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arXiv1996

Influence of hydrodynamic interactions on the ballistic deposition of colloidal particles on solid surfaces

The ballistic deposition of particles by taking hydrodynamic interactions (HI) into account has been studied by means of computer simulations. The radial distribution function of the assembly of particles deposited on a plane has been determined as a function of the coverage and compared to experimental data. It appears that the introduction of HI in the model when compared to the ballistic model predictions leads to a better agreement between experiment and simulation in particular for the radial distribution function.

cond-mat↗

arXiv1996

A Dynamical Theory of Electron Transfer: Crossover from Weak to Strong Electronic Coupling

We present a real-time path integral theory for the rate of electron transfer reactions. Using graph theoretic techniques, the dynamics is expressed in a formally exact way as a set of integral equations. With a simple approximation for the self-energy, the rate can then be computed analytically to all orders in the electronic coupling matrix element. We present results for the crossover region between weak (nonadiabatic) and strong (adiabatic) electronic coupling and show that this theory provides a rigorous justification for the salient features of the rate expected within conventional electron transfer theory. Nonetheless, we find distinct characteristics of quantum behavior even in the strongly adiabatic limit where classical rate theory is conventionally thought to be applicable. To our knowledge, this theory is the first systematic dynamical treatment of the full crossover region.

chem-ph↗

arXiv1996

A Computational Study of Thirteen-atom Ar-Kr Cluster Heat Capacities

Heat capacity curves as functions of temperature were calculated using Monte Carlo methods for the series of Ar_{13-n}Kr_n clusters (0 <= n <= 13). The clusters were modeled classically using pairwise additive Lennard-Jones potentials. J-walking (or jump-walking) was used to overcome convergence difficulties due to quasiergodicity present in the solid-liquid transition regions, as well as in the very low temperature regions where heat capacity anomalies arising from permutational isomers were observed. Substantial discrepancies between the J-walking results and the results obtained using standard Metropolis Monte Carlo methods were found. Results obtained using the atom-exchange method, another Monte Carlo variant designed for multi-component systems, were mostly similar to the J-walker results. Quench studies were also done to investigate the clusters' potential energy surfaces; in each case, the lowest energy isomer had an icosahedral-like symmetry typical of homogeneous thirteen-atom rare gas clusters, with an Ar atom being the central atom.

chem-ph↗

arXiv1996

A Variational Approach to Nonlocal Exciton-Phonon Coupling

In this paper we apply variational energy band theory to a form of the Holstein Hamiltonian in which the influence of lattice vibrations (optical phonons) on both local site energies (local coupling) and transfers of electronic excitations between neighboring sites (nonlocal coupling) is taken into account. A flexible spanning set of orthonormal eigenfunctions of the joint exciton-phonon crystal momentum is used to arrive at a variational estimate (bound) of the ground state energy for every value of the joint crystal momentum, yielding a variational estimate of the lowest polaron energy band across the entire Brillouin zone, as well as the complete set of polaron Bloch functions associated with this band. The variation is implemented numerically, avoiding restrictive assumptions that have limited the scope of previous assaults on the same and similar problems. Polaron energy bands and the structure of the associated Bloch states are studied at general points in the three-dimensional parameter space of the model Hamiltonian (electronic tunneling, local coupling, nonlocal coupling), though our principal emphasis lay in under-studied area of nonlocal coupling and its interplay with electronic tunneling; a phase diagram summarizing the latter is presented. The common notion of a "self-trapping transition" is addressed and generalized.

cond-mat↗

arXiv1996

Feynman-Kac Kernels in Markovian Representations of the Schroedinger Interpolating Dynamics

