7,795 research outputs found
AdS/QHE: Towards a Holographic Description of Quantum Hall Experiments
Transitions among quantum Hall plateaux share a suite of remarkable
experimental features, such as semi-circle laws and duality relations, whose
accuracy and robustness are difficult to explain directly in terms of the
detailed dynamics of the microscopic electrons. They would naturally follow if
the low-energy transport properties were governed by an emergent discrete
duality group relating the different plateaux, but no explicit examples of
interacting systems having such a group are known. Recent progress using the
AdS/CFT correspondence has identified examples with similar duality groups, but
without the DC ohmic conductivity characteristic of quantum Hall experiments.
We use this to propose a simple holographic model for low-energy quantum Hall
systems, with a nonzero DC conductivity that automatically exhibits all of the
observed consequences of duality, including the existence of the plateaux and
the semi-circle transitions between them. The model can be regarded as a
strongly coupled analog of the old `composite boson' picture of quantum Hall
systems. Non-universal features of the model can be used to test whether it
describes actual materials, and we comment on some of these in our proposed
model.Comment: LaTex 52 pages 11 figures. Repost improves the discussion of the
probe approximation; corrects minor errors; adds references. Second repost
generalizes charged solution and improves scaling discussio
Stability of quantum motion and correlation decay
We derive a simple and general relation between the fidelity of quantum
motion, characterizing the stability of quantum dynamics with respect to
arbitrary static perturbation of the unitary evolution propagator, and the
integrated time auto-correlation function of the generator of perturbation.
Surprisingly, this relation predicts the slower decay of fidelity the faster
decay of correlations is. In particular, for non-ergodic and non-mixing
dynamics, where asymptotic decay of correlations is absent, a qualitatively
different and faster decay of fidelity is predicted on a time scale 1/delta as
opposed to mixing dynamics where the fidelity is found to decay exponentially
on a time-scale 1/delta^2, where delta is a strength of perturbation. A
detailed discussion of a semi-classical regime of small effective values of
Planck constant is given where classical correlation functions can be used to
predict quantum fidelity decay. Note that the correct and intuitively expected
classical stability behavior is recovered in the classical limit hbar->0, as
the two limits delta->0 and hbar->0 do not commute. In addition we also discuss
non-trivial dependence on the number of degrees of freedom. All the theoretical
results are clearly demonstrated numerically on a celebrated example of a
quantized kicked top.Comment: 32 pages, 10 EPS figures and 2 color PS figures. Higher resolution
color figures can be obtained from authors; minor changes, to appear in
J.Phys.A (March 2002
Theory of quantum Loschmidt echoes
In this paper we review our recent work on the theoretical approach to
quantum Loschmidt echoes, i.e. various properties of the so called echo
dynamics -- the composition of forward and backward time evolutions generated
by two slightly different Hamiltonians, such as the state autocorrelation
function (fidelity) and the purity of a reduced density matrix traced over a
subsystem (purity fidelity). Our main theoretical result is a linear response
formalism, expressing the fidelity and purity fidelity in terms of integrated
time autocorrelation function of the generator of the perturbation.
Surprisingly, this relation predicts that the decay of fidelity is the slower
the faster the decay of correlations. In particular for a static
(time-independent) perturbation, and for non-ergodic and non-mixing dynamics
where asymptotic decay of correlations is absent, a qualitatively different and
faster decay of fidelity is predicted on a time scale 1/delta as opposed to
mixing dynamics where the fidelity is found to decay exponentially on a
time-scale 1/delta^2, where delta is a strength of perturbation. A detailed
discussion of a semi-classical regime of small effective values of Planck
constant is given where classical correlation functions can be used to predict
quantum fidelity decay. Note that the correct and intuitively expected
classical stability behavior is recovered in the classical limit, as the
perturbation and classical limits do not commute. The theoretical results are
demonstrated numerically for two models, the quantized kicked top and the
multi-level Jaynes Cummings model. Our method can for example be applied to the
stability analysis of quantum computation and quantum information processing.Comment: 29 pages, 11 figures ; Maribor 2002 proceeding
A one-parameter family of interpolating kernels for Smoothed Particle Hydrodynamics studies
A set of interpolating functions of the type f(v)={(sin[v pi/2])/(v pi/2)}^n
is analyzed in the context of the smoothed-particle hydrodynamics (SPH)
technique. The behaviour of these kernels for several values of the parameter n
has been studied either analytically as well as numerically in connection with
several tests carried out in two dimensions. The main advantage of this kernel
relies in its flexibility because for n=3 it is similar to the standard widely
used cubic-spline, whereas for n>3 the interpolating function becomes more
centrally condensed, being well suited to track discontinuities such as shock
fronts and thermal waves.Comment: 36 pages, 12 figures (low-resolution), published in J.C.
Surface acoustic wave attenuation by a two-dimensional electron gas in a strong magnetic field
The propagation of a surface acoustic wave (SAW) on GaAs/AlGaAs
heterostructures is studied in the case where the two-dimensional electron gas
(2DEG) is subject to a strong magnetic field and a smooth random potential with
correlation length Lambda and amplitude Delta. The electron wave functions are
described in a quasiclassical picture using results of percolation theory for
two-dimensional systems. In accordance with the experimental situation, Lambda
is assumed to be much smaller than the sound wavelength 2*pi/q. This restricts
the absorption of surface phonons at a filling factor \bar{\nu} approx 1/2 to
electrons occupying extended trajectories of fractal structure. Both
piezoelectric and deformation potential interactions of surface acoustic
phonons with electrons are considered and the corresponding interaction
vertices are derived. These vertices are found to differ from those valid for
three-dimensional bulk phonon systems with respect to the phonon wave vector
dependence. We derive the appropriate dielectric function varepsilon(omega,q)
to describe the effect of screening on the electron-phonon coupling. In the low
temperature, high frequency regime T << Delta (omega_q*Lambda
/v_D)^{alpha/2/nu}, where omega_q is the SAW frequency and v_D is the electron
drift velocity, both the attenuation coefficient Gamma and varepsilon(omega,q)
are independent of temperature. The classical percolation indices give
alpha/2/nu=3/7. The width of the region where a strong absorption of the SAW
occurs is found to be given by the scaling law |Delta \bar{\nu}| approx
(omega_q*Lambda/v_D)^{alpha/2/nu}. The dependence of the electron-phonon
coupling and the screening due to the 2DEG on the filling factor leads to a
double-peak structure for Gamma(\bar{\nu}).Comment: 17 pages, 3 Postscript figures, minor changes mad
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