Colored noise in the fractional Hall effect: duality relations and exact results

We study noise in the problem of tunneling between fractional quantum Hall edge states within a four probe geometry. We explore the implications of the strong-weak coupling duality symmetry existent in this problem for relating the various density-density auto-correlations and cross-correlations between the four terminals. We identify correlations that transform as either ``odd'' or ``anti-symmetric'', or ``even'' or ``symmetric'' quantities under duality. We show that the low frequency noise is colored, and that the deviations from white noise are exactly related to the differential conductance. We show explicitly that the relationship between the slope of the low frequency noise spectrum and the differential conductance follows from an identity that holds to {\it all} orders in perturbation theory, supporting the results implied by the duality symmetry. This generalizes the results of quantum supression of the finite frequency noise spectrum to Luttinger liquids and fractional statistics quasiparticles.Comment: 14 pages, 3 figure

Correlations in one dimensional quantum impurity problems with an external field

We study response functions of integrable quantum impurity problems with an external field at $T=0$ using non perturbative techniques derived from the Bethe ansatz. We develop the first steps of the theory of excitations over the new, field dependent ground state, leading to renormalized (or ``dressed'') form-factors. We obtain exactly the low frequency behaviour of the dynamical susceptibility $\chi''(\omega)$ in the double well problem of dissipative quantum mechanics (or equivalently the anisotropic Kondo problem),and the low frequency behaviour of the AC noise $S_t(\omega)$ for tunneling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in $\chi''(\omega)$ and $S_t(\omega)$. Our results differ significantly from previous perturbative approaches.Comment: harvmac, epsf, 37pgs, 2figs. modified some reference

Supersymmetry on a lattice and Dirac fermions in a random vector potential

We study two-dimensional Dirac fermions in a random non-Abelian vector potential by using lattice regularization. We consider U(N) random vector potential for large $N$. The ensemble average with respect to random vector potential is taken by using lattice supersymmetry which we introduced before in order to investigate phase structure of supersymmetric gauge theory. We show that a phase transition occurs at a certain critical disorder strength. The ground state and low-energy excitations are studied in detail in the strong-disorder phase. Correlation function of the fermion local density of states decays algebraically at the band center because of a quasi-long-range order of chiral symmetry and the chiral anomaly cancellation in the lattice regularization (the species doubling). In the present study, we use the lattice regularization and also the Haar measure of U(N) for the average over the random vector potential. Therefore topologically nontrivial configurations of the vector potential are all included in the average. Implication of the present results for the system of Dirac fermions in a random vector potential with noncompact Gaussian distribution is discussed.Comment: Final version appeared in Nucl.Phys.B575(2000)61

Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at E=0E=0 without Doubling

Random bond Hamiltonians of the $\pi$ flux state on the square lattice are investigated. It has a special symmetry and all states are paired except the ones with zero energy. Because of this, there are always zero-modes. The states near $E=0$ are described by massless Dirac fermions. For the zero-mode, we can construct a random lattice fermion without a doubling and quite large systems ( up to $801 \times 801$) are treated numerically. We clearly demonstrate that the zero-mode is given by a critical wave function. Its multifractal behavior is also compared with the effective field theory.Comment: 4 pages, 2 postscript figure

Magnetic Field Dependence of the Level Spacing of a Small Electron Droplet

The temperature dependence of conductance resonances is used to measure the evolution with the magnetic field of the average level spacing $\Delta\epsilon$ of a droplet containing $\sim 30$ electrons created by lateral confinement of a two-dimensional electron gas in GaAs. $\Delta\epsilon$ becomes very small ($< 30\mu$eV) near two critical magnetic fields at which the symmetry of the droplet changes and these decreases of $\Delta\epsilon$ are predicted by Hartree-Fock (HF) for charge excitations. Between the two critical fields, however, the largest measured $\Delta\epsilon= 100\mu$eV is an order of magnitude smaller than predicted by HF but comparable to the Zeeman splitting at this field, which suggests that the spin degrees of freedom are important. PACS: 73.20.Dx, 73.20.MfComment: 11 pages of text in RevTeX, 4 figures in Postscript (files in the form of uuencoded compressed tar file