Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz

The exactly solvable Lieb-Liniger model of interacting bosons in one-dimension has attracted renewed interest as current experiments with ultra-cold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss the novel features of the solutions, and how they deviate from the well-known string solutions [H. B. Thacker, Rev. Mod. Phys.\ \textbf{53}, 253 (1981)] at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive 1D Bose gas on a ring.Comment: 13 pages, 12 figure

Weak Interactions in Dimethyl Sulfoxide (DMSO)-Tertiary Amide Solutions: The Versatility of DMSO as a Solvent

The structures of equimolar mixtures of the commonly used polar aprotic solvents dimethylformamide (DMF) and dimethylacetamide (DMAc) in dimethyl sulfoxide (DMSO) have been investigated via neutron diffraction augmented by extensive hydrogen/deuterium isotopic substitution. Detailed 3-dimensional structural models of these solutions have been derived from the neutron data via Empirical Potential Structure Refinement (EPSR). The intermolecular center-of-mass (CoM) distributions show that the first coordination shell of the amides comprises ∼13-14 neighbors, of which approximately half are DMSO. In spite of this near ideal coordination shell mixing, the changes to the amide-amide structure are found to be relatively subtle when compared to the pure liquids. Analysis of specific intermolecular atom-atom correlations allows quantitative interpretation of the competition between weak interactions in the solution. We find a hierarchy of formic and methyl C-H···O hydrogen bonds forms the dominant local motifs, with peak positions in the range of 2.5-3.0 Å. We also observe a rich variety of steric and dispersion interactions, including those involving the O═C-N amide π-backbones. This detailed insight into the structural landscape of these important liquids demonstrates the versatility of DMSO as a solvent and the remarkable sensitivity of neutron diffraction, which is critical for understanding weak intermolecular interactions at the nanoscale and thereby tailoring solvent properties to specific applications

Strong structuring arising from weak cooperative O-H···π and C-H···O hydrogen bonding in benzene-methanol solution

Weak hydrogen bonds, such as O-H···π and C-H···O, are thought to direct biochemical assembly, molecular recognition, and chemical selectivity but are seldom observed in solution. We have used neutron diffraction combined with H/D isotopic substitution to obtain a detailed spatial and orientational picture of the structure of benzene-methanol mixtures. Our analysis reveals that methanol fully solvates and surrounds each benzene molecule. The expected O-H···π interaction is highly localised and directional, with the methanol hydroxyl bond aligned normal to the aromatic plane and the hydrogen at a distance of 2.30 Å from the ring centroid. Simultaneously, the tendency of methanol to form chain and cyclic motifs in the bulk liquid is manifest in a highly templated solvation structure in the plane of the ring. The methanol molecules surround the benzene so that the O-H bonds are coplanar with the aromatic ring while the oxygens interact with C-H groups through simultaneous bifurcated hydrogen bonds. This demonstrates that weak hydrogen bonding can modulate existing stronger interactions to give rise to highly ordered cooperative structural motifs that persist in the liquid phase

Spin-ice physics in cadmium cyanide

Spin-ices are frustrated magnets that support a particularly rich variety of emergent physics. Typically, it is the interplay of magnetic dipole interactions, spin anisotropy, and geometric frustration on the pyrochlore lattice that drives spin-ice formation. The relevant physics occurs at temperatures commensurate with the magnetic interaction strength, which for most systems is 1–5 K. Here, we show that non-magnetic cadmium cyanide, Cd(CN)2, exhibits analogous behaviour to magnetic spin-ices, but does so on a temperature scale that is nearly two orders of magnitude greater. The electric dipole moments of cyanide ions in Cd(CN)2 assume the role of magnetic pseudospins, with the difference in energy scale reflecting the increased strength of electric vs magnetic dipolar interactions. As a result, spin-ice physics influences the structural behaviour of Cd(CN)2 even at room temperature.ISSN:2041-172

