551 research outputs found
Universal Scaling of Strong-Field Localization in an Integer Quantum Hall Liquid
We study the Landau level localization and scaling properties of a disordered
two-dimensional electron gas in the presence of a strong external magnetic
field. The impurities are treated as random distributed scattering centers with
parameterized potentials. Using a transfer matrix for a finite-width strip
geometry, we calculate the localization length as a function of system size and
electron energy. The finite-size localization length is determined by
calculating the Lyapunov exponents of the transfer matrix. A detailed
finite-size scaling analysis is used to study the critical behavior near the
center of the Landau bands. The influence of varying the impurity
concentration, the scattering potential range and its nature, and the Landau
level index on the scaling behavior and on the critical exponent is
systematically investigated. Particular emphasis is put on studying the effects
of finite range of the disorder potential and Landau level coupling on the
quantum localization behavior. Our numerical results, which are carried out on
systems much larger than those studied before, indicate that pure
-function disorder in the absence of any Landau level coupling gives
rise to non-universal localization properties with the critical exponents in
the lowest two Landau levels being substantially different. Inclusion of a
finite potential range and/or Landau level mixing may be essential in producing
universality in the localization.Comment: 28 pages, Latex, 17 figures (available upon request), #phd0
Scaling Behavior of the Activated Conductivity in a Quantum Hall Liquid
We propose a scaling model for the universal longitudinal conductivity near
the mobility edge for the integer quantum Hall liquid. We fit our model with
available experimental data on exponentially activated conductance near the
Landau level tails in the integer quantum Hall regime. We obtain quantitative
agreement between our scaling model and the experimental data over a wide
temperature and magnetic field range.Comment: 9 pages, Latex, 2 figures (available upon request), #phd0
Universal flow diagram for the magnetoconductance in disordered GaAs layers
The temperature driven flow lines of the diagonal and Hall magnetoconductance
data (G_{xx},G_{xy}) are studied in heavily Si-doped, disordered GaAs layers
with different thicknesses. The flow lines are quantitatively well described by
a recent universal scaling theory developed for the case of duality symmetry.
The separatrix G_{xy}=1 (in units e^2/h) separates an insulating state from a
spin-degenerate quantum Hall effect (QHE) state. The merging into the insulator
or the QHE state at low temperatures happens along a semicircle separatrix
G_{xx}^2+(G_{xy}-1)^2=1 which is divided by an unstable fixed point at
(G_{xx},G_{xy})=(1,1).Comment: 10 pages, 5 figures, submitted to Phys. Rev. Let
A Unified Model for Two Localisation Problems: Electron States in Spin-Degenerate Landau Levels, and in a Random Magnetic Field
A single model is presented which represents both of the two apparently
unrelated localisation problems of the title. The phase diagram of this model
is examined using scaling ideas and numerical simulations. It is argued that
the localisation length in a spin-degenerate Landau level diverges at two
distinct energies, with the same critical behaviour as in a spin-split Landau
level, and that all states of a charged particle moving in two dimensions, in a
random magnetic field with zero average, are localised.Comment: 7 pages (RevTeX 3.0) plus 4 postscript figure
Rigidity of minimal submanifolds in hyperbolic space
We prove that if an -dimensional complete minimal submanifold in
hyperbolic space has sufficiently small total scalar curvature then has
only one end. We also prove that for such there exist no nontrivial
harmonic 1-forms on
A Farewell to Liouvillians
We examine the Liouvillian approach to the quantum Hall plateau transition,
as introduced recently by Sinova, Meden, and Girvin [Phys. Rev. B {\bf 62},
2008 (2000)] and developed by Moore, Sinova and Zee [Phys. Rev. Lett. {\bf 87},
046801 (2001)]. We show that, despite appearances to the contrary, the
Liouvillian approach is not specific to the quantum mechanics of particles
moving in a single Landau level: we formulate it for a general disordered
single-particle Hamiltonian. We next examine the relationship between
Liouvillian perturbation theory and conventional calculations of
disorder-averaged products of Green functions and show that each term in
Liouvillian perturbation theory corresponds to a specific contribution to the
two-particle Green function. As a consequence, any Liouvillian approximation
scheme may be re-expressed in the language of Green functions. We illustrate
these ideas by applying Liouvillian methods, including their extension to Liouvillian flavors, to random matrix ensembles, using numerical
calculations for small integer and an analytic analysis for large .
We find that behavior at is different in qualitative ways from that
at . In particular, the limit expressed using Green
functions generates a pathological approximation, in which two-particle
correlation functions fail to factorize correctly at large separations of their
energy, and exhibit spurious singularities inside the band of random matrix
energy levels. We also consider the large treatment of the quantum Hall
plateau transition, showing that the same undesirable features are present
there, too
Liouvillian Approach to the Integer Quantum Hall Effect Transition
We present a novel approach to the localization-delocalization transition in
the integer quantum Hall effect. The Hamiltonian projected onto the lowest
Landau level can be written in terms of the projected density operators alone.
This and the closed set of commutation relations between the projected
densities leads to simple equations for the time evolution of the density
operators. These equations can be used to map the problem of calculating the
disorder averaged and energetically unconstrained density-density correlation
function to the problem of calculating the one-particle density of states of a
dynamical system with a novel action. At the self-consistent mean-field level,
this approach yields normal diffusion and a finite longitudinal conductivity.
While we have not been able to go beyond the saddle point approximation
analytically, we show numerically that the critical localization exponent can
be extracted from the energetically integrated correlation function yielding
in excellent agreement with previous finite-size scaling
studies.Comment: 9 pages, submitted to PR
Non-Markovian entanglement dynamics in coupled superconducting qubit systems
We theoretically analyze the entanglement generation and dynamics by coupled
Josephson junction qubits. Considering a current-biased Josephson junction
(CBJJ), we generate maximally entangled states. In particular, the entanglement
dynamics is considered as a function of the decoherence parameters, such as the
temperature, the ratio between the reservoir cutoff
frequency and the system oscillator frequency , % between
the characteristic frequency of the %quantum system of interest, and
the cut-off frequency of %Ohmic reservoir and the energy levels
split of the superconducting circuits in the non-Markovian master equation. We
analyzed the entanglement sudden death (ESD) and entanglement sudden birth
(ESB) by the non-Markovian master equation. Furthermore, we find that the
larger the ratio and the thermal energy , the shorter the
decoherence. In this superconducting qubit system we find that the entanglement
can be controlled and the ESD time can be prolonged by adjusting the
temperature and the superconducting phases which split the energy
levels.Comment: 13 pages, 3 figure
Electron Localization in a 2D System with Random Magnetic Flux
Using a finite-size scaling method, we calculate the localization properties
of a disordered two-dimensional electron system in the presence of a random
magnetic field. Below a critical energy all states are localized and the
localization length diverges when the Fermi energy approaches the
critical energy, {\it i.e.} . We find that
shifts with the strength of the disorder and the amplitude of the random
magnetic field while the critical exponent () remains unchanged
indicating universality in this system. Implications on the experiment in
half-filling fractional quantum Hall system are also discussed.Comment: 4 pages, RevTex 3.0, 5 figures(PS files available upon request),
#phd1
Duality and Non-linear Response for Quantum Hall Systems
We derive the implications of particle-vortex duality for the electromagnetic
response of Quantum Hall systems beyond the linear-response regime. This
provides a first theoretical explanation of the remarkable duality which has
been observed in the nonlinear regime for the electromagnetic response of
Quantum Hall systems.Comment: 7 pages, 1 figure, typeset in LaTe
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