Differential geometry of the Lie algebra of the quantum plane

We present a differential calculus on the extension of the quantum plane obtained by considering that the (bosonic) generator x is invertible and by working with polynomials in ln x instead of polynomials in x. We construct the quantum Lie algebra associated with this extension and obtain its Hopf algebra structure and its dual Hopf algebra.     

Free field realization of the level-2 elliptic algebra Ux,p ([^(\mathfraks\mathfrakl)]2 )*)U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}}_2 )*)

We give a level-2 representation of the elliptic algebra in terms of one free boson and one free fermion. We show that -modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the coset . Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Search for minimal quantum group SUq(2) gauge field theory

Different possibilities for the introduction of quantum group gauge fields are discussed. The case of the quantum group SU_q(2) is considered in more detail. We seek for a construction of the quantum group gauge fields which possesses a minimal set of usual c-number fields. It turns out that in this construction the components of the quantum group gauge field take values in the quantum Euclidean space.     

A subalgebra of loop algebra A2^～ and its applications

A subalgebra of loop algebra A2^～ and its expanding loop algebra G^- are constructed. It follows that both resulting integrable Hamiltonian hierarchies are obtained. As a reduction case of the first hierarchy, a generalized nonlinear coupled Schroedinger equation, the standard heat-conduction and a formalism of the well known Ablowitz, Kaup, Newell and Segur hierarchy are given, respectively. As a reduction case of the second hierarchy, the nonlinear Schroedinger and modified Korteweg de Vries hierarchy and a new integrable system are presented. Especially, a coupled generalized Burgers equation is generated.     

High-field magnetic phases of a two-leg spin ladder: Cu2(C5H12N2)2Cl4

CHCupCl is a two-leg spin-ladder where the Cu⁺⁺ ions are coupled by superexchange. Its magnetic properties change dramatically as a function of a magnetic field. Below the critical field H_c1, there is a singlet ground state separated from the triplet excited state by an energy gap. Between H_c1 and H_c2, several magnetic phases have been observed. Above 1 K, dynamical studies reveal a disordered quantum critical phase. At lower temperatures, a 3-D ordered phase has been observed in specific heat and NMR studies. New NMR results on the 3D-ordered and quantum critical phases are presented in this short report.     

Magnetic hysteresis loops in molecular-based magnetic materials AFeFe(C2O4)3

A molecular-based magnetic material AFe^IIFe^III(C₂O₄)₃ (A = organic cation) with a honeycomb structure is studied. The molecular-based magnet system consists of mixed spin-2 and spin- 5/2 honeycomb lattices with ferrimagnetic interlayer coupling. The magnetization, hysteresis loops and initial susceptibility have been calculated using a numerical method which includes both the longitudinal and transverse fields. We investigated the magnetic reversal of the system and found the existence of triple hysteresis loop patterns, affected by the anisotropy, longitudinal and transverse fields, and interlayer and intralayer exchange.     

Full relativistic calculations of the quadrupole and electric field gradients for C2, N2, and O2

In the present work we calculate the energies,quadrupole moments,and electric field gradients(EFGs) of molecules C2,N2,and O2 based on the DIRRCI method with basis aug-cc-pVTZ-DK.We prove that the quadratic force constant k2 is the product of charge and EFG at its equilibrium nuclear distance.The dipole charge distributions for these symmetrical molecules are all in equilibrium,however,the quadrupole charge distributions are far from equilibrium;among these,there is the most remarkable deviation from equilibrium for N2,for its many charges concentrate on two sides of the molecule,which is in agreement with the well-known characteristic of the nitrogen molecule.The relativistic effect is remarkable even for the same period.     

A new (in)finite-dimensional algebra for quantum integrable models

A new (in)finite-dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite-dimensional representations are constructed and mutually commuting quantities—which ensure the integrability of the system—are written in terms of the fundamental generators of the new algebra. Relation with the deformed Dolan–Grady integrable structure recently discovered by one of the authors and Terwilliger's tridiagonal algebras is described. Remarkably, this (in)finite-dimensional algebra is a “q-deformed” analogue of the original Onsager's algebra arising in the planar Ising model. Consequently, it provides a new and alternative algebraic framework for studying massive, as well as conformal, quantum integrable models.     

Conformal quantum mechanics as the CFT1 dual to AdS2

A (0+1)-dimensional candidate theory for the CFT₁ dual to AdS₂ is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose “non-primary character” conspires with the “non-invariance of the vacuum” to give precisely the correlation functions in a conformally invariant theory.     

Topological representations of quantum groups and conformal field theory

These are three introductory lectures on the relation between representations of affine Kac-Moody algebras, homology of configuration spaces with local coefficient systems, and quantum groups. The first lecture contains background on highest weight representations of affine Kac-Moody algebras. In the second lecture, conformal blocks, the Friedan-Shenker connection and the Knizhnik-Zamolodchikov (KZ) equation are reviewed. In the third lecture, the case of sl_z is studied in more detail. Integral representations of solutions of the KZ equation are derived, and recent results, obtained in collaboration with C. Wieczerkowski, on the relation between integration cycles and representations of U_q (sl₂) are explained.     

