Non perturbative calculations for three particles in a linear chain within the generalized Hubbard model

A real-space method has been introduced to study the pairing problem within the generalized Hubbard Hamiltonian. This method includes the bond-charge interaction term as an extension of the previously proposed mapping method [1] for the Hubbard model. The generalization of the method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space, where the problem can be solved exactly. In a one-dimensional lattice, we analyzed the three particle correlation by calculating the binding energy at the ground state, using different values of the bond-charge, the on-site (U) and the nearest-neighbor (V) interactions. A pairing asymmetry is found between electrons and holes for the generalized hopping amplitude, where the hole pairing is not always easier than the electron case. For some special values of the hopping parameters and for all kinds of interactions in the Hubbard Hamiltonian, an analytical solution is obtained. Received 21 January 2000 and Received in final form 18 July 2000     

Cooperative decay of a linear chain of molecules including explicit spatial dependence

The decay of an ensemble of two-level molecules is described by a quantum-mechanical formalism involving single molecule operators. Equations of motion are obtained for the operators by means of a pertubative analysis, containing spontaneous decay terms and those that connect different molecules. A travelling wave solution is presented for the relaxation of one-dimensional chain of molecules.     

Thermodynamic properties of solid naphthalene: Cell model and quasiharmonic calculations

Cell model and quasihannonic calculations have been made for solid naphthalene, using the atom-atom approximation for intermolecular interactions. Throughout the temperature range examined (78–323 K) the cell model is found to be superior to the quasiharmonic approximation in describing the basic thermodynamic functions of the crystal. An attempt is also made to extend the cell model to calculate the elasticity tensor and thermal expansion.     

Application of a method of linear scaling of frequencies in calculations of the normal vibrations of polyatomic molecules

The frequencies of the harmonic vibrations of 88 compounds consisting of atoms of the first period are calculated in the approximation of the hybrid density functional B3LYP with the 6-31G* basis set. Using 1189 frequencies from experimental IR and Raman spectra of these compounds in the gas phase and the corresponding theoretical frequencies, the coefficients of the function of linear scaling are found by the least squares method. The method of linear scaling of frequencies is applied to the prediction of the 108 vibrational frequencies of a porphin molecule. A conclusion is made that this method is promising for the interpretation of vibrational spectra of complex molecules and, in combination with the Pulay method of scaling of a quantum-mechanical field, for the determination of harmonic force constants.     

A quasi-analytic model of a linear Stark accelerator/decelerator for polar molecules

This article describes a quasi-analytic model of a linear Stark accelerator/decelerator for polar molecules in both their low- and high-field seeking states, and examines the dynamics of the acceleration/deceleration process and its phase stability. The requisite time-dependent inhomogeneous Stark fields, used in current experiments, are Fourier-analyzed and found to consist of a superposition of partial waves with well-defined phase velocities. The kinematics of the interaction of molecules with the partial waves is discussed and the notion of a phase of a molecule in a travelling field is introduced. Next, the net potential and the net force that act on the molecules are derived. A special case, the first-harmonic accelerator/decelerator, is introduced. This represents a model system many of whose properties can be obtained analytically. The first-harmonic accelerator/decelerator dynamics is presented and discussed along with that of the isomorphic biased-pendulum problem. Finally, the general properties of the velocity of the molecules in a phase-stable accelerator/decelerator are examined.Received: 11 August 2004, Published online: 23 November 2004PACS: 32.60. + i Zeeman and Stark effects - 39.10. + j Atomic and molecular beam sources and techniques - 45.50.-j Dynamics and kinematics of a particle and a system of particles - 29.17. + w Electrostatic, collective, and linear accelerators     

Thermodynamic properties of the XX model in a chain with a period two and three coupling

The exact solutions for the energy spectrum of the XX model with a periodic coupling and an external transverse magnetic field h are obtained. The diagonalization procedure is discussed, and analytical and numerical solutions are given. Using the solutions for period-two coupling, the free energy, entropy, and specific heat are calculated as functions of temperature and applied transverse external magnetic field. Their expressions show that below a particular value v and above a value u of the magnetic field |h|, the entropy and the specific heat vanish exponentially in the low temperature limit.     

Refractive index sensing using a linear graded plasmonic chain of metal nano-particles

We study the transmission efficiency of optical signals through a graded linear chain of spherical silver nano-particles placed parallel to a silver substrate by using the Green’s function formalisms and the dipole approximation. A sensor based on plasmon resonance shifts is also discussed. The obtained spectral sensitivity is more than 273.17?nm/RIU in the visible light region, which makes such a structure an excellent candidate for liquid detection.     

Fragment distribution of thermal decomposition for lignin monomer by QMD calculations using the excited and charged model molecules

Simulations with a quantum molecular dynamics (QMD) method (MD with MO) were demonstrated on the thermal decomposition of lignin monomer at the ground state including excited and positive charged states. Geometry and energy optimized results of the lignin monomer at the singlet and triplet states in single excitation, and at (+2) positive charged state by semi-empirical AM1 MO calculations were used as the initial MD step of QMD calculations. In the QMD calculations, we controlled the total energy of the system using Nóse-Hoover thermostats in the total energy range of 0.69-0.95 eV, and the sampling position data with a time step of 0.5 fs were carried out up to 5000 steps at 50 different initial conditions. The calculated neutral, positive and negative charged fragment distributions of the monomer model with 0.82 eV energy control were obtained as 90.6, 3.5, and 5.9% to the total fragments, respectively. The ratios seem to correspond well with to the values observed experimentally in SIMS.     