Probabilistic solutions of the so called Schrödinger boundary data problem provide for a unique Markovian interpolation between any two strictly positive probability densities designed to form the input-output statistics data for the process taking place in a finite-time interval. The key issue is to select the jointly continuous in all variables positive Feynman-Kac kernel, appropriate for the phenomenological (physical) situation. We extend the existing formulations of the problem to cases when the kernel is \it not \rm a fundamental solution of a parabolic equation, and prove the existence of a continuous Markov interpolation in this case. Next, we analyze the compatibility of this stochastic evolution with the original parabolic dynamics, while assumed to be governed by the temporally adjoint pair of (parabolic) partial differential equations, and prove that the pertinent random motion is a diffusion process. In particular, in conjunction with Born's statistical interpretation postulate in quantum theory, we consider stochastic processes which are compatible with the Schrödinger picture quantum evolution.

quant-ph↗

arXiv1996

Evidence for Non-Random Hydrophobicity Structures in Protein Chains

The question of whether proteins originate from random sequences of amino acids is addressed. A statistical analysis is performed in terms of blocked and random walk values formed by binary hydrophobic assignments of the amino acids along the protein chains. Theoretical expectations of these variables from random distributions of hydrophobicities are compared with those obtained from functional proteins. The results, which are based upon proteins in the SWISS-PROT data base, convincingly show that the amino acid sequences in proteins differ from what is expected from random sequences in a statistical significant way. By performing Fourier transforms on the random walks one obtains additional evidence for non-randomness of the distributions. We have also analyzed results from a synthetic model containing only two amino-acid types, hydrophobic and hydrophilic. With reasonable criteria on good folding properties in terms of thermodynamical and kinetic behavior, sequences that fold well are isolated. Performing the same statistical analysis on the sequences that fold well indicates similar deviations from randomness as for the functional proteins. The deviations from randomness can be interpreted as originating from anticorrelations in terms of an Ising spin model for the hydrophobicities. Our results, which differ from previous investigations using other methods, might have impact on how permissive with respect to sequence specificity the protein folding process is -- only sequences with non-random hydrophobicity distributions fold well. Other distributions give rise to energy landscapes with poor folding properties and hence did not survive the evolution.

chem-ph↗

arXiv1995

Bond Orientational Order, Molecular Motion and Free Energy of High Density DNA Mesophases

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid crystalline phase digram: a higher-density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction; and a lower-density cholesteric region with fluid-like positional order. X-rays scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a six-fold azimuthal modulation of the first order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order that had been expected from the change in optical birefringence patterns and that is consistent with a rapid onset of molecular positional disorder. This change in motion was previously inferred from intermolecular force measurements and is now confirmed by $\rm ^{31}P$ NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between $\sim 120$ mg/ml to $\sim 600$ mg/ml, allows measurement of the free energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states.

chem-ph↗

arXiv1994

Comparison of electron density functional models

Presented here are calculations of the distortion of the density of an electron gas due to the electrostatic field of a proton. Several models based upon the local density approximation (LDA) of density functional theory [linear response theory, Kohn-Sham (KS), optimized Thomas-Fermi theory (OTF), and OTF plus perturbation corrections] are compared with one another. These models, in turn, are compared with available results of quantum Monte Carlo (QMC) calculations for the same system. Comparison of the KS results with the OTF results shows a very reasonable agreement that seems to be progressively improvable. This provides encouragement for the application of the OTF model to condensed phase systems. The QMC calculations of the density do not agree well with the density functional results. The reasons for this poor agreement are not clear. This particular system is expected to be an ideal one for application of the LDA and, thus, the poor agreement is of fundamental importance. The lack of detail presented in the available QMC results leads us to conclude that the QMC calculations should be attempted again. in print: Molec. Phys. 82, 245-261(1994)

chem-ph↗

arXiv1995

Integral equation theory for the electrode-electrolyte interface with the central force water model. Results for an aqueous solution of sodium chloride

