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arXiv1996

Weak Chirality in Ordered DNA Phases

Recent experiments on aligned DNA show hexatic order with no sign of macroscopic chirality. I make the analogy between smectic liquid crystals and chiral hexatics and show how the absence of chirality cannot occur in a thermodynamic phase of chiral molecules. In addition, I discuss the microscopic origin of chiral mesophases in liquid crystals and show that, within the context of central forces between "atoms" on "molecules", chiral interactions can occur only if there are biaxial correlations between the mesogens. Weak biaxial correlations can therefore lead to small cholesteric pitches.

cond-mat↗
arXiv1995

Hyper-Systolic Parallel Computing

A new class of parallel algorithms is introduced that can achieve a complexity of O(n^3/2) with respect to the interprocessor communication, in the exact computation of systems with pairwise mutual interactions of all elements. Hitherto, conventional methods exhibit a communicational complexity of O(n^2). The amount of computation operations is not altered for the new algorithm which can be formulated as a kind of h-range problem, known from the mathematical field of Additive Number Theory. We will demonstrate the reduction in communicational expense by comparing the standard-systolic algorithm and the new algorithm on the connection machine CM5 and the CRAY T3D. The parallel method can be useful in various scientific and engineering fields like exact n-body dynamics with long range forces, polymer chains, protein folding or signal processing.

hep-lat↗
arXiv1995

Real Space Renormalization-Group for Configurational Random Walk Models on a Hierarchical Lattice. The Asymptotic End-to-End Distance of a Weakly SARW in Dimension Four

We present a real space renormalization-group map for probabilities of random walks on a hierarchical lattice. From this, we study the asymptotic behavior of the end-to-end distance of a weakly self- avoiding random walk (SARW) that penalizes the (self-)intersection of two random walks in dimension four on the hierarchical lattice.

hep-th↗
arXiv1995

Quantum Algebraic Symmetries in Nuclei and Molecules

Various applications of quantum algebraic techniques in nuclear and molecular physics are briefly reviewed. Emphasis is put in the study of the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, the Bloch--Brink $α$-cluster model and possibly the shell structure in deformed atomic clusters.

nucl-th↗
arXiv1996

Algebraic model of an oblate top

We consider an algebraic treatment of a three-body system. In particular, we develop the formalism for a system of three identical objects and discuss an application to nonstrange baryon resonances which are interpreted as vibrational and rotational excitations of an oblate symmetric top. We derive closed expressions for a set of elementary form factors that appear in the calculation of both electromagnetic, strong and weak couplings of baryons.

nucl-th↗
arXiv1996

A general algebraic model for molecular vibrational spectroscopy

We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and configuration space formulations, leading to new interactions in the algebraic model. This approach incorporates the full power of group theoretical techniques and provides reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules.

chem-ph↗
arXiv1996

Extended Two--Particle Green's Functions and Optical Potentials for Two--Particle Scattering by Many--Body Targets

An extension of the fermionic particle--particle propagator is presented, that possesses similar algebraic properties to the single--particle Green's function. In particular, this extended two--particle Green's function satisfies Dyson's equation and its self energy has the same analytic structure as the the self energy of the single--particle Green's function. For the case of a system interacting by one--particle potentials only, the two--particle self energy takes on a particularly simple form, just like the common self energy does. The new two--particle self energy also serves as a well behaved optical potential for the elastic scattering of a two--particle projectile by a many--body target. Due to its analytic structure, the two--particle self energy avoids divergences that appear with effective potentials derived by other means.

chem-ph↗
arXiv1995

Solving the Coulomb Schrodinger Equation in d=2+1 via Sinc Collocation

We solve the non-relativistic Coulomb Shrodinger equation in d = 2+1 via sinc collocation. We get excellent convergence using a generalized sinc basis set in position space. Since convergence in position space could not be obtained with more common numerical techniques, this result helps to corroborate the conjecture that the use of a localized basis set within the context of light cone quantization can yield much better convergence. All of the computations presented here were performed on an IBM-compatible PC with an Intel 486DX2-66 microchip.

quant-ph↗
arXiv1997

Symmetry-adapted algebraic description of stretching and bending vibrations of ozone

The vibrational excitations of ozone, including both bending and stretching vibrations, are studied in the framework of a symmetry-adapted algebraic approach. This method is based on the isomorphism between the U(2) algebra and the one-dimensional Morse oscillator, and the introduction of point group symmetry techniques. The use of symmetry-adapted interactions, which in the harmonic limit have a clear physical interpretation, makes it possible to systematically include higher order terms and anharmonicities. A least-square fit to all published experimental levels (up to ten quanta) of 16 O_3 and 18 O_3 yields a r.m.s. deviation of 2.5 and 1.0 1/cm, respectively.

