Dimensional Ladder Research Articles

A New Mn(II) Coordination Polymer Based on Tetranuclear Clusters: Synthesis, Structure and Magnetic Property

A new Mn(II) coordination polymer with the formula {[Mn2(bma)2(2,2′-bpy)(H2O)]}n (1) (H2bma = 2-benzylmalonicacid, 2,2′-bpy = 2,2′-bispyridine), was hydrothermally synthesized and then characterized by single-crystal X-ray diffraction. Complex 1 possesses infinite one dimensional ladder structure based on linear tetranuclear Mn(II) clusters. TGA experiment shows that complex 1 can maintain its framework integrity before 225 °C. In addition, the magnetic data indicate the existence of dominant antiferromagnetic behavior within the tetranuclear cluster.

Hamiltonian approach to the torsional anomalies and its dimensional ladder

Torsion can cause various anomalies in various dimensions, including the $\left(3+1\right)$-dimensional $[(3+1)D]$ Nieh-Yan anomaly, the $\left(2+1\right)$D Hughes-Leigh-Fradkin (HLF) parity anomaly, and the $\left(3+1\right)$D, $\left(1+1\right)$D chiral energy-momentum anomaly. We study these anomalies from the Hamiltonian approach. We derive the $\left(1+1\right)$D chiral energy-momentum anomaly from the single-body Hamiltonian. We then show how other torsional anomalies can be related to the $\left(1+1\right)$D chiral energy-momentum anomaly in a straightforward way. Finally, the Nieh-Yan anomaly and the $\left(3+1\right)$D chiral energy-momentum anomaly are obtained from the parity anomaly and the HLF effective action, respectively. Hence, we have constructed the dimensional ladder for the torsional anomalies from the single-body Hamiltonian picture.

Renormalization group analysis for the quasi-one-dimensional superconductor BaFe2S3

Motivated by the discovery of superconductivity in the two-leg, quasi-one dimensional ladder compound, BaFe$_2$S$_3$ we present a renormalization group study of electrons moving on a two leg, two orbital ladder, subjected to Hubbard repulsion $U$ and Hund's coupling $J$. In our calculations, we adopt tightbinding parameters obtained from ab-initio studies on this material. At incommensurate filling, the long wavelength analysis displays four phases as a function of $0 \leq J/U <1$. We show that a fully gapped superconductor is stabilized at sufficiently large Hund's coupling, the relative phases at the three Fermi points are "+,-,-". By contrast, when the system is tuned to half filling, Umklapp scattering gives rise to Mott insulating phases. We discuss the general implications of our study for the broad class of iron-based superconductors.

Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy

We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S2k−1 in the SO(2k−1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S2k−1 to the one-dimension higher SO(2k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah–Patodi–Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.

A multidimensional ruin problem and an associated notion of duality

ABSTRACTWe consider a dimensional general Cramer–Lundberg type network, with initial capital operating under a risk diversifying treaty; this is described in terms of the appropriate Skorokhod problem (SP) in determined by a reflection matrix R. Ruin of the insurance network is defined as the marginal deficit of each company being positive (and hence surplus of each company being 0) at the same time. The corresponding ruin problem is studied using the associated regulated random walk {(Y(a)n, Z(a)n)} with {Z(a)n} denoting the reflected part, and {Y(a)n} the pushing part. A dual process is introduced through time reversal at sample path level over finite time horizon; the stochastic analogue is again a regulated random walk in starting at 0; let {Wn} denote the reflected part of the dual regulated random walk. It is shown that ruin for the insurance network corresponds to {Wn} hitting the open upper orthant with vertex at R− 1a before hitting the boundary of even at the sample path level. Under natural hypotheses, we show that the ruin probability is for some n ⩾ 1) boundary hitting time of storage process) A notion of dimensional ladder height distribution is defined, and a Pollaczek–Khinchine formula is derived. An expression for the ladder height distribution is given. (One-dimensional ladder height distributions are known for about 50 years.) Some examples are presented.

