arXiv subjects

K. Ishikawa

Publications and source records attributed to K. Ishikawa.

44 records · Page 3Linked to original sources

arXiv1998

Duality Relation among Periodic Potential Problems in the Lowest Landau Level

Using a momentum representation of a magnetic von Neumann lattice, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic short-range potential problems in the lowest Landau level.We find that the energy spectra satisfy a duality relation between a period of the potential and a magnetic length. The energy spectra consist of the Hofstadter-type bands and flat bands. We also study the connection between a periodic short-range potential problem and a tight-binding model.

cond-mat.mes-hall↗

arXiv1998

Abelian Chern-Simons Term in Superfluid 3He-A

We show in this paper that Abelian Chern-Simons term is induced in 2+1 and 3+1 dimensional rotating superfluid $^{3}$He-A and plays important roles in its dynamics. Because U(1) symmetry is spontaneously broken in $^{3}$He-A, Goldstone mode appears and contributes to induced Chern-Simons term. We found that the coefficient of Chern-Simons term, which is equivalent to Hall conductance, depends on an infra-red cut off of the Goldstone mode, and that the orbital angular momentum of $^{3}$He-A in a cylinder geometry is derived from Chern-Simons term.

cond-mat.supr-con↗

arXiv1996

Integer Quantum Hall Effect with Realistic Boundary Condition : Exact Quantization and Breakdown

A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator in the momentum representation, is realized. In QHR, the Hall conductance is given by a topological invariant of the momentum space and is quantized exactly. The edge states do not modify the value and topological property of $σ_{xy}$ in QHR. We next compute distribution of current based on effective action and find a finite amount of current in the bulk and the edge, generally. Due to the Hall electric field in the bulk, breakdown of the QHE occurs. The critical electric field of the breakdown is proportional to $B^{3/2}$ and the proportional constant has no dependence on Landau levels in our theory, in agreement with the recent experiments.

cond-mat↗

arXiv1995

Dynamical Symmetry Breaking in Einstein Universe

We investigate four-fermion interactions with $N$-component fermion in Einstein universe for arbitrary space-time dimensions ($2 \leq D<4$). It is found that the effective potential for composite operator $\overlineψψ$ is calculable in the leading order of the $1/N$ expansion. The resulting effective potential is analyzed by varying the curvature of the space-time and is found to exhibit the symmetry restoration through the second-order phase transition. The critical curvature at which the dynamical fermion mass disappears is analytically calculated.

hep-th↗

arXiv1995

Scalar and Spinor Two-Point Functions in Einstein Universe

Two-point functions for scalar and spinor fields are investigated in Einstein universe ($R \otimes S^{\sN-1}$). Equations for massive scalar and spinor two-point functions are solved and the explicit expressions for the two-point functions are given. The simpler expressions for massless cases are obtained both for the scalar and spinor cases.

hep-th↗

arXiv1994

Is Hall Conductance in Hall Bar Geometry a Topological Invariant?

A deep connection between the Hall conductance in realistic situation and a topological invariant is pointed out based on von-Neumann lattice representation in which Landau level electrons have minimum spatial extensions. We show that the Hall conductance has no finite size correction in quantum Hall regime, but a coefficient of induced Chern-Simons term in QED$_3$ has a small finite size correction, although both of them are similar topological invariant.

cond-mat↗

arXiv1994

Magnetic von-Neumann lattice for two-dimensional electrons in the magnetic field

One-particle eigenstates and eigenvalues of two-dimensional electrons in the strong magnetic field with short range impurity and impurities, cosine potential, boundary potential, and periodic array of short range potentials are obtained by magnetic von-Neumann lattice in which Landau level wave functions have minimum spatial extensions. We find that there is a dual correspondence between cosine potential and lattice kinetic term and that the representation based on the von-Neumann lattice is quite useful for solving the system's dynamics.

cond-mat↗

arXiv1993

Lattice Calculation of Glueball Matrix Elements

Matrix elements of the form $ <0| Tr \; g^{2}GG |G> $ are calculated using the lattice QCD Monte Carlo method. Here, $|G>$ is a glueball state with quantum numbers $ 0^{++}$, $ 2^{++}$, $ 0^{-+}$ and $G$ is the gluon field strength operator. The matrix elements are obtained from the hybrid correlation functions of the fuzzy and plaquette operators performed on the $12^{4}$ and $14^{4}$ lattices at $β= 5.9 $ and $5.96$ respectively. These matrix elements are compared with those from the QCD sum rules and the tensor meson dominance model. They are the non-perturbative matrix elements needed in the calculation of the partial widths of $J/Ψ$ radiative decays into glueballs.

hep-lat↗