Conductance plateau transitions in quantum Hall wires with spatially correlated random magnetic fields

Quantum transport properties in quantum Hall wires in the presence of spatially correlated disordered magnetic fields are investigated numerically. It is found that the correlation drastically changes the transport properties associated with the edge state, in contrast to the naive expectation that the correlation simply reduces the effect of disorder. In the presence of correlation, the separation between the successive conductance plateau transitions becomes larger than the bulk Landau level separation determined by the mean value of the disordered magnetic fields. The transition energies coincide with the Landau levels in an effective magnetic field stronger than the mean value of the disordered magnetic field. For a long wire, the strength of this effective magnetic field is of the order of the maximum value of the magnetic fields in the system. It is shown that the effective field is determined by a part where the stronger magnetic field region connects both edges of the wire.Comment: 7 pages, 10 figure

Quantum transport properties of two-dimensional systems in disordered magnetic fields with a fixed sign

Quantum transport in disordered magnetic fields is investigated numerically in two-dimensional systems. In particular, the case where the mean and the fluctuation of disordered magnetic fields are of the same order is considered. It is found that in the limit of weak disorder the conductivity exhibits a qualitatively different behavior from that in the conventional random magnetic fields with zero mean. The conductivity is estimated by the equation of motion method and by the two-terminal Landauer formula. It is demonstrated that the conductance stays on the order of $e^2/h$ even in the weak disorder limit. The present behavior can be interpreted in terms of the Drude formula. The Shubnikov-de Haas oscillation is also observed in the weak disorder regime.Comment: 6 pages, 7 figures, to appear in Phys. Rev.

Box representations of embedded graphs

A $d$-box is the cartesian product of $d$ intervals of $\mathbb{R}$ and a $d$-box representation of a graph $G$ is a representation of $G$ as the intersection graph of a set of $d$-boxes in $\mathbb{R}^d$. It was proved by Thomassen in 1986 that every planar graph has a 3-box representation. In this paper we prove that every graph embedded in a fixed orientable surface, without short non-contractible cycles, has a 5-box representation. This directly implies that there is a function $f$, such that in every graph of genus $g$, a set of at most $f(g)$ vertices can be removed so that the resulting graph has a 5-box representation. We show that such a function $f$ can be made linear in $g$. Finally, we prove that for any proper minor-closed class $\mathcal{F}$, there is a constant $c(\mathcal{F})$ such that every graph of $\mathcal{F}$ without cycles of length less than $c(\mathcal{F})$ has a 3-box representation, which is best possible.Comment: 16 pages, 6 figures - revised versio

Unconventional conductance plateau transitions in quantum Hall wires with spatially correlated disorder

Quantum transport properties in quantum Hall wires in the presence of spatially correlated random potential are investigated numerically. It is found that the potential correlation reduces the localization length associated with the edge state, in contrast to the naive expectation that the potential correlation increases it. The effect appears as the sizable shift of quantized conductance plateaus in long wires, where the plateau transitions occur at energies much higher than the Landau band centers. The scale of the shift is of the order of the strength of the random potential and is insensitive to the strength of magnetic fields. Experimental implications are also discussed.Comment: 5 pages, 4 figure

Generalized Conformal Symmetry and Oblique AdS/CFT Correspondence for Matrix Theory

The large N behavior of Matrix theory is discussed on the basis of the previously proposed generalized conformal symmetry. The concept of `oblique' AdS/CFT correspondence, in which the conformal symmetry involves both the space-time coordinates and the string coupling constant, is proposed. Based on the explicit predictions for two-point correlators, possible implications for the Matrix-theory conjecture are discussed.Comment: LaTeX, 10 pages, 2 figures, written version of the talk presented at Strings'9

The J_1-J_2 antiferromagnet with Dzyaloshinskii-Moriya interaction on the square lattice: An exact diagonalization study

We examine the influence of an anisotropic interaction term of Dzyaloshinskii-Moriya (DM) type on the groundstate ordering of the J_1-J_2 spin-1/2-Heisenberg antiferromagnet on the square lattice. For the DM term we consider several symmetries corresponding to different crystal structures. For the pure J_1-J_2 model there are strong indications for a quantum spin liquid in the region of 0.4 < J_2/J_1 < 0.65. We find that a DM interaction influences the breakdown of the conventional antiferromagnetic order by i) shifting the spin liquid region, ii) changing the isotropic character of the groundstate towards anisotropic correlations and iii) creating for certain symmetries a net ferromagnetic moment.Comment: 7 pages, RevTeX, 6 ps-figures, to appear in J. Phys.: Cond. Ma

Anomalous diffusion at the Anderson transitions

Diffusion of electrons in three dimensional disordered systems is investigated numerically for all the three universality classes, namely, orthogonal, unitary and symplectic ensembles. The second moment of the wave packet $$ at the Anderson transition is shown to behave as $\sim t^a (a\approx 2/3)$. From the temporal autocorrelation function $C(t)$, the fractal dimension $D_2$ is deduced, which is almost half the value of space dimension for all the universality classes.Comment: Revtex, 2 figures, to appear in J. Phys. Soc. Jpn.(1997) Fe

The Neutron Electric Dipole Moment in the Instanton Vacuum: Quenched Versus Unquenched Simulations

We investigate the role played by the fermionic determinant in the evaluation of the CP-violating neutron electric dipole moment (EDM) adopting the Instanton Liquid Model. Significant differences between quenched and unquenched calculations are found. In the case of unquenched simulations the neutron EDM decreases linearly with the quark mass and is expected to vanish in the chiral limit. On the contrary, within the quenched approximation, the neutron EDM increases as the quark mass decreases and is expected to diverge as (1/m)**Nf in the chiral limit. We argue that such a qualitatively different behavior is a parameter-free, semi-classical prediction and occurs because the neutron EDM is sensitive to the topological structure of the vacuum. The present analysis suggests that quenched and unquenched lattice QCD simulations of the neutron EDM as well as of other observables governed by topology might show up important differences in the quark mass dependence, for mq < Lambda(QCD).Comment: 8 pages, 3 figures, 2 table