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arXiv1996

Scaling and Scale Breaking in Polyelectrolyte

We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain-length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introducing a renormalization of the strength of the nearest- neighbour interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems. The high temperature behaviour is well reproduced by the analytical high-$T$ expansions even for fairly low temperatures and system sizes. In addition, results from low-$T$ expansions, where the coefficients have been computed numerically, are presented. These results approximate well the corresponding Monte Carlo results at realistic temperatures. A corresponding analysis of screened chains is performed. The situation here is complicated by the appearance of an additional parameter, the screening length. A window is found in parameter space, where scaling holds for the end-to-end distance. This window corresponds to situations where the range of the potential interpolates between the bond length and the size of the chain. This scaling behaviour, which is verified by Monte Carlo results, is consistent with Flory scaling. Also for the screened chain a blocking approach can be devised, that performs well for low temperatures, whereas the low-$T$ expansion is inaccurate at realistic temperatures.

chem-ph↗

arXiv1996

Van der Waals clusters in the ultra-quantum limit: a Monte Carlo study

Bosonic van der Waals clusters of sizes three, four and five are studied by diffusion quantum Monte-Carlo techniques. In particular we study the unbinding transition, the ultra-quantum limit where the ground state ceases to exist as a bound state. We discuss the quality of trial wave functions used in the calculations, the critical behavior in the vicinity of the unbinding transition, and simple improvements of the diffusion Monte Carlo algorithm.

chem-ph↗

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↗

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↗

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↗

arXiv1996

On the absence of bound-state stabilization through short ultra-intense fields

We address the question of whether atomic bound states begin to stabilize in the short ultra-intense field limit. We provide a general theory of ionization probability and investigate its gauge invariance. For a wide range of potentials we find an upper and lower bound by non-perturbative methods, which clearly exclude the possibility that the ultra intense field might have a stabilizing effect on the atom. For short pulses we find almost complete ionization as the field strength increases.

quant-ph↗

arXiv1997

On the Influence of Pulse Shapes on Ionization Probability

We investigate analytical expressions for the upper and lower bounds for the ionization probability through ultra-intense shortly pulsed laser radiation. We take several different pulse shapes into account, including in particular those with a smooth adiabatic turn-on and turn-off. For all situations for which our bounds are applicable we do not find any evidence for bound-state stabilization.

quant-ph↗

arXiv1994

Exciton effects in soliton and bipolaron lattice states of doped electron-phonon Peierls systems

Exciton effects on soliton and bipolaron lattice states are investigated using an electron-lattice Peierls model with long-range Coulomb interactions. The Hartree-Fock (HF) approximation and the single-excitation configuration- interaction (single-CI) method are used to obtain optical absorption spectra. We discuss the following properties: (1) The attraction between the excited electron and the remaining hole makes the excitation energy smaller when the correlations are taken into account by the single-CI. The oscillator strengths of the lower excited states become relatively larger than in the HF calculations. (2) We look at variations of relative oscillator strengths of two or three kinds of excitons described by the single-CI. While the excess-electron concentration is small, the ratio of the oscillator strengths of the exciton with the lowest energy increases almost linearly. The oscillator strengths accumulate at this exciton as the concentration increases.

cond-mat↗

arXiv1996

Ab initio simulations of liquid systems: Concentration dependence of the electric conductivity of NaSn alloys

Liquid NaSn alloys in five different compositions (20, 40, 50, 57 and 80% sodium) are studied using density functional calculations combined with molecular dynamics(Car-Parrinello method). The frequency-dependent electric conductivities for the systems are calculated by means of the Kubo-Greenwood formula. The extrapolated DC conductivities are in good agreement with the experimental data and reproduce the strong variation with the concentration. The maximum of conductivity is obtained, in agreement with experiment, near the equimolar composition. The strong variation of conductivity, ranging from almost semiconducting up to metallic behaviour, can be understood by an analysis of the densities-of-states.

mtrl-th↗

arXiv1995

A Lattice-Gas Model of Microemulsions

We develop a lattice gas model for the nonequilibrium dynamics of microemulsions. Our model is based on the immiscible lattice gas of Rothman and Keller, which we reformulate using a microscopic, particulate description so as to permit generalisation to more complicated interactions, and on the prescription of Chan and Liang for introducing such interparticle interactions into lattice gas dynamics. We present the results of simulations to demonstrate that our model exhibits the correct phenomenology, and we contrast it with both equilibrium lattice models of microemulsions, and to other lattice gas models.

comp-gas↗

arXiv1994

Stability of the Hydrogen and Hydrogen-like Molecules

We present a simple proof of the stability of the hydrogen molecule $(M^+M^+m^-m^-)$. It does not rely on the proton-to-electron mass ratio $M/m$ being very large, and actually holds for arbitrary values of $M/m$. Some asymmetric molecules of the type $(m_1^+m_2^+m_3^-m_4^-)$ are also stable. Possible applications to molecules containing antiparticles and to exotic hadrons in the quark model are briefly outlined. Revtex Version 3.0, 4 Figures available on request by Fax or Mail.

chem-ph↗

arXiv1994

Li$_5$ as a pseudorotating planar cluster

A pseudorotating state of Li$_5$ observed in a recent EPR experiment is investigated using the local density functional method. The calculated isotropic spin population indicates that a planar $C_{2v}$ structure is more consistent with the experimental result than a suggested trigonal bipyramid. A new pseudorotating state based on the planar structure is proposed.

chem-ph↗

arXiv1994

Quasi-classical path integral approach to supersymmetric quantum mechanics

{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet, Bandrauk and Campbell when SUSY is good. When SUSY is broken, we arrive at a new quantization formula, which is found as good as and even sometime better than the WKB formula in evaluating energy spectra for certain one-dimensional bound state problems. The wave functions in the stationary phase approximation are also derived for SUSY and broken SUSY cases. Insofar as a broken SUSY case is concerned, there are strong indications that the new quasi-classical approximation formula always overestimates the energy eigenvalues while WKB always underestimates.

cond-mat↗