Combined effect of frustration and dimerization in ferrimagnetic chains and square lattice

Within the zero-temperature linear spin-wave theory we have investigated the effect of frustration and dimerization of a Heisenberg system with alternating spins $s_{1}$ and $s_{2}$ on one- and two-dimensional lattices. The combined effect most visibly appears in the elementary excitation spectra. In contrast to the ground state energy that decreases with dimerization and increases with frustration, the excitation energies are shown to be suppressed in energy by both dimerization and frustration. The threshold value of frustration that signals a transition from a classical ferrimagnetic state to a spiral state, decreases with dimerization, showing that dimerization further helps in the phase transition. The correlation length and sublattice magnetization decrease with both dimerization and frustration indicating the destruction of the long-range classical ferrimagnetic. The linear spin wave theory shows that in the case of a square lattice, dimerization initially opposes the frustration-led transition to a spiral magnetic state, but then higher magnitudes of lattice deformation facilitate the transition. It also shows that the transition to spiral state is inhibited in a square lattice beyond a certain value of dimerization.Comment: 8 pages, latex, 12 postscript figure

Spin-dependent electron transport through a ferromagnetic domain wall

We present a theoretical study of spin-dependent transport through a ferromagnetic domain wall. With an increase of the number of components of the exchange coupling, we have observed that the variance of the conductance becomes half. As the strength of the domain wall magnetization is increased, negative magnetoresistance is also observed.Comment: accepted in Proceedings of Localisation 2002 Conference, Tokyo, Japan (to be published as supplement of J. Phys. Soc. Japan

How to construct a coordinate representation of a Hamiltonian operator on a torus

The dynamical system of a point particle constrained on a torus is quantized \`a la Dirac with two kinds of coordinate systems respectively; the Cartesian and toric coordinate systems. In the Cartesian coordinate system, it is difficult to express momentum operators in coordinate representation owing to the complication in structure of the commutation relations between canonical variables. In the toric coordinate system, the commutation relations have a simple form and their solutions in coordinate representation are easily obtained with, furthermore, two quantum Hamiltonians turning up. A problem comes out when the coordinate system is transformed, after quantization, from the Cartesian to the toric coordinate system.Comment: 17 pages, LaTeX, 1 Figure included as a compressed uuencoded postscript fil

Ground State Property of an Alternating Spin Ladder Involving Two Kinds of Inter-Chain Interactions

The ground state property of the alternating spin ladder is studied in the case that the system involves an antiferromagnetic intra-chain interaction as well as two kinds of inter-chain interactions; one is between spins of the same magnitude and the other is between spins with different magnitudes. The calculation has been carried out by the exact diagonalization method. As a consequence of the competition among interactions, the system is revealed to show an interesting variety of phases in the ground state property. Its phase diagram is exhibited in the parameter space of the system. We find that, however small the total amount of the inter-chain interactions is, the ferrimagnetic ground state becomes unstable in a certain region. In this case, which of the ferrimagnetic and the singlet ground state to appear is determined only by the ratio between the inter-chain interactions regardless of their total amount. The nature of two phases appearing in the singlet region of the phase diagram and the type of the phase transition between them are also discussed. The results are ensured by comparing with those of obtained in other models which are contained in our model as special limiting cases.Comment: 12 pages, 9 PostScript figure

Stress concentration in the vicinity of a hole defect under conditions of Hertzian contact

Two dimensional photoelastic stress analyses were conducted for epoxy resin models containing a hole defect under the conditions of Hertzian contact. Stress concentrations around the defect were determined as a function of several parameters. The effect of tangential traction on the stress concentration was also determined. Sharp stress concentrations occur in the vicinity of both the left and the right side of the hole. The stress concentration becomes more distinct the larger the hole diameter and the smaller distance between the hole and the contact surface. The stress concentration is greatest when the disk imposing a normal load is located at the contact surface directly over the hole. The magnitude and the location of stress concentration varies with the distance between the Hertzian contact area and the hole. The area involved in a process of rolling contact fatigue is confined to a shallow region at both sides of the hole. It was found that the effect of tangential traction is comparatively small on the stress concentration around the hole

Diversity, Stability, Recursivity, and Rule Generation in Biological System: Intra-inter Dynamics Approach

Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for the differentiation provides the diversity and stability of cell society. Relevance of the theory to cell biology is discussed.Comment: 19 pages, Int.J. Mod. Phes. B (in press

Chiral Lagrangian and spectral sum rules for dense two-color QCD

We analytically study two-color QCD with an even number of flavors at high baryon density. This theory is free from the fermion sign problem. Chiral symmetry is broken spontaneously by the diquark condensate. Based on the symmetry breaking pattern we construct the low-energy effective Lagrangian for the Nambu-Goldstone bosons. We identify a new epsilon-regime at high baryon density in which the quark mass dependence of the partition function can be determined exactly. We also derive Leutwyler-Smilga-type spectral sum rules for the complex eigenvalues of the Dirac operator in terms of the fermion gap. Our results can in principle be tested in lattice QCD simulations.Comment: 24 pages, 1 table, no figur