Near Critical States of Random Dirac Fermions

Random Dirac fermions in a two-dimensional space are studied numerically. We realize them on a square lattice using the $\pi$-flux model with random hopping. The system preserves two symmetries, the time-reversal symmetry and the symmetry denoted by ${{\cal H},\gamma}=0$ with a $4\times 4$ matrix $\gamma$ in an effective field theory. Although it belongs to the orthogonal ensemble, the zero-energy states do not localize and become critical. The density of states vanishes at zero energy as $\sim E^{\alpha}$ and the exponent $\alpha$ changes with strength of the randomness, which implies the existence of the critical line. Rapid growth of the localization length near zero energy is suggested and the eigenstates near zero energy exhibit anomalous behaviour which can be interpreted as a critical slowing down in the available finite-size system. The level-spacing distributions close to zero energy deviate from both the Wigner surmise and the Poissonian, and exhibit critical behaviour which reflects the existence of critical states at zero energy.Comment: latex209, REVTEX, 6 figure

Optimum design of magnetic field environment for axonal growth control in nerve cell regeneration process using electromagnetic field analyses

In this study, an optimum magnetic field environment for the nerve axonal extension and control of axonal growth direction in the nerve cell generation process was searched by using electromagnetic finite element analyses. Recently, the developments of 3D-scaffold structures employing biodegradable polymers have been an attracting attention for the clinical treatments of damaged nerve tissues. The magnetic stimulation is introduced to accelerate the regeneration speed of nerve axon inside the 3D-scaffold. According to experimental observation of Blackman, C.F. and his research group (1993) [1], it was found that 50 Hz AC magnetic field has promoted the regeneration of axonal extension in the case of pheochromocytoma cells (PC12). They identified the optimum configuration of the coil and the threshold value of driving current for the initiation of PC12 axon growth. However, they did not evaluate analytically the magnetic flux density and the magnetic field in the cell culture liquid for the PC12 axon growth initiation. Therefore, at first we employed the electromagnetic finite element analyses (FEA) to evaluate the magnetic flux density in the case of Blackman’s experiment. Simultaneously, we identified the relative magnetic permeability of Dulbecco’s Modified Eagle Medium (DMEM) as 1.01 at 50 Hz. Finally, we obtained the value of magnetic flux density inside DMEM as 4.2 T. Next, we try to design the configuration of Helmholtz coil, which can generate an optimum magnetic field to stimulate most effectively for PC12 axon extension. It is confirmed that the magnetic field gradient affect the extensional speed of PC12 axon, which can be achieved by setup the one peripheral coil and two coils at the center. We found an optimum configuration of Helmholtz coil to generate the magnetic field environment and fabricate an experimental bioreactor for PC12 cell culture. We examined the effectiveness of magnetic stimulation for PC12 nerve axon’s extension quantitatively. Further, we try to find the relationship between the magnetic field gradient and the direction of nerve axon’s extension

Correlation effects on the Fermi surface of the two-dimensional Hubbard model

Effects of electron correlation on the Fermi surface is investigated for the two-dimensional Hubbard model by the quantum Monte Carlo method. At first, an infinitesimal doping from the half filling is focused on and the momentum dependent charge susceptibility $\kappa(k)=\frac {dn(k)}{d\mu}$ is calculated at a finite temperature. At the temperature $T \sim \frac {t^2} U$, it shows peak structure at $(\pm \pi/2,\pm \pi/2)$ on the Fermi surface (line). It is consistent with the mean-field prediction of the d-wave pairing state or the staggerd flux state. This momentum dependent structure disappears at the high temperature $T \approx U$. After summarizing the results of the half filling case, we also discuss the effects of the doping on the momentum dependent charge susceptibility. The anisotropic structure at half filling fades out with sufficient doping.Comment: 6 pages, 3 figures; proceedings of ISSP

Reconstruction of the spontaneously broken gauge theory in non-commutative geometry

The scheme previously proposed by the present authors is modified to incorporate the strong interaction by affording the direct product internal symmetry. We do not need to prepare the extra discrete space for the color gauge group responsible for the strong interaction to reconstruct the standard model and the left-right symmetric gauge model(LRSM). The approach based on non-commutative geometry leads us to presents many attractive points such as the unified picture of the gauge and Higgs field as the generalized connection on the discrete space; Minkowski space multipied by N-points discrete space. This approach leads us to unified picture of gauge and Higgs fields as the generalized connection. The standard model needs N=2 discrete space for reconstruction in this formalism. \lr is still alive as a model with the intermediate symmetry of the spontaneously broken SO(10) grand unified theory(GUT). N=3 discrete space is needed for the reconstruction of LRSM to include two Higgs bosons $\phi$ and $\xi$ which are as usual transformed as (2,2*,0)$ and (1,3,-2) under left-handed SU(2)x right-handed SU(2)x U(1), respectively. xi is responsible to make the right handed-neutrino Majorana fermion and so well explains the seesaw mechanism. Up and down quarks have the different masses through the vacuum expectation value of phi.Comment: 21 page

BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry

Noncommutative geometry(NCG) on the discrete space successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory, in which the Higgs boson field is regarded as a kind of gauge field on the discrete space. We could construct the generalized differential geometry(GDG) on the discrete space $M_4\times Z_N$ which is very close to NCG in case of $M_4\times Z_2$. GDG is a direct generalization of the differential geometry on the ordinary manifold into the discrete one. In this paper, we attempt to construct the BRST invariant formulation of spontaneously broken gauge theory based on GDG and obtain the BRST invariant Lagrangian with the t'Hooft-Feynman gauge fixing term.Comment: 15 page

Exact Results on Superconductivity due to Interband Coupling

We present a family of exactly solvable models at arbitrary filling in any dimensions which exhibit novel superconductivity with interband pairing. By the use of the hidden $SU(2)$ algebra the Hamiltonians were diagonalized explicitly. The zero-temperature phase diagrams and the thermodynamic properties are discussed. Several new properties are revealed which are different from those of the BCS-type superconductor

Sum Rule of the Hall Conductance in Random Quantum Phase Transition

The Hall conductance $\sigma_{xy}$ of two-dimensional {\it lattice} electrons with random potential is investigated. The change of $\sigma_{xy}$ due to randomness is focused on. It is a quantum phase transition where the {\it sum rule} of $\sigma_{xy}$ plays an important role. By the {\it string} (anyon) gauge, numerical study becomes possible in sufficiently weak magnetic field regime which is essential to discuss the floating scenario in the continuum model. Topological objects in the Bloch wavefunctions, charged vortices, are obtained explicitly. The anomalous plateau transitions ($\Delta \sigma_{xy}= 2,3,... >1$) and the trajectory of delocalized states are discussed.Comment: 7 pages RevTeX, 4 postscript figures, to appear in Physical Review Letter