Method of configuration interaction in calculations of the spectral characteristics of atoms and molecules

For He, Be, Ne, and Mg atoms and their isoelectronic series, calculations of the dipole dynamic polarizability, energies, and strengths of the oscillators of the lowest electronic transitions are made within the scope of the method of configuration interaction. This very method is also used to calculate the dipole dynamic polarizability of a number of molecules of hydrides and N₂ and CO₂ molecules. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 4, pp. 427–432, July–August, 2000.     

Multi-parameter global calculations of fission fragments using a simplified two-dimensional scission-point model

Exploiting the concept of the dinuclear system,the interaction potential energy of two fragments that are quite close to each other is analyzed.A semi-classical method is used to calculate fission fragment yields using a simplified two-dimensional scission-point model.By considering the tip-to-tip orientation at the scission point of the fission process,we investigate the mass,charge,and kinetic-energy distributions of the fission fragments,for excitation energies in the 0-20 MeV range.Our results show that the fission fragment distributions are reproduced quite well,including the recent experimental results for the isotone chain[D Ramos et al.Phys.Rev.C 97,054612(2018)].Thus,the simplified model is useful for multi-parameter global measurements of fission products.     

Study on the chemiluminescence resonance energy transfer between luminol and fluorescent dyes using a linear CCD spectrometer

Chemiluminescence (CL) has been a useful tool for analytical applications. Fluorescein can be used to enhance CL emission of luminol. With three-dimensional (3D) dynamic CL spectrum obtained from a linear CCD (charge-coupled device) flow-injection CL spectrometer, the fluorescein enhanced CL analysis was studied. The enhanced process can be described with chemiluminescence resonance energy transfer (CRET) at certain fluorescein concentrations. In the process of CRET, fluorescein enlarges CL intensity but does not join the CL reaction. Compared with classic luminol-Co²⁺ CL system, the fluorescein-enhanced system exhibits stronger CL signal with the linear range and detection limit for traces of Co²⁺ unchanged.     

Simulation of monthly mean circulation anomalies using a linear anomay model

Summary The El Ni?o event of 1982–1983 is studied using a linearized model derived from a complete GCM. The model describes the response to a heating distribution of an atmosphere with fully tridimensional basic state. The numerical results show that the 1983 circulation can be reasonably simulated by idealized heating distributions, but better results are obtained if heating derived from observed Outgoing Longwave Radiation (OLR) is used. The usage of a fully tridimensional basic state also improves the simulation over traditional zonally symmetric models. Extension of the simulations to other years (Januaries 1977–1984) yields some exceptional good case, but mixed results in most cases.     

Anchoring of alkyl chain molecules on oxide surface using silicon alkoxide

Chemical states of the interfaces between octadecyl-triethoxy-silane (ODTS) molecules and sapphire surface were measured by X-ray photoelectron spectroscopy (XPS) and near edge X-ray absorption fine structure (NEXAFS) using synchrotron soft X-rays. The nearly self-assembled monolayer of ODTS was formed on the sapphire surface. For XPS and NEXAFS measurements, it was elucidated that the chemical bond between silicon alkoxide in ODTS and the surface was formed, and the alkane chain of ODTS locates upper side on the surface. As a result, it was elucidated that the silicon alkoxide is a good anchor for the immobilization of organic molecules on oxides.     

Lattice dynamics of incommensurate composite Rb-IV and a realization of the monatomic linear chain model

Longitudinal-acoustic (LA) phonons have been studied by inelastic x-ray scattering in the high-pressure incommensurate host-guest system Rb-IV in the pressure range of 16.3 to 18.4 GPa. Two LA-like phonon branches are observed along the direction of the incommensurate wave vector, which are attributed to separate lattice vibrations in the host and guest subsystems. The derived sound velocities for the host and the guest, v(h) and v(g), respectively, are similar in magnitude [v(h)=v(g)=3840(100) m/s at 18 GPa], but our results indicate rather different pressure dependences of dv(h)/dP=140(60) m/s GPa(-1) and dv(g)/dP=280(80) m/s GPa(-1). The observations for the one-dimensional Rb guest chains are reproduced quantitatively on the basis of the monatomic linear chain model and the measured compressibility of the chains.     

Restricted linear least square treatment processing of heteronuclear spectra of biomolecules using the ANAFOR strategy

We explore the use of a processing procedure based on restricted least square minimization as a tool for reducing the time versus resolution dilemma often encountered for biomolecular multidimensional spectra. Using a 2D spectrum as a reference, we obtain the necessary input of frequency components and linewidths. Combined even with a limited time evolution in the indirect dimension, the amplitudes of the correlation peaks in all planes of the 3D spectra can be extracted, and can be used to reconstruct the interferograms in the third dimension. Parameters such as number of lines, threshold choice, resolution, lineshape, number of experimental data points and finally signal to noise ratio of the spectrum are examined starting from a triple-resonance HNCA spectrum of ubiquitin.     

Approximate step response of a nonlinear hydraulic mount using a simplified linear model

A simplified dynamic stiffness type linear model is used to analytically find the step responses of a nonlinear hydraulic mount in terms of the transmitted force and top chamber pressure. The closed form solution could be efficiently implemented with effective mount parameters, and peak value and the decay curve predictions could provide some insight into the nonlinear behavior. The analytical solutions to an ideal step input correlate well with both numerical simulations (of the same linear model) and measurements when a step-like displacement excitation is applied to fixed and free decoupler mounts.     

Testing of linear polarizer using photorefractive effect

A new method is developed to test linear polarizers using two-wave mixing in photorefractive Bi₁₂TiO₂₀ (Bismuth Titanium Oxide, BTO). The extinction ratios obtained from this method was comparable with the literature values and the method is also useful for qualitative analysis of linear polarizers. Detailed theoretical and experimental analysis is given in the paper.