Correlation functions of the chiral Potts chain from conformal field theory and finite-size corrections

We study the incommensurate phase of the N = 3 superintegrable chiral Potts chain by computing the leading finite-size corrections to the low-lying energy levels. These results are used to study the asymptotic behavior of the correlation functions. In particular we analyze the difference between the regions above and below the self-dual point.     

Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field

We study the correlation function 〈σ₀^x(t)σ_n^x(0)〉 of the transverse Ising model in a critical field whose hamiltonian is $\text{1}\text{2}\text{Σ}{}_{\mathrm{l}}\text{{σ}{}_{\mathrm{l}}{}^{\mathrm{x}}\text{σ}{}_{\mathrm{l+1}}{}^{\mathrm{x}}\text{?σ}{}_{\mathrm{l}}{}^{\mathrm{z}}\text{}}$. At an arbitrary temperature T we relate the autocorrelation to a Fredholm determinant. Moreover at T = 0 the correlations are given by a Painlevé V function for all n. The long-time asymptotic behavior of this function is found and the connection problem is studied. This result contains oscillatory terms which are related to the density of states at the Brillouin zone boundary.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

A comparison of parabolic wave theories for linearly elastic solids

The Schrödinger equation describes a theory for propagating scalar waves which is frequently termed a parabolic theory. This theory has been demonstrated to provide a paraxial, or narrow-angled, approximation to the theory of acoustic wave propagation, described by the Helmholtz equation, by a variety of seemingly different procedures. Several authors have considered the question of an approximation to the time harmonic equations of linear elastodynamics, which is parabolic in the above described sense. Since none of the deivation procedures employed can be termed rigorous, and since the results of these procedures are different, the validity of each of the theories is suspect and all should be considered further. In this paper we consider three parabolic theories of elastodynamics; by Hudson, by Landers and Claerbout, and by McCoy; and apply them in turn to a computational experiment that can be solved in the perturbation limit using the exact equations of elastodynamics. The principal conclusion achieved is that an approximate theory for propagating vector waves must be based on a representation of the vector wave field, that explicitly incorporates different wave speeds for the dilitational and rotational components, if predictions of the approximate theory are to approach those of the exact formulation for narrow angles.     

Modelling rotations,vibrations, and rovibrational couplings in astructural molecules – a case study based on the H+5 molecular ion

One-dimensional (1D) and two-dimensional (2D) models are investigated, which help to understand the unusual rovibrational energy-level structure of the astronomically relevant and chemically interesting astructural molecular ion H⁺₅. Due to the very low hindering barrier characterising the 1D torsion-only vibrational model of H⁺₅, this model yields strongly divergent energy levels. The results obtained using a realistic model for the torsion potential, including the computed (near) degeneracies, can be rationalised in terms of the model with no barrier. Coupling of the torsional motion with a single rotational degree of freedom is also investigated in detail. It is shown how the embedding-dependent rovibrational models yield energy levels that can be rationalised via the 2D vibrational model containing two independent torsions. Insight into the complex rovibrational energy level structure of the models and of H⁺₅ is gained via variational nuclear motion and diffusion Monte Carlo computations and by the analysis of the wavefunctions they provide. The modelling results describing the transition from the zero barrier limit to the large barrier limit should prove to be useful for the important class of molecules and molecular ions that contain two weakly coupled internal rotors.     

Combined experimental/theoretical investigation of the He+ICl interactions. I. Rovibronic spectrum of He...ICl complexes in the ICl B-X, 3-0 region

Transitions of two different stereoisomers of the He...ICl(X,v" = 0) weakly bound complex, one with a T-shaped orientation and another that is most likely linear, have been observed in laser-induced fluorescence experiments performed in the ICl B-X region. Here we present experimental and theoretical results aimed at confirming the previous assignments and at gaining additional insights into the He+ICl interactions. High resolution action spectra were recorded in the same region to identify those features that could be attributed to transitions of the He...I35Cl(X,v" = 0) isomers and not to higher-order complexes, Hen...I35Cl, where n > or = 2, or I37Cl containing species. Calculations of the rovibronic spectra of the He...I35Cl complexes in the ICl B-X, 2-0 and 3-0 regions were performed using an ab initio potential energy surface for the He+ICl(X,v" = 0) ground state and two different pairwise additive potentials for the He+ICl(B,v' = 2,3) excited states. The rotation-vibration energies and wave functions for the He cdots, three dots, centered I35Cl complexes were obtained for all bound states with total angular momentum J < 10 using both of these potentials. Electronic spectra were generated using these results, assuming that the transition moment lies along the ICl bond and is not perturbed by the presence of the helium atom. The calculations qualitatively reproduce the He cdots, three dots, centered I35Cl action spectrum and strongly support the previous assignments. The calculations also indicate that some of the spectral congestion observed near the linear band may be attributed to transitions of the linear isomer to multiple intermolecular levels in the excited state. Coriolis coupling strongly mixes He cdots, three dots, centered ICl(B,v') states with rotational excitation, making simulations and assignments of the linear band observed in the experimental spectrum difficult.     

Structures of protein-protein complexes are docked using only NMR restraints from residual dipolar coupling and chemical shift perturbations

NMR structures of protein-protein and protein-ligand complexes rely heavily on intermolecular NOEs. Recent work has shown that if no significant conformational changes occur upon complex formation residual dipolar coupling can replace most of the NOE restraints in protein-protein complexes, while restraints derived from chemical shift perturbations can largely replace intermolecular NOEs in protein-ligand structures. By combining restraints from chemical shift perturbations with orientation restraints derived from measurements of residual dipolar couplings, we show that the structure of the EIN-HPr complex can be calculated without NOE restraints. The final structure, built from the crystal structures of EIN and HPr in their uncomplexed form and docked only with NMR restraints, places HPr within 2.5 A of the position determined from the mean NMR structure of the complex.