Quantum lump dynamics on the two-sphere

It is well known that the low-energy classical dynamics of solitons of Bogomol'nyi type is well approximated by geodesic motion in M_n, the moduli space of static n-solitons. There is an obvious quantization of this dynamics wherein the wavefunction evolves according to the Hamiltonian H_0 equal to (half) the Laplacian on M_n. Born-Oppenheimer reduction of analogous mechanical systems suggests, however, that this simple Hamiltonian should receive corrections including k, the scalar curvature of M_n, and C, the n-soliton Casimir energy, which are usually difficult to compute, and whose effect on the energy spectrum is unknown. This paper analyzes the spectra of H_0 and two corrections to it suggested by work of Moss and Shiiki, namely H_1=H_0+k/4 and H_2=H_1+C, in the simple but nontrivial case of a single CP^1 lump moving on the two-sphere. Here M_1=TSO(3), a noncompact kaehler 6-manifold invariant under an SO(3)xSO(3) action, whose geometry is well understood. The symmetry gives rise to two conserved angular momenta, spin and isospin. A hidden isometry of M_1 is found which implies that all three energy spectra are symmetric under spin-isospin interchange. The Casimir energy is found exactly on the zero section of TSO(3), and approximated numerically on the rest of M_1. The lowest 19 eigenvalues of H_i are found for i=0,1,2, and their spin-isospin and parity compared. The curvature corrections in H_1 lead to a qualitatively unchanged low-level spectrum while the Casimir energy in H_2 leads to significant changes. The scaling behaviour of the spectra under changes in the radii of the domain and target spheres is analyzed, and it is found that the disparity between the spectra of H_1 and H_2 is reduced when the target sphere is made smaller.Comment: 35 pages, 3 figure

Sharp increase of the effective mass near the critical density in a metallic 2D electron system

We find that at intermediate temperatures, the metallic temperature dependence of the conductivity \sigma(T) of 2D electrons in silicon is described well by a recent interaction-based theory of Zala et al. (Phys. Rev. B 64, 214204 (2001)). The tendency of the slope d\sigma/dT to diverge near the critical electron density is in agreement with the previously suggested ferromagnetic instability in this electron system. Unexpectedly, it is found to originate from the sharp enhancement of the effective mass, while the effective Lande g factor remains nearly constant and close to its value in bulk silicon

A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity

We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document may be used as a concise, yet informal, discursive and peripatetic conceptual guide-cum-terminological glossary to the voluminous technical research literature on the subject. In a bonus section at the end, we dwell on the significance of introducing new conceptual terminology in future QG research by means of `poetic language'Comment: 16 pages, preliminary versio

Electronic structure of a Mn12 molecular magnet: Theory and experiment

金沢大学大学院自然科学研究科物質情報解析We used site-selective and element-specific resonant inelastic x-ray scattering (RIXS) to study the electronic structure and the electron interaction effects in the molecular magnet [Mn12 O12 (C H3 COO)16 (H2 O)4] 2C H3 COOH 4 H2 O, and compared the experimental data with the results of local spin density approximation +U electron structure calculations which include the on-site Coulomb interactions. We found a good agreement between theory and experiment for the Coulomb repulsion parameter U=4 eV. In particular, the p-d band separation of 1.8 eV has been found from the RIXS spectra, which is in accordance with the calculations. Similarly, the positions of the peaks in the XPS spectra agree with the calculated densities of p and d states. Using the results of the electronic structure calculations, we determined the intramolecular exchange parameters, and used them for diagonalization of the Mn12 spin Hamiltonian. The calculated exchanges gave the correct ground state with the total spin S=10. © 2007 The American Physical Society

Synthesis of a small heat shock protein is part of the developmental program of late seed maturation.

Small heat-shock proteins (sHSPs) accumulate in plants in response to high-temperature stress. Specific sHSPs, the cytosolic class I and class II proteins, are also expressed in the absence of stress in maturing seeds of several species, and a role for these proteins in desiccation tolerance, dormancy, or germination has been hypothesized. We demonstrate that class I sHSPs are expressed during Arabidopsis seed development in a pattern similar to that previously observed in other species: they are first detected during mid-maturation, are most abundant in dry seeds, and decline rapidly during germination. Although the class I sHSP family in Arabidopsis appears to consist of four genes, expression of a single gene, Athsp 17.4, accounts for the majority of sHSPs in maturing seeds. sHSP levels were also examined in seeds of several Arabidopsis mutants with reduced sensitivity to abscisic acid inhibition, including aba1, abi1, and abi2, abi3-1, abi3-6, abi4, and abi5-1. The abi3-1 mutant has 10-fold reduced levels of sHSPs; sHSPs are undetectable in the abi3-6 mutant. All other mutants were indistinguishable from wild type. These results suggest that sHSP expression in seeds is regulated by the ABI3 response pathway and wild-type levels of sHSPs are not sufficient for seed dormancy and not necessary for desiccation tolerance. However, roles in either process cannot be ruled out. In total the data indicate that the expression of sHSPs in seeds is part of the normal developmental program of late seed maturation and the presence of sHSPs has adaptive significance for plant reproduction

Testing the magnetism of polymerized fullerene

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Co and Al co-doping for ferromagnetism in ZnO:Co diluted magnetic semiconductors

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