Chlorine K X-ray absorption-edge structures of CIS-[Pt(NH3)2Cl2], trans-[Pt(NH3)2Cl2], trans-[Pd(NH3)2Cl2] and (NH4)2PdCl4

The K absorption-edge spectra of the ligand chlorine ion in square-planar complex compounds cis- and trans-[Pt(NH₃)₂Cl₂], trans-[Pd(NH₃)₂Cl₂], and (NH₄)₂PdCl₄ are reported and discussed in connection with the chlorine K absorption spectra of K₂PtCl₄ and K₂PdCl₄, reported previously. The observed chemical shift of a white line at the absorption threshold is interpreted in terms of the difference of the ligand-field splitting of electronic states for metal ions. The white line is attributed to the electronic transition from the Cl^? ls level to the lowest unoccupied antibonding molecular orbital (MO), which is specified by a $\text{MO}\text{b}{}_{\mathrm{1g}}\text{(σ}{}^1\text{)}$ in the square-planar complex with D_4h symmetry. The other absorption structures are regarded as continuum “shape resonances” of the outgoing electron trapped by the cage of the surrounding atoms. The effect of geometrical isomerism is found in the chlorine K absorption spectra of cis- and trans-[Pt(NH₃)₂Cl₂].     

Effective activation energy Ue(T,J,H) in textured Bi1.84Pb0.4Sr2Ca2Cu3Oy silver-clamped thick films

We have measured the resistivity of textured Bi_1.84Pb_0.4Sr₂Ca₂Cu₃O_y silver-clamped thick films as a function of temperature, current density ranging from 10 to 1×10³ A/cm² and magnetic field up to 0.3 T. We find that the effective activation energy U_e follows U_e(T,J,H)=U₀(1−T/T_p)^mln(J_c0/J)H⁻ with m=1.75 for Hab-plane and 2.5 for Hc-axis and =0.76 for Hab and 0.97 for Hc, for the current density regime above 100 A/cm², where T_p is a function of applied magnetic field and current density. This result suggests the effective activation energy U_e be correlated with the temperature, current density and magnetic field. The possible dissipative mechanisms responsible for the temperature, current density and magnetic field dependence of the effective activation energy are discussed.     

Structure and magnetic properties of a new single-molecule magnet [Mn11Fe1O12 (CH3COO)16(H2O)4].2CH3COOH.4H2O

A new single-molecule magnet [Mn₁₁Fe₁O₁₂ (CH₃COO)₁₆(H₂O)₄]?2CH₃COOH?4H₂O (Mn₁₁Fe₁) has been synthesized.The structure has been studied by the single crystal x-ray diffraction. The difference of Jahn--Teller distortion between Fe³⁺ and Mn³⁺ ion reveals that Fe³⁺ ion substitutes for Mn³⁺ ion on the Mn(3) sites in the Mn₁₂ skeleton. The temperature dependence of the magnetization gives a blocking temperature T_B=1.9K for Mn₁₁Fe₁. Based on the magnetization process analysis of the crystal at T=2K, we suggest that Mn₁₁Fe₁ has the ground state with a total spin S= 11/2.     

Dissociations of O2 molecules on ultrathin Pb(111) films: first-principles plane wave calculations

Using first-principles calculations, we systematically study the dissociations of O₂ molecules on different ultrathin Pb(111) films. According to our previous work revealing the molecular adsorption precursor states for O₂, we further explore why there are two nearly degenerate adsorption states on Pb(111) ultrathin films, but no precursor adsorption states existing at all on Mg(0001) and Al(111) surfaces. The reason is concluded to be the different surface electronic structures. For the O₂ dissociation, we consider both the reaction channels from gas-like and molecularly adsorbed O₂ molecules. We find that the energy barrier for O₂ dissociation from the molecular adsorption precursor states is always smaller than that from O₂ gas. The most energetically favorable dissociation process is found to be the same on different Pb(111) films, and the energy barriers are found to be influenced by the quantum size effects of Pb(111) films.     

On the nature of the SO4/Ag(111) and SO4/Au(111) surface bonding

The nature of sulfate-Ag(111) and sulfate-Au(111) surface bonding has been investigated at the SCF + MP2 level of theory. Convergence of binding energy with cluster size is investigated and, unlike neutral adsorbates, large clusters are required in order to obtain reliable binding energies. In the most stable adsorption mode, sulfate binds to the surface via three oxygen atoms (C_3v symmetry) with a binding energy of 159.3 kcal/mol on Ag(111) and 143.9 kcal/mol on Au(111). The geometry of adsorbed sulfate was optimized at the SCF level. While the bond length between sulfur and the oxygens coordinated to the surface increases, the sulfur-uncoordinated oxygen bond length decreases. This weakening and strengthening of the bonds, respectively, is consistent with bond order conservation in adsorbates on metal surfaces. Although a charge transfer of 0.4 electrons towards the metal is observed, the adsorbate remains very much sulfate-like. The molecular orbital analysis indicates that there is also some charge back-donation towards unoccupied orbitals of sulfate. This results in an increased electron density around sulfur as revealed in the electron density difference maps. Analysis of the Laplacian of the charge density of free sulfate provides a suitable framework to understand the nature of the different charge transfer processes and allows us to establish some similarities with the CO- and SO₂-metal bondings.     

EPR evidence of local lattice mode in K3H(SO4)2 and Rb3H(SO4)2 fast-proton conductors

The observation of an anomalous temperature dependence of Mn²⁺ EPR spectra linewidth and nonaxial crystal-field parameter in K₃H(SO₄)₂ and Rb₃H(SO₄)₂ allows one to suggest the presence of “local mode” predicted by Yamada (Ferroelectrics 170 (1995) 23). The activation energy for this kind of excitation was found and equals 11.3 (0.5) and 7.4 (0.3) meV for Mn²⁺ doped K₃H(SO₄)₂ and Rb₃H(SO₄)₂, respectively.