The structure of an aqueous solution of sodium chloride at a planar electrode is investigated by integral equation techniques. With the central force water model the aqueous electrolyte is modelled as a mixture of sodium and chloride ions and partially charged hydrogen and oxygen atoms interacting via effective spherically symmetric pair potentials. The bulk correlation functions are obtained from the Ornstein-Zernike equation. With the Wertheim-Lovett-Mou-Buff equation we have calculated the density profiles at the uncharged and charged electrode. Steric interactions between the differently sized ions and the ice-like water structure near the electrode dominates the ionic distribution. This model electrolyte also responds differently to opposite charges on the electrode.

chem-ph↗

arXiv1995

The Atomic and Electronic Structure of Liquid N- Methylformamide as Determined from Diffraction Experiments

The structure of liquid N-methylformamide (NMF) has been investigated using synchrotron radiation at 77 and 95 keV. The use of high energy photons has several advantages, in this case especially the large accessible momentum transfer range, the low absorption and the direct comparability with neutron diffraction. The range of momentum transfer covered is 0.6 Å$^{-1} <$ Q $<$24.0 Å$^{-1}$. Neutron diffraction data on the same sample in the same momentum transfer range have been published previously. In that study two differently isotope - substituted species were investigated. In order to compare neutron and photon diffraction data properly Reverse Monte Carlo (RMC-) simulations have been performed. Some modifications had to be added to the standard RMC- code introducing different constraints for inter- and intramolecular distances as these distances partly overlap in liquid NMF. RMC- simulations having only the neutron data as input were carried out in order to test the quality of the X-ray data. The photon structure factor calculated from the RMC- configurations is found to agree well with the present experimental data, while it deviates considerably from earlier X-ray work using low energy photons (17 keV). Finally we discuss whether the different interaction mechanisms of neutrons and photons can be used to directly access the electronic structure in the liquid. Evidence is presented that the elastic self scattering part of liquid NMF is changed with respect to the independent atom approximation. This modification can be accounted for by a simple charged atoms model.

chem-ph↗

arXiv1996

Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling

In this first of three articles on the optical absorption of electrons in half-filled Peierls-distorted chains we present analytical results for non-interacting tight-binding electrons. We carefully derive explicit expressions for the current operator, the dipole transition matrix elements, and the optical absorption for electrons with a cosine dispersion relation of band width $W$ and dimerization parameter $δ$. New correction (``$η$''-)terms to the current operator are identified. A broad band-to-band transition is found in the frequency range $Wδ< ω< W$ whose shape is determined by the joint density of states for the upper and lower Peierls subbands and the strong momentum dependence of the transition matrix elements.

cond-mat↗

arXiv1996

Exact results for the optical absorption of strongly correlated electrons in a half-filled Peierls-distorted chain

In this second of three articles on the optical absorption of electrons in a half-filled Peierls-distorted chain we present exact results for strongly correlated tight-binding electrons. In the limit of a strong on-site interaction $U$ we map the Hubbard model onto the Harris-Lange model which can be solved exactly in one dimension in terms of spinless fermions for the charge excitations. The exact solution allows for an interpretation of the charge dynamics in terms of parallel Hubbard bands with a free-electron dispersion of band-width $W$, separated by the Hubbard interaction $U$. The spin degrees of freedom enter the expressions for the optical absorption only via a momentum dependent but static ground state expectation value. The remaining spin problem can be traced out exactly since the eigenstates of the Harris-Lange model are spin-degenerate. This corresponds to the Hubbard model at temperatures large compared to the spin exchange energy. Explicit results are given for the optical absorption in the presence of a lattice distortion $δ$ and a nearest-neighbor interaction $V$. We find that the optical absorption for $V=0$ is dominated by a peak at $ω=U$ and broad but weak absorption bands for $| ω-U | \leq W$. For an appreciable nearest-neighbor interaction, $V>W/2$, almost all spectral weight is transferred to Simpson's exciton band which is eventually Peierls-split.

