Rings of integral quaternions

A quaternion order derived from an integral ternary quadratic form f = Σa_ijx_ix_j of discriminant d = 4 det (a_ij) is m-maximal if m is not divisible by any prime p such that p² | d, or p 6; d and c_p = 1. If R is m-maximal and m is a product p₁ … p_r of primes, then any primitive element α of R has unique right-divisor ideals of each norm p₁ … p_k (k = 1, …, r). This generalizes Lipschitz's ninety-year-old theorem. We characterize m-maximal orders, study their ideals, and show how the preceding result yields formulas for the number of representations of integers by certain quaternary quadratic forms.     

Simulation studies of the scattering of a solitary wave by a mass impurity in a chain of nonlinear oscillators

We have simulated large amplitude motion in cyclic one-dimensional lattices of Morse potential oscillators with a mass impurity, and have observed an unexpected persistence of solitary wave behavior for which we are unable to discover a satisfactory explanation. In solitary wave motion as a function of cycle length and of initial energy, the most common feature of the dynamics is an initial energy plateau with regular oscillatory energy exchange between the solitary wave and other excitations of the lattice, followed by rapid decay. Some systems show no decay at all through 1000 impurity interactions, while others show no significant plateau before decaying. For some cycle lengths there are energy bands in which the solitary wave propagates indefinitely long, with small amplitude oscillatory exchange of energy with the lattice. No regularities were found.     

On the order of itinerant antiferromagnetic phase transitions and superconducting phase transitions in an exchange field

The coefficients of the second and fourth order terms in a Landau expansion of the free energy are evaluated for an itinerant antiferromagnetic transition. The choice of spatial dependence is found to play an important role. A first order transition is obtained for a range of values of the band structure parameters. However if values appropriate to Cr are used it is found that the contribution from the shift in the Fermi level is sufficiently large to give second order transitions even when magnetostrictive effects are included. In the mathematically similar problem of a superconductor in an exchange field it is found that the transition from normal to superconducting states is first order near the triple point with an upper and possibly a lower critical point where the transition changes to second order.     

Charged Π-phase kinks in lightly doped polyacetylene

If polyacetylene is viewed as a Peierls-distorted linear chain it is concluded that extra electrons or holes added to polyacetylene via light doping will be accomodated in polyacetylene in the form of charged π-phase kinks, rather than filling available electron band states.     

Isomerization and dissociation dynamics of HCN in a picosecond infrared laser field: a full-dimensional classical study

We report a full-dimensional study of the classical dynamics of HCN-->HNC isomerization and of HCN rovibrational dissociation driven by a strong but nonionizing picosecond infrared laser field. The dynamics of the isolated molecule and of the molecule in liquid Ar have both been studied. Our theoretical and numerical results show that when all degrees of freedom are accounted for the field induced molecular dynamics can be totally different from what was found in previous studies, where the HCN molecule is restricted to a plane containing the external field. It is shown that as HCN is driven by an infrared laser field, the rotation of the H atom around the C-N bond provides an important and highly efficient energy absorption mechanism. In the presence of a monochromatic picosecond infrared laser field with an intensity of 10(13) W/cm(2), this energy absorption mechanism generates considerable HCN-->HNC isomerization yield or high rovibrational dissociation yield without molecular preorientation or prealignment. Our study of the field induced isomerization and dissociation dynamics of the same system in liquid Ar shows that the picosecond isomerization dynamics is insignificantly affected by the surrounding atomic liquid whereas the dissociation yield may be greatly suppressed in a high density liquid. The implications of this study for full-dimensional quantum dynamics of multiphoton rovibrational excitation and dissociation of triatomics are briefly discussed.     

Phase transitions in the liquid-vapor interface of dilute alloys of Bi in Ga: new experimental studies

We report the results of measurements of x-ray reflectivity and grazing incidence x-ray diffraction from the liquid-vapor interfaces of four dilute alloys of Bi in Ga with mole fractions x(Bi)=0.0032, 0.0023, 0.00037, and 0.000037. The monolayer coverage of the alloys with x(Bi)=0.0023, and x(Bi)=0.00037 is about 0.85 and only very slightly temperature dependent. The monolayer coverage in the lowest-concentration alloy, with x(Bi)=0.000037, ranged from 0.82 at 29 degrees C to 0.58 at 110 degrees C. In none of these alloys, down to the lowest temperature used, 29 degrees C, can we find any evidence for crystallization of the Bi monolayer that segregates as the outermost stratum of the liquid-vapor interface. Drawing on theoretical arguments we propose that the transitions inferred from the second-harmonic generation and plasma generation studies of dilute Bi in Ga alloys are from the liquid state to the hexatic state of the Bi monolayer. The data for the alloy with x(Bi)=0.000037 suggest that near 80 degrees C there is a disordered phase-to-disordered phase transition.     

Theory of the soft phonon mode and dielectric constant below the Peierls transition temperature

We discuss, within mean field theory, the behavior of the soft phonon mode and static dielectric constant below the Peierls transition temperature in a one-dimensional band conductor.