Exactly solvable XY model of the spin Peierls transition

The exact solution of the problem of the ground state of theXY-spin system on a deformed chain is found. At finite magnetizationm it is characterized by the double periodic structure and has a finite-band spectrum of spin excitations. Atm 0 the phase transition from the incommensurate into the dimerized state is accompanied by the soliton lattice formation.     

Evaluation of Multicenter Electronic Attraction, Electric Field and Electric Field Gradient Integrals with Screened and Nonscreened Coulomb Potentials over Integer and Noninteger n Slater Orbitals

By the use of complete orthonormal sets of -exponential-type orbitals, where ( = 1, 0, –1, –2,...) the multicenter electronic attraction (EA), electric field (EF) and electric field gradient (EFG) integrals of nonscreened and Yukawa-like screened Coulomb potentials are expressed through the two-center overlap integrals with the same screening constants and the auxiliary functions introduced in our previous paper (I.I. Guseinov, J. Phys. B, 3 (1970) 1399). The recurrence relations for auxiliary functions are useful for the calculation of multicenter EA, EF and EFG integrals for arbitrary integer and noninteger values of principal quantum numbers, screening constants, and location of slater-type orbitals. The convergence of the series is tested by calculating concrete cases.     

Pressure effects on 2p5 3p - 2p5 3d transitions in neon

The collisional broadening and shift of four spectral lines of neon (747.2, 748.8, 753.5, 754.4 nm) arising from 2p⁵ 3p - 2p⁵ 3d transitions, emitted from a low-pressure glow discharge in pure neon and neon-helium mixtures have been measured using a Fabry-Perot interferometer. The values of pressure broadening and shift coefficients are determined and analyzed in terms of the impact theory.     

The Linear Fokker-Planck Equation for the Ornstein-Uhlenbeck Process as an (Almost) Nonlinear Kinetic Equation for an Isolated N-Particle System

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation. An erratum to this article can be found at     

Looking at Fokker-Planck dynamics with a noisy instrument

We consider the class of experiments which can be characterized by a Fokker-PIanck dynamics corresponding to the overdamped motion of a state point in a suitable stochastic potential. We assume that the general form of the potential is known (or can be guessed with reasonable accuracy), but that its parameters are to be determined experimentally by measurements made with a noisy instrument. This possible method for determining the potential parameters, which exploits the system's own internal stochastic motion in order to explore rapidly its available parameter space, is substantially more efficient than traditional methods involving time averages of single point measurements, and yet does not appear to have been previously considered. The method could be important when, for example, the experiment must be completed in a limited time owing either to the expense of the experimental materials or to the temporary stationarity of the preparation, situations which are commonly encountered in experimental biochemistry and biology.     

Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential

Using exact diagonalisation and Density Matrix Renormalisation group (DMRG) approach we analyse the transition to a localised state of a weakly interacting quasi-1D Bose gas subjected to a quasiperiodic potential. The analysis is performed by calculating the superfluid fraction, density profile, momentum distribution and visibility for different periodicities of the second lattice and in the presence (or not) of a weak repulsive interaction. It is shown that the transition is sharper towards the maximally incommensurate ratio between the two lattice periodicities, and shifted to higher values of the second lattice strength by weak repulsive interactions. We also relate our results to recent experiments.     

Autoionization of an ultracold Rydberg gas through resonant dipole coupling

We investigate a possible mechanism for the autoionization of ultracold Rydberg gases, based on the resonant coupling of Rydberg pair states to the ionization continuum. Unlike an atomic collision where the wave functions begin to overlap, the mechanism considered here involves only the long-range dipole interaction and is in principle possible in a static system. It is related to the process of intermolecular Coulombic decay (ICD). In addition, we include the interaction-induced motion of the atoms and the effect of multi-particle systems in this work. We find that the probability for this ionization mechanism can be increased in many-particle systems featuring attractive or repulsive van der Waals interactions. However, the rates for ionization through resonant dipole coupling are very low. It is thus unlikely that this process contributes to the autoionization of Rydberg gases in the form presented here, but it may still act as a trigger for secondary ionization processes. As our picture involves only binary interactions, it remains to be investigated if collective effects of an ensemble of atoms can significantly influence the ionization probability. Nevertheless our calculations may serve as a starting point for the investigation of more complex systems, such as the coupling of many pair states proposed in [P.J. Tanner et al., Phys. Rev. Lett. 100, 043002 (2008)].     

Predicting XAFS scattering path cumulants and XAFS spectra for metals (Cu,Ni, Fe,Ti, Au) using molecular dynamics simulations

The ability of molecular dynamics (MD) simulations to support the analysis of X‐ray absorption fine‐structure (XAFS) data for metals is evaluated. The low‐order cumulants (ΔR, σ², C₃) for XAFS scattering paths are calculated for the metals Cu, Ni, Fe, Ti and Au at 300 K using 28 interatomic potentials of the embedded‐atom method type. The MD cumulant predictions were evaluated within a cumulant expansion XAFS fitting model, using global (path‐independent) scaling factors. Direct simulations of the corresponding XAFS spectra, χ(R), are also performed using MD configurational data in combination with the FEFFab initio code. The cumulant scaling parameters compensate for differences between the real and effective scattering path distributions, and for any errors that might exist in the MD predictions and in the experimental data. The fitted value of ΔR is susceptible to experimental errors and inadvertent lattice thermal expansion in the simulation crystallites. The unadjusted predictions of σ² vary in accuracy, but do not show a consistent bias for any metal except Au, for which all potentials overestimate σ². The unadjusted C₃ predictions produced by different potentials display only order‐of‐magnitude consistency. The accuracy of direct simulations of χ(R) for a given metal varies among the different potentials. For each of the metals Cu, Ni, Fe and Ti, one or more of the tested potentials was found to provide a reasonable simulation of χ(R). However, none of the potentials tested for Au was sufficiently accurate for this purpose.     

Accurate calculation of the scattering length for the cooling of hydrogen atoms by lithium atoms

An improved ab initio calculation has been performed for the potential for the LiH a ³Σ⁺ state, using two very large basis sets. The Basis Set Superposition Error (BSSE) correction has been determined for both basis sets and the non-Born-Oppenheimer correction estimated to be negligible. The best potential is approximately 10% deeper than the previous estimate. Vibrational energies and scattering lengths have been calculated for ^6,7LiH(D) with both potentials, with and without the BSSE correction, and also with an estimated potential expected to bracket the true potential. The ⁷LiH scattering length is estimated to be (45 ± 4)a₀ and hence the low-energy cross-section in the best a ³Σ⁺ potential is about half that calculated previously. Enhanced cooling by ⁷Li of trapped H atoms remains feasible. Received 30 April 2001