constraint and the Green’s function approach has been implemented to get the low energy spectrum and the corresponding thermodynamic properties. To find the critical field (B _c ) we have looked for the Bose-Einstein condensation of quasi-particles (magnons) which takes place when the magnon spectrum vanishes at the ordering spiral wave vector. We have also obtained the dispersion of magnon spectrum in the critical magnetic field for each anisotropy parameter to find the spiral wave vector where the spectrum gets its minimum. The magnon energies show a linear dispersion relation close to the quantum critical point. The effect of hard core boson interaction on the single particle excitation energies leads to a temperature dependence of the magnon spectrum versus magnetic field. We have also studied the behavior of specific heat and static structure factor versus temperature and magnetic field.     

Entropic analysis of quantum phase transitions from uniform to spatially inhomogeneous phases

We propose a new approach to study quantum phase transitions in low-dimensional fermionic or spin models that go from uniform to spatially inhomogeneous phases such as dimerized, trimerized, or incommensurate phases. It is based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.     

Propagation of transverse hypersound in solution with stratification region

The fine structure of the Rayleigh line wing depolarized spectrum in a form of a triplet caused by the light scattering by transverse hypersonic waves was detected in a critical solution with a closed stratification region at low temperatures. The propagation velocity of transverse hypersound and its absorbance were measured. The temperature dependence of the shear modulus in solution was calculated. The temperature dependence of the shear modulus was compared to temperature dependences of limiting bulk elastic moduli. The results obtained suggest that the solution structure changes in passing through the stratification region at changing temperature.     

Cyclotron resonance of Dirac ferions in HgTe quantum wells

Cyclotron resonance of single-valley two-dimensional Dirac fermions in HgTe-based quantum wells has been experimentally investigated. The thickness of the wells is close to the critical value corresponding to the transition from the direct energy spectrum to the inverted spectrum. Under terahertz laser irradiation, transitions between the ground and first Landau levels, as well as between the first and second Landau levels, have been observed. Low magnetic fields corresponding to the cyclotron resonance, as well as the strong dependence of the position of the resonance on the electron density, indicate the Dirac character of the spectrum in these quantum wells. It has been shown that disorder plays an important role in the formation of the spectrum of two-dimensional Dirac fermions.     

Analytical solutions of exact renormalization group equations

We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of physical behaviour such as fixed points governing the universal behaviour near second-order phase transitions, critical exponents, first-order transitions (some of which are radiatively induced) and tricritical behaviour.     

Dynamics of quantum fluctuations in an anharmonic crystal model

For a model given previously by the authors describing a structural phase transition we compute theq-mode critical fluctuations of momentum and displacement as a function of the critical temperatures, the wave vectorq, and a fading-out external field. An explicit dependence on the rates of fading out is obtained. In order to define the critical fluctuation operators we prove a reconstruction theorem, which is of model-independent value. Finally we study the critical spectrum and get rigorous results on the soft modes and the central peak.