High energy behaviour of the scattering amplitude in the presence of confined channels

The two-channel potential scattering problem in three space-dimensions is considered in the case when one channel is permanently confined. Two examples of confining potentials are considered: the harmonic oscillator and the infinite well. The two cases give radically different results: for the infinite well there is no high-energy limit; in the case of the harmonic oscillator the amplitude has properties similar to that of dual absorptive models.     

Reaction-Diffusion Processes, Critical Dynamics, and Quantum Chains

The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schrödinger equation in which the wave function is the probability distribution and the Hamiltonian is that of a quantum chain with nearest neighbor interactions. Since many one-dimensional quantum chains are integrable, this opens a new field of applications. At the same time physical intuition and probabilistic methods bring new insight into the understanding of the properties of quantum chains. A simple example is the asymmetric diffusion of several species of particles which leads naturally to Hecke algebras and q-deformed quantum groups. Many other examples are given. Several relevant technical aspects like critical exponents, correlation functions, and finite-size scaling are also discussed in detail.     

Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring. II. The Charged System and the Two-Component Burgers Equations

We further study the stochastic model discussed in ref. 2 in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. We extend the analysis of this model to the case when the densities of the charged particles are not the same. The mean-field equations describing the model are coupled nonlinear differential equations that we call the two-component Burgers equations. We find roundabout weak solutions of these equations. These solutions are used to describe the properties of the stationary states of the stochastic model. The values of the currents and of various two-point correlation functions obtained from Monte-Carlo simulations are compared with the mean-field results. Like in the case of equal densities, one finds a pure phase, a mixed phase and a disordered phase.     

Finite-size effects in the three-state quantum asymmetric clock model

The one-dimensional quantum hamiltonian of the asymmetric three-state clock model is studied using finite-size scaling. Various boundary conditions are considered on chains containing up to eight sites. We calculate the boundary of the commensurate phase and the mass gap index. The model shows an interesting finite-size dependence in connexion with the presence of the incommensurate phase indicating that for the infinite system there is no Lifshitz point.     

Non-universality in Z3 symmetric spin systems

The critical exponent ν of the mass gap is calculated for a one-dimensional, Z₃ symmetric quantum chain. Using the strong coupling expansion and finite-size scaling it is shown that ν varies continuously from $\text{5}\text{6}\text{to}\text{1}$.     

Solvent dependence of the structure and magnetic ordering of ferrimagnetic manganese(III) meso-tetraphenylporphyrin tetracyanoethenide, [MnTPP]+[TCNE]*-

Tetraphenylporphinatomanganate(III) tetracyanoethenide, [MnTPP][TCNE], is the prototype of a growing family of linear chain (1-D) coordination polymers that magnetically order as ferrimagnets. [MnTPP][TCNE].xS [S = PhMe (x = 2), 1,2-C(6)H(4)Me(2) (x = 1), 1,2-C(6)H(4)Cl(2) (x = 3), 1,2,4-C(6)H(3)Cl(3) (x = 2), and 1,3-C(6)H(4)Cl(2) (x = 2)] have been prepared and structurally and magnetically characterized. All form 1-D chain structures with intrachain Mn.Mn separations ranging from 9.202 to 10.218 A. The 173 K crystal structure of [MnTPP][TCNE].2PhMe has been rerefined, revealing that the [TCNE](*)(-) is 2-fold-disordered and coordinated to Mn(III) by a pair of trans cyano nitrogen atoms to form parallel one-dimensional chains. The two orientations of [TCNE](*)(-) are related by a 180 degrees rotation about the diagonal axis joining the trans nitrogen atoms bound to Mn(III). The major form has an occupancy of 83.3(4)% with a Mn-N(TCNE) distance of 2.328(3) A and a MnNC angle of 146.8(8) degrees. The minor form, with 16.7(4)% occupancy, has a Mn-N(TCNE) distance of 2.176(15) A and a MnNC angle of 152.3(39) degrees. Lattice packing and molecular bonding imply static as opposed to dynamic disorder. The magnetic properties depend on the type and quantity of the solvent present in the structure. Desolvation via heating in n-octane (127 degrees C), n-dodecane (216 degrees C), and/or vacuum thermolysis (175 degrees C) leads to numerous different desolvated materials with differing magnetic properties. At higher temperatures the magnetic susceptibility can be fit by the Curie-Weiss expression, chi varies with (T - theta)(-1), with theta = 44, 52, 72, 55, and 77 K for the toluene, 1,2-xylene, 1,2-dichlorobenzene, 1,3-dichlorobenzene, and 1,2,4-trichlorobenzene solvates, respectively. The T(c)'s were taken as the maximum in 10 Hz chi'(T) and are 7.8, 9.2, 11.3, 10.8, and 8.2 K for the PhMe, 1,2-xylene, 1,2-dichlorobenzene, 1,3-dichlorobenzene, and 1,2,4-trichlorobenzene solvates, respectively. Upon desolvation the T(c)'s increase for the PhMe, 1,2-xylene, 1,2,4-trichlorobenzene solvates and decrease for the 1,2- and 1,3-dichlorobenezene solvates. The compounds show one-dimensional ferrimagnetic exchange behavior at high temperatures with intrachain exchange of J/k(b) = -63, -99, -234, -100, and -200 K for toluene, 1,2-xylene, 1,2-dichlorobenzene, 1,3-dichlorobenzene, and 1,2,4-trichlorobenzene solvates, respectively, as determined from fits to the Seiden expression, which models isolated 1-D interactions among alternating S = 2 classical and S = (1)/(2) quantum spins. For variation in the temperature at which the peak occurs per decade of frequency, phi, (DeltaT(f)/T(f))/Delta(log omega) is 0.167, 0.168, 0.066, 0.171, and 0.024 for toluene, 1,2-xylene, 1,2-dichlorobenzene, 1,3-dichlorobenzene, and 1,2,4-trichlorobenzene, respectively, typical of spin glass behavior. Since [TCNE](*)(-) is only disordered for the PhMe solvate and all five solvates exhibit spin glass behavior, the spin glass behavior cannot be attributed to this disorder.     

Preparation and characterization of MgB2 superconductor

The MgB₂ superconductor, synthesized using solid-state and liquid-phase sintering methods, have been characterized for various properties. The upper critical field, irreversibility line and critical current density have been determined using magnetization data. The current-voltage characteristics recorded under an applied magnetic field revealed the existence of vortex glass transition. The surface analysis using X-ray photoelectron spectroscopy shows that MgB₂ is sensitive to atmospheric degradation.     

A remarkable connection between the representations of the Lie superalgebras osp(1, 2n) and the Lie algebras o(2n+1)

We show that there is a one-to-one correspondence between the graded representations of osp(1, 2n) and the non-spinorial representations of o(2n+1). The Clebsch-Gordan series for osp(1, 2n) reduce to the corresponding series for o(2n+1) and the properly defined Casimir operators of order at least up to four have the same eigenvalues.Supported by the Deutsche Forschungsgemeinschaft     

Spectra of quantum chains without the Yang-Baxter equation

We study one-dimensional reaction-diffusion models described by master equations and their associated two-state quantum hamiltonians. By choosing appropriate rates, the equations of motion decouple into certain subsets. We solve the first subset which has a close relation to the problem of lattice electrons in an electric field. In this way we obtain L(L − 1) + 1 energy levels of a quantum chain with L sites. The corresponding hamiltonian depends on seven parameters and does not look integrable using conventional methods. As an application, we compute the dynamical critical exponent of a new type of kinetic Ising model.