chem-ph↗
arXiv1995

Excitonic - vibronic coupled dimers: A dynamic approach

The dynamical properties of exciton transfer coupled to polarization vibrations in a two site system are investigated in detail. A fixed point analysis of the full system of Bloch - oscillator equations representing the coupled excitonic - vibronic flow is performed. For overcritical polarization a bifurcation converting the stable bonding ground state to a hyperbolic unstable state which is basic to the dynamical properties of the model is obtained. The phase space of the system is generally of a mixed type: Above bifurcation chaos develops starting from the region of the hyperbolic state and spreading with increasing energy over the Bloch sphere leaving only islands of regular dynamics. The behaviour of the polarization oscillator accordingly changes from regular to chaotic.

chem-ph↗
arXiv1995

Renormalized Equilibria of a Schloegl Model Lattice Gas

A lattice gas model for Schloegl's second chemical reaction is described and analyzed. Because the lattice gas does not obey a semi-detailed-balance condition, the equilibria are non-Gibbsian. In spite of this, a self-consistent set of equations for the exact homogeneous equilibria are described, using a generalized cluster-expansion scheme. These equations are solved in the two-particle BBGKY approximation, and the results are compared to numerical experiment. It is found that this approximation describes the equilibria far more accurately than the Boltzmann approximation. It is also found, however, that spurious solutions to the equilibrium equations appear which can only be removed by including effects due to three-particle correlations.

comp-gas↗
arXiv1995

"The numerical accuracy of truncated Ewald sums for periodic systems with long-range Coulomb interactions"

Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in the Ewald formulation. We derive an optimal choice for the Fourier-space cutoff given a screening parameter $η$. We find that the number of vectors in Fourier space required to achieve a given accuracy scales with $η^3$. The proposed method can be used to determine computationally efficient parameters for Ewald sums, to assess the quality of Ewald-sum implementations, and to compare different implementations.

chem-ph↗
arXiv1994

On the Mechanism of the Primary Charge Separation in Bacterial Photosynthesis

We present a detailed analysis of the mechanism of the primary charge separation process in bacterial photosynthesis using real-time path integrals. Direct computer simulations as well as an approximate analytical theory have been employed to map out the dynamics of the charge separation process in many regions of the parameter space relevant to bacterial photosynthesis. Two distinct parameter regions, one characteristic of sequential transfer and the other characteristic of superexchange, have been found to yield charge separation dynamics in agreement with experiments. Nonadiabatic theory provides accurate rate estimates for low-lying and very high-lying bacteriochlorophyll state energies, but it breaks down in between these two regimes.

chem-ph↗
arXiv1995

Density functional theory using an optimized exchange-correlation potential

We have performed self-consistent calculations for first and second row atoms using a variant of density-functional theory, the optimized effective potential method, with an approximation due to Krieger, Li and Iafrate and a correlation-energy functional developed by Colle and Salvetti. The mean absolute deviation of first-row atomic ground-state energies from the exact non-relativistic values is 4.7 mH in our scheme, as compared to 4.5 mH in a recent configuration-interaction calculation. The proposed scheme is significantly more accurate than the conventional Kohn-Sham method while the numerical effort involved is about the same as for an ordinary Hartree-Fock calculation.

chem-ph↗
arXiv1995

Global geometry optimization of clusters using a growth strategy optimized by a genetic algorithm

A new strategy for global geometry optimization of clusters is presented. Important features are a restriction of search space to favorable nearest-neighbor distance ranges, a suitable cluster growth representation with diminished correlations, and easy transferability of the results to larger clusters. The strengths and possible limitations of the method are demonstrated for Si10 using an empirical potential.

chem-ph↗
arXiv1996

On The Low-Frequency Vibrational Modes of C$_{60}$

The vibrational spectrum of C$_{60}$ is compared to the spectrum of a classical isotropic elastic spherical shell. We show correlations between the low frequency modes of C$_{60}$ and those of the spherical shell. We find the spherical model gives the approximate frequency ordering for the low frequency modes. We estimate a Poisson ratio of $σ\approx 0.30$ and a transverse speed of sound of $v_s\approx 1800$ m/s for the equivalent elastic shell. We also find that $ω({\rm M_1})/ω({\rm M_0})=\sqrt{3\over 2}$ for the shell modes ${\rm M_0}$ and ${\rm M_1}$, independent of elastic constants. We find that this ratio compares favorably with an experimental value of 1.17.

mtrl-th↗
arXiv1996

Fractal Dimension of Disordered Submonolayers: Determination from He Scattering Data

We propose a novel method to measure the fractal dimension of a submonolayer metal adatom system grown under conditions of limited diffusivity on a surface. The method is based on measuring the specular peak attenuation of He atoms scattered from the surface, as a function of incidence energy. The (Minkowski) fractal dimension thus obtained is that of contours of constant electron density of the adatom system. Simulation results are presented, based on experimental data. A coverage dependent fractal dimension is found from a two-decade wide scaling regime.

chem-ph↗