Conformation driven complexation of two analogous benzimidazole based tripodal ligands with Ag(I) resulting in a trigonal prism and a coordination polymer

Two analogous tripodal ligands, namely, 1,3,5-tris(benzimidazol-1-ylmethyl)-2,4,6-triethylbenzene (1-Et) and 1,3,5-tris(benzimidazol-1-ylmethyl)-2,4,6-trimethoxybenzene (1-OMe) have been used for comple-xation with silver(I) tetrafluoroborate. A trinuclear Ag(I) salt, formulated as [Ag 3 (1-Et) 2 ] 3+ (BF 4 )\(^{\mathrm {\mathbf {-}}}_{\mathrm {\mathbf {3}}}\) ∙7CH 3 CN ∙y H 2 O was formed in the complexation reaction of 1-Et with silver(I) tetrafluoroborate, which consists of a trigonal prismatic cation formed by three bicoordinated Ag(I) coordinated with two 1-Et ligands. In case of the 1-OMe ligand, however, a one dimensional ladder, formulated as [(Ag(1-OMe)OH 2 ) + (BF 4 ) − ∙MeOH] \(_{\mathrm {\mathbf {\infty } }}\) was obtained which is constituted of a tetracoordinated Ag(I) center in a distorted tetrahedral environment. The crystal structures of the ligand hydrates namely 1-Et ∙H 2 O and 1-OMe ∙3.6H 2 O have been discussed along with the structure of methanol solvate-hydrate of 1-Et. The imidazole rings of the Bim groups in 1-Et in the crystal structures of the ligand as well as in its coordination complex with the Ag(I) are pointed inward with respect to the central ring, whereas it is pointed outwards in the crystal structures of 1-OMe as well as its Ag(I) complex. Complexation of silver(I) tetrafluoroborate with two analogous benzimidazole based tripodal ligands namely 1-Et and 1-OMe, led to the formation of a zero dimensional trigonal prism in case of the former, whereas a one dimensional coordination polymeric ladder in case of the latter. The complexation reactions in respective cases are found to depend on the conformation of the ligating center of the two ligands.

PH dependent synthesis of structurally diverse praseodymium(III) coordination polymers based on isomeric ligands

Reactions of two isomeric ligands, 5-(n-pyridyl)tetrazole-2-acetato potassium salt (Kn-pytza, n=2,4) and PrCl3·6H2O under solvothermal conditions, afforded three new complexes, [Pr(2-pytza)(SO4)(H2O)3]·H2O(1), [Pr(4-pytza)3(H2O)2]·2H2O (2) and [Pr4(4-pytza)5(OH)4(H2O)7Cl]Cl2·4H2O (3), whose structures are controlled by not only the different positions of the nitrogen atom of the pyridine ring but also the pH value of the solvent system. These compounds have been characterized by elemental analysis, IR and single crystal X-ray diffraction. The X-ray analysis reveals that compound 1 is a two dimensional layer structure made up of a Pr2O6 binuclear unit and the tridentate bridging SO42− ligand; compound 2 is an unusual one dimensional ladder like chain structure consisting of a Pr2O10 binuclear unit and 4-pytza which acts as a tetradentate ligand via the pyridine-N and the carboxylate group in a μ1,1,3-COO bridging mode while compound 3 is an unprecedented two dimensional network composed of a tetranuclear cubane-shaped Pr4(OH)48+ cluster (SBU) and tridentate 4-pytza via the pyridine-N and the carboxylate group in a μ1,3-COO bridging mode. Various hydrogen bonds exist to assemble the 1D chains or 2D layers into 3D supramolecular network structures. Furthermore, the luminescence properties investigated at room temperature in the solid state show only intraligand emission for 1 and both intraligand and characteristic peaks of Pr3+ for either compound 2 or 3.

On the spectrum of excitations in some strong coupling gauge models

The spectrum of spinless excitations in (3+1)-dimensional ladder QED with additional four-fermion interaction and in (2+1)-dimensional QED is considered.

Explicit construction of anomalies

We demonstrate explicitly the dimensional ladder which links the d + 2 dimensional chiral anomaly, the d + 1 dimensional parity anomaly and the d-dimensional gauge anomaly. We solve the two- and three-dimensional problems of massless fermions in a background instanton gauge potential, discuss the structure of the anomalous effective actions and show the equality of the topological invariants relevant to the different anomalies.

Two- and four-dimensional anomalies with an instanton background

The dimensional ladder which joins the d-dimensional gauge anomaly to the ( d + 2)-dimensional chiral anomaly is illustrated by solving explicitly the four- and two-dimensional problems of chiral fermions in a background instanton gauge potential.