Compressible Anisotropic States around the Half-Filled Landau Levels

Using the von Neumann lattice formalism, we study compressible anisotropic states around the half-filled Landau levels in the quantum Hall system. In these states the unidirectional charge density wave (UCDW) state seems to be the most plausible state. The charge density profile and Hartree-Fock energy of the UCDW are calculated self-consistently. The wave length dependence of the energy for the UCDW is also obtained numerically. We show that the UCDW is regarded as a collection of the one-dimensional lattice Fermi-gas systems which extend to the uniform direction. The kinetic energy of the gas system is generated dynamically from the Coulomb interaction.Comment: 6 pages, 5 figures, accepted version for publication in PR

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.Comment: 6 pages, 3 figures, final version to appear in PR

Stability of the compressible quantum Hall state around the half-filled Landau level

We study the compressible states in the quantum Hall system using a mean field theory on the von Neumann lattice. In the lowest Landau level, a kinetic energy is generated dynamically from Coulomb interaction. The compressibility of the state is calculated as a function of the filling factor $\nu$ and the width $d$ of the spacer between the charge carrier layer and dopants. The compressibility becomes negative below a critical value of $d$ and the state becomes unstable at $\nu=1/2$. Within a finite range around $\nu=1/2$, the stable compressible state exists above the critical value of $d$.Comment: 4 pages, 4 Postscript figures, RevTe

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 $\sigma_{xy}$ 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.Comment: 48 pages, figures not included, some additions and revision

Scalar form factors and nuclear interactions

The scalar-isoscalar term in the two-pion exchange $NN$ potential is abnormally large and does not respect the hierarchy of effects predicted by chiral perturbation theory. We argue that this anomaly is associated with non-perturbative effects, which are also present in the $\pi N$ scalar form factor.Comment: Talk given at the 20EFB, Pisa, Italy, September 2007. 3 pages and 4 figure

Continuum Annulus Amplitude from the Two-Matrix Model

An explicit expression for continuum annulus amplitudes having boundary lengths $\ell_{1}$ and $\ell_{2}$ is obtained from the two-matrix model for the case of the unitary series; $(p,q) = (m + 1, m)$. In the limit of vanishing cosmological constant, we find an integral representation of these amplitudes which is reproduced, for the cases of the $m = 2~(c=0)$ and the $m \rightarrow \infty~(c=1)$, by a continuum approach consisting of quantum mechanics of loops and a matter system integrated over the modular parameter of the annulus. We comment on a possible relation to the unconventional branch of the Liouville gravity.Comment: 9 pages, OU-HET 190, revised version. A part of the conclusions has been corrected. A new result on integral representation of the annulus amplitudes has been adde

Persistence of Covalent Bonding in Liquid Silicon Probed by Inelastic X-ray Scattering

Metallic liquid silicon at 1787K is investigated using x-ray Compton scattering. An excellent agreement is found between the measurements and the corresponding Car-Parrinello molecular dynamics simulations. Our results show persistence of covalent bonding in liquid silicon and provide support for the occurrence of theoretically predicted liquid-liquid phase transition in supercooled liquid states. The population of covalent bond pairs in liquid silicon is estimated to be 17% via a maximally-localized Wannier function analysis. Compton scattering is shown to be a sensitive probe of bonding effects in the liquid state.Comment: 5pages, 3 postscript figure

Differential decay rate for B→πlνB \to \pi l \nu semileptonic decays

We present our study on $B \to \pi l \nu$ semileptonic decay form factors with NRQCD action for heavy quark from a quenched lattice QCD simulation at $\beta$=5.9 on a $16^3\times 48$ lattice. We obtain form factors defined in the context of heavy quark effective theory by Burdman et al. and find that their $1/m_B$ correction is small. The limit of physical heavy and light quark masses can be performed without introducing any model function, and we obtain a prediction for the differential decay rate $d\Gamma/dq^2$. We also discuss the soft pion limit of the form factors.Comment: Lattice 2000, 4 pages, 4 figures, Late

Non-perturbative renormalization for a renormalization group improved gauge action

Renormalization constants of vector ($Z_V$) and axial-vector ($Z_A$) currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schr\"odinger functional method. Non-perturbative values of $Z_V$ and $Z_A$ turn out to be smaller than the one-loop perturbative values by $O(10$ at $a^{-1}\approx 1$ GeV. A sizable scaling violation of meson decay constants $f_\pi$ and $f_\rho$ observed with the one-loop renormalization factors remains even with non-perturbative renormalization.Comment: Lattice2001(improvement), 3 pages, 7 figure

The quantum phase transition of itinerant helimagnets

We investigate the quantum phase transition of itinerant electrons from a paramagnet to a state which displays long-period helical structures due to a Dzyaloshinskii instability of the ferromagnetic state. In particular, we study how the self-generated effective long-range interaction recently identified in itinerant quantum ferromagnets is cut-off by the helical ordering. We find that for a sufficiently strong Dzyaloshinskii instability the helimagnetic quantum phase transition is of second order with mean-field exponents. In contrast, for a weak Dzyaloshinskii instability the transition is analogous to that in itinerant quantum ferromagnets, i.e. it is of first order, as has been observed in MnSi.Comment: 5 pages RevTe