Incoherent neutron scattering studies of select inorganic systems

Spectroscopic measurements are detailed within this thesis, utilising incoherent neutron scattering to examine the dynamics of various condensed-matter systems, from nanosecond to sub-femtosecond timescales. The body of this work is divided into two distinct areas of research.I. Nuclear Momentum Measurements of Multiple MassesDeep inelastic neutron scattering (DINS) is used to probe the nuclear momentum distributions and kinetic energies of individual atomic species in sodium hydride (both in bulk and as nanoparticulates within a silica matrix), enriched lithium-7 fluoride and lithium tetra-ammoniate. Extension of DINS to examine heavier (M&gt;4amu) nuclei is detailed, accomplished by the application of a simple stoichiometric fixing technique within the standard DINS theory and analysis protocols. The validity and accuracy of such simultaneous measurements are discussed.II. The Dynamics of Coordinated Ammonia in Zeolite AInelastic neutron scattering (INS) and quasielastic neutron scattering (QENS) are utilised in the examination of vibrational and stochastic dynamics of the ammonia molecule, as coordinated to the internal surface of a zeolite host. Both sodium and copper-exchanged forms of zeolite-A are studied, with proton-weighted, low energy phonon-modes and rotational processes being observed and assigned.</p

Incoherent neutron scattering studies of select inorganic systems : I. Nuclear momentum measurements of multiple masses, II. The dynamics of coordinated ammonia in zeolite A

Spectroscopic measurements are detailed within this thesis, utilising incoherent neutron scattering to examine the dynamics of various condensed-matter systems, from nanosecond to sub-femtosecond timescales. The body of this work is divided into two distinct areas of research. I. Nuclear Momentum Measurements of Multiple Masses Deep inelastic neutron scattering (DINS) is used to probe the nuclear momentum distributions and kinetic energies of individual atomic species in sodium hydride (both in bulk and as nanoparticulates within a silica matrix), enriched lithium-7 fluoride and lithium tetra-ammoniate. Extension of DINS to examine heavier (M>4amu) nuclei is detailed, accomplished by the application of a simple stoichiometric fixing technique within the standard DINS theory and analysis protocols. The validity and accuracy of such simultaneous measurements are discussed. II. The Dynamics of Coordinated Ammonia in Zeolite A Inelastic neutron scattering (INS) and quasielastic neutron scattering (QENS) are utilised in the examination of vibrational and stochastic dynamics of the ammonia molecule, as coordinated to the internal surface of a zeolite host. Both sodium and copper-exchanged forms of zeolite-A are studied, with proton-weighted, low energy phonon-modes and rotational processes being observed and assigned.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Synthesis, PtS-type structure, and anomalous mechanics of the Cd(CN)2 precursor Cd(NH3)2[Cd(CN)4]

We report the nonaqueous synthesis of Cd(CN)2 by oxidation of cadmium metal with Hg(CN)2 in liquid ammonia. The reaction proceeds via an intermediate of composition Cd(NH3)2[Cd(CN)4], which converts to Cd(CN)2 on prolonged heating. Powder X-ray diffraction measurements allow us to determine the crystal structure of the previously-unreported Cd(NH3)2[Cd(CN)4], which we find to adopt a twofold interpenetrating PtS topology. We discuss the effect of partial oxidation on the Cd/Hg composition of this intermediate, as well as its implications for the reconstructive nature of the deammination process. Variable-temperature X-ray diffraction measurements allow us to characterise the anisotropic negative thermal expansion (NTE) behaviour of Cd(NH3)2[Cd(CN)4] together with the effect of Cd/Hg substitution; ab initio density functional theory (DFT) calculations reveal a similarly anomalous mechanical response in the form of both negative linear compressibility (NLC) and negative Poisson's ratios

Strong structuring arising from weak cooperative O-H···π and C-H···O hydrogen bonding in benzene-methanol solution

Abstract Weak hydrogen bonds, such as O-H···π and C-H···O, are thought to direct biochemical assembly, molecular recognition, and chemical selectivity but are seldom observed in solution. We have used neutron diffraction combined with H/D isotopic substitution to obtain a detailed spatial and orientational picture of the structure of benzene-methanol mixtures. Our analysis reveals that methanol fully solvates and surrounds each benzene molecule. The expected O-H···π interaction is highly localised and directional, with the methanol hydroxyl bond aligned normal to the aromatic plane and the hydrogen at a distance of 2.30 Å from the ring centroid. Simultaneously, the tendency of methanol to form chain and cyclic motifs in the bulk liquid is manifest in a highly templated solvation structure in the plane of the ring. The methanol molecules surround the benzene so that the O-H bonds are coplanar with the aromatic ring while the oxygens interact with C-H groups through simultaneous bifurcated hydrogen bonds. This demonstrates that weak hydrogen bonding can modulate existing stronger interactions to give rise to highly ordered cooperative structural motifs that persist in the liquid phase