Low-temperature phases of itinerant fermions interacting with classical phonons: The static Holstein model

We consider models of independent itinerant fermions interacting with classical continuous or discrete variables (spins), the static Holstein model being a special case. We prove for all values of the fermion-spin coupling and a special value of the fermion chemical potential and classical magnetic field, at which the average fermion density is one-half and the average total spin is zero, that there are two degenerate ground states of period two with antiferromagnetic order for the spins and fermions. The existence of two corresponding low-temperature phases is proven for large coupling and dimension two or more by using a Peierls argument. This generalizes results of Kennedy and Lieb for the Falicov-Kimball model.Dedicated to Philippe Choquard on the occasion of his 65th birthday.     

Chemical shift anisotropy edited complete unraveling of overlapped 1H NMR spectra of enantiomers: application to small chiral molecules

The differential values of NMR spectral parameters like chemical shift anisotropies, dipolar couplings and quadrupolar couplings of enantiomers in chiral liquid crystalline media are employed not only for their visualization but also for their quantification. Large differences in chemical shift anisotropies and the quadrupolar couplings between the enantiomers enable the use of 13C and extensive 2H NMR detection for such a purpose. In spite of high magnetic moment, high sensitivity and abundant presence of protons in all the chiral molecules, 1H detection is not routinely employed due to severe overlap of unresolved transitions arising from short and long distance couplings. Furthermore, the doubling of the spectra from two enantiomers and their indistinguishable overlap due to negligible difference in chemical shift anisotropies hampers their discrimination. The present study demonstrates the use of proton chemical shift anisotropy as an exclusive parameter for such a discrimination. The method employs the non-selective excitation of homonuclear Nth quantum coherence of N coupled protons. The simultaneous flipping of all the coupled spins results in a single transition in the multiple quantum dimension at the cumulative sum of their anisotropic chemical shifts for each enantiomer, with the measurable difference between them, resulting in their complete unraveling.     

A perturbative approach to spectrum and correlation functions of the chiral Potts model

The massive high-temperature phase of the chiral Potts quantum chain is studied using perturbative methods. For the ₃-chain we present high-temperature expansions for the ground-state energy and the dispersion relations of the two single-particle states as well as two-particle states at general values of the parameters. We also present a perturbative argument showing that a large class of massive _n-spin quantum chains have quasiparticle spectra withn-1 fundamental particles. It is known from earlier investigations that—at special values of the parameters—some of the fundamental particles exist only for limited ranges of the momentum. In these regimes our argument is not rigorous, as one can conclude from a discussion of the radius of convergence of the perturbation series. We also derive correlation functions from a perturbative evaluation of the ground-state for the ₃-chain. In addition to an exponential decay we observe an oscillating contribution. The oscillation length seems to be related to the asymmetry of the dispersion relations. We show that this relation is exact at special values of the parameters for general _n using a form factor expansion.     

Nonequilibrium phase transition in stochastic lattice gases: Simulation of a three-dimensional system

We report results of computer simulations of a three-dimensional lattice gas of interacting particles subject to a uniform external fieldE. The dynamics of the system is given by hoppings of particles to nearby empty sites with rates biased for jumps in the direction ofE. As for the two-dimensional system we find that here too there exists a critical temperature,T _c (E) such that forT < T _c (E) the systems orders in a very anisotropic phase with striplike typical configurations parallel to the field.T _c (E) increases withE but substantially less strongly than in two dimensions. There is a break in the slope of the saturation current atT _c (E). Our data are consistent with the critical exponent being mean field.     

Band selective small flip angle COSY: a simple experiment for the analyses of 1H NMR spectra of small chiral molecules

The NMR spectroscopic discrimination of enantiomers in the chiral liquid crystalline solvent is more often carried out using ²H detection in its natural abundance. The employment of ¹H detection for such a purpose is severely hampered due to significant loss of resolution in addition to indistinguishable overlap of the spectra from the two enantiomers. This study demonstrates that the band selected small flip angle homonuclear correlation experiment is a simple and robust technique that provides unambiguous discrimination, very high spectral resolution, reduced multiplicity of transitions, relative signs of the couplings and enormous saving of instrument time.     

An application of a combined gradient system to stabilize a mechanical system

A gradient system and a skew-gradient system can be merged into a combined gradient system. The differential equations of the combined gradient system are established and its property is studied. If a mechanical system can be represented as a combined gradient system, the stability of the mechanical system can be studied by using the property of the combined gradient system. Some examples are given to illustrate the applications of the results.     

Structure of molecules in crystalline lattice obtained by a modified method of molecular mechanics: Calculations of<Superscript>13</Superscript>C chemical shifts

A program for the calculation of the geometric structure of molecular crystals on the basis of the methods of molecular mechanics (MM) has been developed. A standard MM method has been modified by including force fields taking into account the specific (H-bond and van der Waals) interactions and the periodicity of the crystal lattice of an arbitrary form and symmetry. The geometric parameters of the molecule in a crystal calculated by this method are in agreement with the experimental X-ray data within reasonable accuracy. The nuclear magnetic resonance¹³C chemical shifts have been calculated for the molecular geometry obtained by the quantum chemical UB3LYP/6-31G(d, p) method. The results of the calculations have been used to explain some unusual NMR spectral data.     

