Numerical study on Anderson transitions in three-dimensional disordered systems in random magnetic fields

The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for systems both with and without an additional random scalar potential. We find the critical exponent $\nu$ for the localization length to be $1.45 \pm 0.09$ with a strong random scalar potential. Without it, the exponent is smaller but increases with the system sizes and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes due to symmetry. Fractal dimensionality of the wave function at the critical point is also estimated by the equation-of-motion method.Comment: 9 pages, 3 figures, to appear in Annalen der Physi

Random Network Models and Quantum Phase Transitions in Two Dimensions

An overview of the random network model invented by Chalker and Coddington, and its generalizations, is provided. After a short introduction into the physics of the Integer Quantum Hall Effect, which historically has been the motivation for introducing the network model, the percolation model for electrons in spatial dimension 2 in a strong perpendicular magnetic field and a spatially correlated random potential is described. Based on this, the network model is established, using the concepts of percolating probability amplitude and tunneling. Its localization properties and its behavior at the critical point are discussed including a short survey on the statistics of energy levels and wave function amplitudes. Magneto-transport is reviewed with emphasis on some new results on conductance distributions. Generalizations are performed by establishing equivalent Hamiltonians. In particular, the significance of mappings to the Dirac model and the two dimensional Ising model are discussed. A description of renormalization group treatments is given. The classification of two dimensional random systems according to their symmetries is outlined. This provides access to the complete set of quantum phase transitions like the thermal Hall transition and the spin quantum Hall transition in two dimension. The supersymmetric effective field theory for the critical properties of network models is formulated. The network model is extended to higher dimensions including remarks on the chiral metal phase at the surface of a multi-layer quantum Hall system.Comment: 176 pages, final version, references correcte

Critical exponent for the quantum spin Hall transition in Z_2 network model

We have estimated the critical exponent describing the divergence of the localization length at the metal-quantum spin Hall insulator transition. The critical exponent for the metal-ordinary insulator transition in quantum spin Hall systems is known to be consistent with that of topologically trivial symplectic systems. However, the precise estimation of the critical exponent for the metal-quantum spin Hall insulator transition proved to be problematic because of the existence, in this case, of edge states in the localized phase. We have overcome this difficulty by analyzing the second smallest positive Lyapunov exponent instead of the smallest positive Lyapunov exponent. We find a value for the critical exponent $\nu=2.73 \pm 0.02$ that is consistent with that for topologically trivial symplectic systems.Comment: 5 pages, 4 figures, submitted to the proceedings of Localisation 201

The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant

We show that the perturbative ${\frak g}$ invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra ${\frak g}$, i.e, the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate the quantum invariants of integral homology 3-spheres [13,14,15], this implies that the LMO invariant dominates the quantum invariants of integral homology 3-spheres.Comment: 30 page

Estradiol, Progesterone, and Transforming Growth Factor α Regulate Insulin-Like Growth Factor Binding Protein-3 (IGFBP3) Expression in Mouse Endometrial Cells

Insulin-like growth factor 1 (IGF1) Is Involved in the proliferation of mouse and rat endometrial cells in a paracrine or autocrine manner. Insulin-like growth factor binding protein-3 (IGFBP3) modulates actions of IGFs directly or indirectly. The present study aimed to determine whether IGFBP3 is Involved In the regulation of proliferation of mouse endometrial cells. Mouse endometrial epithelial cells and stromal cells were isolated, and cultured In a serum free medium. IGF1 stimulated DNA synthesis by endometrial epithelial and stromal cells, and IGFBP3 Inhibited IGF1-induced DNA synthesis. Estradiol-17 beta (E2) decreased the Igfbp3 mRNA level in endometrial stromal cells, whereas It Increased the Igf1 mRNA level. Transforming growth factor alpha (TGF alpha) significantly decreased IGFBP3 expression at both the mRNA and secreted protein levels in endometrial stromal cells. Progesterone (134) did not affect the E2-induced down-regulation of Igfbp3 mRNA expression in endometrial stromal cells, although P4 alone increased Igfbp3 mRNA levels. The present findings suggest that in mouse endometrial stromal cells E2 enhances IGF1 action through enhancement of IGF1 synthesis and reduction of IGFBP3 synthesis, and that TGF alpha affects IGF1 actions through modulation of IGFBP3 levels