Dominant particle-hole contributions to the phonon dynamics in the spinless one-dimensional Holstein model

In the spinless Holstein model at half-filling the coupling of electrons to phonons is responsible for a phase transition from a metallic state at small coupling to a Peierls distorted insulated state when the electron-phonon coupling exceeds a critical value. For the adiabatic case of small phonon frequencies, the transition is accompanied by a phonon softening at the Brillouin zone boundary whereas a hardening of the phonon mode occurs in the anti-adiabatic case. The phonon dynamics studied in this letter do not only reveal the expected renormalization of the phonon modes but also show remarkable additional contributions due to electronic particle-hole excitations.Comment: 7 pages, 4 figures and 1 table included; v2: discussion of Luttinger liquid parameters adde

The application of star-products to noncommutative geometry and gauge theory

We develop a formalism to realize algebras defined by relations on function spaces. For this porpose we construct the Weyl-ordered star-product and present a method how to calculate star-products with the help of commuting vector fields. Concepts developed in noncommutative differential geometry will be applied to this type of algebras and we construct actions for noncommutative field theories. Derivations of star-products makes it further possible to extend noncommutative gauge theory in the Seiberg-Witten formalism with covariant derivatives. In the commutative limit these theories are becoming gauge theories on curved backgrounds. We study observables of noncommutative gauge theories and extend the concept of so called open Wilson lines to general noncommutative gauge theories.Comment: 115 pages, Ph.D. Thesi

Analytical approach to the quantum-phase transition in the one-dimensional spinless Holstein model

We study the one-dimensional Holstein model of spinless fermions interacting with dispersion-less phonons by using a recently developed projector-based renormalization method (PRM). At half-filling the system shows a metal-insulator transition to a Peierls distorted state at a critical electron-phonon coupling where both phases are described within the same theoretical framework. The transition is accompanied by a phonon softening at the Brillouin zone boundary and a gap in the electronic spectrum. For different filling, the phonon softening appears away from the Brillouin zone boundary and thus reflects a different type of broken symmetry state.Comment: 8 pages, 4 figures included; v2: completely revised and extended; v3: minor changes, final version, to be published in Eur. Phys. J.

A nearly planar arrangement of ions in 4,4′-bipiperidinium tetra­cyanido­platinate(II) monohydrate

The title compound, (C10H22N2)[Pt(CN)4]·H2O, was isolated from solution as a mol­ecular salt. The compound contains discrete 4,4′-bipiperidinium cations and tetra­cyano­platinate(II) anions that are involved in a hydrogen-bonding network with one water mol­ecule of hydration. The structure differs from that of the similar acetonitrile solvate, (C10H22N2)[Pt(CN)4]·2CH3CN, in the orientation of the ions relative to one another. The hydrate reported here contains layers of nearly parallel cations and anions with an angle between their mean planes of only 4.35 (11)°, while in the acetonitrile solvate the cations and anions are nearly perpendicular to one another (86.1° between mean planes). The crystal showed partial inversion twinning

Coexistence of superconductivity and charge-density waves in a two-dimensional Holstein model at half-filling

In one dimension the coupling of electrons to phonons leads to a transition from a metallic to a Peierls distorted insulated state if the coupling exceeds a critical value. On the other hand, in two dimensions the electron-phonon interaction may also lead to the formation of Cooper pairs. This competition of superconductivity and charge order (in conjunction with a lattice distortion) is studied in this letter by means of the projector-based renormalization method (PRM). Increasing the electron-phonon interaction, we find a crossover behavior between a purely superconducting state and a charge-density wave where a well-defined parameter range of coexistence of superconductivity and lattice distortion exists.Comment: 11 pages, 2 figure

Participatory Interactive Campaign Developed to Raise Awareness About Poverty in Our Community

Our goal with this research is to use our creative talents to spark change in the way society views and reacts to those living in poverty within our community. A recent study done by the Bush School of Government and Public Services found “slightly more than 28 percent of the population lives at or below the federal poverty line. This includes 26.3 percent of those less than the age of 18, 10.6 percent of those more than age 65, and 15.9 percent of families in Brazos County.” This is an issue that is very close to home, yet so easily overlooked. We began by researching organizations in the area that are currently working to resolve this issue. Our plan is to share what we have learned with the public through interactive posters aimed to open eyes and encourage others to get involved. We also plan on creating a complimentary print and social media campaign to have our message reach a broader audience, especially students at Texas A&M University. Through both the interactive posters and the social media campaign we hope to share the genuine truth about poverty in a way that will leave an impact on our community. Our end goal is to inform people on the reality of poverty in our community, encourage them to take steps to get involved and help solve this issue, and see those living in poverty as people who are not so different than ourselves: people with purpose and dignity

A beam search approach to solve the convex irregular bin packing problem with guillotine cuts

This paper presents a two dimensional convex irregular bin packing problem with guillotine cuts. The problem combines the challenges of tackling the complexity of packing irregular pieces, guaranteeing guillotine cuts that are not always orthogonal to the edges of the bin, and allocating pieces to bins that are not necessarily of the same size. This problem is known as a two-dimensional multi bin size bin packing problem with convex irregular pieces and guillotine cuts. Since pieces are separated by means of guillotine cuts, our study is restricted to convex pieces.A beam search algorithm is described, which is successfully applied to both the multi and single bin size instances. The algorithm is competitive with the results reported in the literature for the single bin size problem and provides the first results for the multi bin size problem

catena-Poly[[[diaqua­(nitrato-κ2 O,O′)(2,2′:6′,2′′-terpyridine-κ3 N,N′,N′′)neodymium(III)]-μ-cyanido-κ2 N:C-[dicyanidoplatinum(II)]-μ-cyanido-κ2 C:N] acetonitrile solvate 2,2′:6′,2′′-terpyridine hemisolvate]

The title compound, {[NdPt(CN)4(NO3)(C15H11N3)(H2O)2]·CH3CN·0.5C15H11N3}n, was isolated from solution as a one-dimensional coordination polymer. The Nd3+ site in the structure has a ninefold coordination with a distorted tricapped trigonal-prismatic geometry, while the PtII ion is coordinated by four cyanide groups in an almost regular square-planar geometry. Cis-bridging by the tetracyanidoplatinate anions links the Nd3+ cations, forming the one-dimensional chains. Additionally, each Nd3+ contains coordin­ation by two water mol­ecules, one tridentate 2,2′:6′,2′′-terpyridine mol­ecule, and one bidentate nitrate anion. 2,2′:6′,2′′-Terpyridine and acetonitrile solvent mol­ecules are incorporated between the chains, the former form π-stacking inter­actions (average inter­planar distance 3.33 Å) with terpyridine mol­ecules located in the chains. Relatively long Pt⋯Pt inter­actions [3.847 (1) Å] are observed in the structure. O—H⋯N and O—H⋯O hydrogen bonding interactions between the consituents consolidates the crystal packing