Modern Physics Letters B

Theoretical analysis and experimental results are presented to demonstrate the universal characteristics of parity-breaking bifurcations for pattern-forming systems in a circular domain. Ordered patterns of concentric rings of cells which form in a premixed flame on a circular burner at low pressure are used to demonstrate these ideas. Cells belonging to stationary rings are symmetric, while those of rotating rings are not. The important characteristics of the experimental results are reproduced in a theoretical model which can be numerically integrated in polar coordinates. Normal form equations for the Fourier–Bessel coefficients of this model lead to parity breaking.

We study Heisenberg spins on an infinite plane. Following an approach developed by Affleck, we find that the Heisenberg Hamiltonian is equivalent in the continuum limit to the nonlinear σ model. And we show that the auxiliary fields, which appear because of the conservation of the number of degrees of freedom, are related to the covariant derivatives of the order parameter. These auxiliary fields have to be taken into account in order to recover the expected values for the coupling constant and magnon velocity in two-dimensions.

We use the Lanczos method to calculate the variance σ²(E, ϕ) of the number of energy levels in an energy window of width E below the Fermi energy for noninteracting disordered electrons on a thin three-dimensional ring threaded by an Aharonov–Bohm flux ϕ. We confirm numerically that for small E the flux-dependent part of σ²(E, ϕ) is well described by the Altshuler–Shklovskii-diagram involving two Cooperons. However, in the absence of electron–electron interactions this result cannot be extrapolated to energies E where the energy-dependence of the average density of states becomes significant. We discuss consequences for persistent currents and argue that for the calculation of the difference between the canonical- and grand canonical current it is crucial to take the electron–electron interaction into account.

The superconducting transition temperature T_c has been studied under quasihydrostatic pressure (QHP) up to 16 GPa for the HgBa₂Ca_n-1Cu_nO_2n+δ [Hg-12{n−1}n] samples with n=4 and 5. The applied pressure shifts T_c toward higher temperature in both cases. But the T_c-enhancement under pressure for these two compounds is significantly smaller than the previously reported universal T_c-enhancement in Hg-1201, Hg-1212 and Hg-1223.

Electronic structure of K₃C₆₀ in the ordered bidirectional and quadridirectional structure (space group ) and in the disordered bidirectional structure (space group ) is examined. As compared with the unidirectional structure (space group ), the lower-energy peak of the conduction band in the structures is split into two, the higher-energy peak is strongly depressed, and the value of DOS at the Fermi level (N(E_F)) is enhanced. Orientational disorder almost completely washs out the structure in the DOS of the conduction band; however, the value of N(E_F) differs slightly from that in the unidirectional structure.

A photopolymerization of C₆₀ molecules occurs in the irradiation of oxygen-free C₆₀ film with visible or ultraviolet light. Results from mass spectroscopy indicate that C₁₁₈ is the principal dimer among the dimers around C₁₂₀. Three most possible isomers of C₁₁₈ are presented and studied. Geometries are optimized with tight-binding method and two techniques. Vibrational modes are also obtained. Their stretching frequencies are from 106 cm⁻¹ to 133 cm⁻¹, which are consistent with the experimental value 116 cm⁻¹.