239 research outputs found
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 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 in the double well problem of dissipative
quantum mechanics (or equivalently the anisotropic Kondo problem),and the low
frequency behaviour of the AC noise for tunneling between edges
in fractional quantum Hall devices. We also obtain exactly the structure of
singularities in and . 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 . 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
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
of a droplet containing electrons created by lateral confinement of a
two-dimensional electron gas in GaAs. becomes very small (eV) near two critical magnetic fields at which the symmetry of the
droplet changes and these decreases of are predicted by
Hartree-Fock (HF) for charge excitations. Between the two critical fields,
however, the largest measured 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
Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at without Doubling
Random bond Hamiltonians of the 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 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 ) 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
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