Saturation by a standing-wave laser of a Doppler-broadened three-level system: Narrow resonance due to stationary molecules

The narrow peak appearing at the center of the velocity distribution of the populations for saturation by a detuned standing-wave laser is analysed theoretically as a function of the relaxation parameters and the pump laser intensity. This peak allows high-resolution spectroscopic measurements when a frequency-unstabilized pump laser and a low intensity high-stability probe laser are used.     

Lehmann rotation of cholesteric droplets subjected to a temperature gradient: Role of the concentration of chiral molecules

We present a systematic study of the Lehmann rotation of cholesteric droplets subjected to a temperature gradient when the concentration of chiral molecules is changed. The liquid crystal chosen is an eutectic mixture of 8CB and 8OCB doped with a small amount of the chiral molecule R811. The angular velocity of the droplets strongly depend on their size and on the concentration of chiral molecules. The Lehmann coefficient is estimated by using three different methods. Our results are consistent with a Lehmann coefficient proportional to the concentration of chiral molecules. We additionally show the existence of a critical size of the droplets below which they change texture and stop rotating.     

Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice

We investigate low-temperature behaviors of a system with chirality-pair interaction on a one-dimensional lattice. In the course of the investigation, we evaluate asymptotic forms of the characteristic values of the integral equation satisfied by the Mathieu functions. It turns out that the low-temperature behavior of correlation length of the chirality-pair correlation function is different from the one for the Ising model of spin ±1 but akin to the one for the Ising model of infinite spin.     

A new approach to the drug release kinetics of a discrete system: SiO2 system obtained by ultrasonic dry spraying

Mesoporous silica materials have already proved to be non-toxic and biocompatible, and also to have large pore volume and very high specific surface area suitable for loading of small molecules. Having this in mind and the fact that silicon dioxide (SiO₂) powders can be so designed to obtain particle structures organized at multi levels, SiO₂ was chosen as a potential carrier for metronidazole, an antibiotic drug. SiO₂ powder was synthesized in two stages: first silica sol was prepared by hydrothermal synthesis and second the sol was converted into powder by dry spraying with simultaneous incorporation of the antibiotic into its structure. Scanning and transmission electron microscopy study revealed very complex structure and sub-structure of SiO₂ particles. Cell viability tests were used for estimation of cytotoxicity of so synthesized SiO₂. The drug release data showed that the system can provide drug release for a long time. Also, the device behavior is fully predictable, according to our theoretical model of multilevel structure design, and gives many opportunities for model investigations of drug release and its kinetics. The pore sizes and their distribution were observed as a limiting factor of drug release kinetics. Therefore, as the pore sizes are given as a set of discrete values, the kinetics of drug release might also be given as a set of corresponding discrete values.     

An alternative definition of the electron propagator in the superoperator form and its relation to linear response theory in a coupled-cluster framework

In this paper it is shown that (i) there exists an alternative definition of the superoperator resolvent for calculation of difference energy satisfying linked cluster theorem for a coupled-cluster choice of the ground-state function which may even be approximate; (ii) the pole-structure of this propagator-like function in superoperator form is shown to contain information similar to that contained in the conventional propagator. (iii) It is demonstrated that suitable “Killer conditions” and completeness of the “operator manifold”—essential for understanding the pole-structure of the propagator—can be established both for an exact and an approximate ground state function in a coupled-cluster form. (iv) It is also demonstrated that difference energies calculated with these propagator-like functions are identical to those obtained from a linear response theory in a coupled-cluster form put forward recently by Mukherjeeet al and Monkhorst.     

Vibrational excitation by positron collisions with molecular gases: a study of O and NO targets

The scattering of slow positrons from and NO molecules is treated using exact static interactions and a model potential for correlation-polarisation forces. The quantum coupled equations for the elastic scattering are extended to vibrationally inelastic processes and the different excitation probabilities are evaluated. Comparison with existing experiments for the NO target indicates that the present calculations provide a realistic treatment of positron scattering below Ps formation and give computational estimates on the efficiency of such projectiles in producing vibrationally excited molecules in the ambient gas. Received: 23 April 1999 / Received in final form: 3 June 1999     

An analysis of the effect of nitrogen and a screened (by free carriers) Coulomb field on the binding energy of hydrogenic shallow donors in GaInAsN

The effect of nitrogen concentration on the screening with free carriers and binding energy of hydrogenic shallow donors in GaInAsN alloys is investigated. The binding energy is calculated using a novel algebraic model which was proposed recently by Gönül et al. (2006) [16], in order to find an analytical solution to the screened Coulomb potential. The results show that the nitrogen concentration is a strong factor in producing a screening field of free carriers and in affecting the binding energy of hydrogenic shallow donors.