cond-mat↗

arXiv1996

Optical absorption of strongly correlated half-filled Mott-Hubbard chains

In this last of three articles on the optical absorption of electrons in a half-filled Peierls-distorted chain we address the dimerized extended Hubbard model in the limit of a large on-site interaction $U$. When the Hubbard interaction is large both compared to the band width $W$ and the nearest neighbor interaction $V$ the charge dynamics is properly described by the Harris-Lange model. This model can be exactly mapped onto a model of free spinless Fermions in parallel (Hubbard-)bands of width $W$ which are eventually Peierls-split. To determine the coherent absorption features at low temperatures we design and employ the ``no-recoil approximation'' in which we assume that the momentum transfer to the spin degrees of freedom can only be $Δq_S=0$ or $Δq_S=π/a$ during an optical excitation. We present explicit analytical results for the optical absorption in the presence of a lattice dimerization $δ$ and a nearest-neighbor interaction $V$ for the Néel and dimer state. We find that the coherent part of the optical absorption for $V=0$ is given by a single peak at $ω=U$ and broad but weak absorption bands for $Wδ\leq |ω-U| \leq W$. The central peak at $ω=U$ only vanishes for $δ=0$ in the Néel state. For an appreciable nearest neighbor interaction $V>W/2$ almost all spectral weight is transferred to the $Δq_C=0$-exciton and the $Δq_C=π/a$-exciton whose relative spectral weights very sensitively depend on both the lattice and the spin dimerization of the ground state.

cond-mat↗

arXiv1996

Tunneling with the Lorentz Force and the Friction

We present a semiclassical study of a transport process, the tunneling, in the presence of a magnetic field and a dissipative environment. We have found that the problem can be mapped onto an effective one-dimensional one, and the tunneling rate is strongly affected by the magnetic field, such as a complete suppression by a large parallel magnetic field, an example of the dynamical localization. In such case a small perpendicular component of the field, or the dissipation, can enhance the tunneling rate. In the small parallel field and finite temperatures the tunneling rate is finite. Explicit expressions will be presented in those cases. If viewing the tunneling in the presence of a magnetic field as a dissipative tunneling process, by varying the magnetic field and the potential one can obtain the dissipative spectral function between the subohmic $s =0$ and the superohmic $s = \infty$. In combination with a real dissipative spectral function, the effect of the magnetic field can map the spectral function from $s $ to $2-s$, with $s>2$ mapping to $ s = 0$, revealing a dual symmetry between the friction and the Lorentz force. Two cases relevant to experiments, the edge state tunneling in a Hall bar and the tunneling near the dynamical localization will be discussed in detail.

cond-mat↗

arXiv1994

Supersymmetric classical mechanics

We study the classical properties of a supersymmetric system which is often used as a model for supersymmetric quantum mechanics. It is found that the classical dynamics of the bosonic as well as the fermionic degrees of freedom is fully described by a so--called quasi--classical solution. We also comment on the importance of this quasi--classical solution in the semi--classical treatment of the supersymmetric quantum model.

cond-mat↗

arXiv1995

Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices

A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable representation of the Hamiltonian, and the Toeplitz property of the asymptotic part of the obtained {\it infinite} matrix is used. Thus, the problem is reduced to the inversion of a {\it finite} matrix.

cond-mat↗

arXiv1995

EQUIVALENCES BETWEEN STOCHASTIC SYSTEMS

Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and between stochastic and soluble {\em non-stochastic} models. The results agree with experiments on one-dimensional annihilation-coagulation processes.

cond-mat↗

arXiv1995

Sequence Dependence of Self-Interacting Random Chains

We study the thermodynamic behavior of the random chain model proposed by Iori, Marinari and Parisi, and how this depends on the actual sequence of interactions along the chain. The properties of randomly chosen sequences are compared to those of designed ones, obtained through a simulated annealing procedure in sequence space. We show that the transition to the folded phase takes place at a smaller strength of the quenched disorder for designed sequences. As a result, folding can be relatively fast for these sequences.

chem-ph↗