214 research outputs found
Correlation Functions in Disordered Systems
{Recently, we found that the correlation between the eigenvalues of random
hermitean matrices exhibits universal behavior. Here we study this universal
behavior and develop a diagrammatic approach which enables us to extend our
previous work to the case in which the random matrix evolves in time or varies
as some external parameters vary. We compute the current-current correlation
function, discuss various generalizations, and compare our work with the work
of other authors. We study the distribution of eigenvalues of Hamiltonians
consisting of a sum of a deterministic term and a random term. The correlation
between the eigenvalues when the deterministic term is varied is calculated.}Comment: 19 pages, figures not included (available on request), Tex,
NSF-ITP-93-12
Electron Standing Wave Formation in Atomic Wires
Using the Landauer formulation of transport theory and tight binding models
of the electronic structure, we study electron transport through atomic wires
that form 1D constrictions between pairs of metallic nano-contacts. Our results
are interpreted in terms of electron standing waves formed in the atomic wires
due to interference of electron waves reflected at the ends of the atomic
constrictions. We explore the influence of the chemistry of the atomic
wire-metal contact interfaces on these standing waves and the associated
transport resonances by considering two types of atomic wires: gold wires
attached to gold contacts and carbon wires attached to gold contacts. We find
that the conductance of the gold wires is roughly for the
wire lengths studied, in agreement with experiments. By contrast, for the
carbon wires the conductance is found to oscillate strongly as the number of
atoms in the wire varies, the odd numbered chains being more conductive than
the even numbered ones, in agreement with previous theoretical work that was
based on a different model of the carbon wire and metal contacts.Comment: 14 pages, includes 6 figure
Vortex dissipation and level dynamics for the layered superconductors with impurities
We study parametric level statistics of the discretized excitation spectra
inside a moving vortex core in layered superconductors with impurities. The
universal conductivity is evaluated numerically for the various values of
rescaled vortex velocities from the clean case to the dirty limit
case. The random matrix theoretical prediction is verified numerically in the
large regime. On the contrary in the low velocity regime, we observe
which is consistent with the theoretical
result for the super-clean case, where the energy dissipation is due to the
Landau-Zener transition which takes place at the points called ``avoided
crossing''.Comment: 10 pages, 4 figures, REVTeX3.
Spectral form factor in a random matrix theory
In the theory of disordered systems the spectral form factor , the
Fourier transform of the two-level correlation function with respect to the
difference of energies, is linear for and constant for
. Near zero and near its exhibits oscillations which have
been discussed in several recent papers. In the problems of mesoscopic
fluctuations and quantum chaos a comparison is often made with random matrix
theory. It turns out that, even in the simplest Gaussian unitary ensemble,
these oscilllations have not yet been studied there. For random matrices, the
two-level correlation function exhibits several
well-known universal properties in the large N limit. Its Fourier transform is
linear as a consequence of the short distance universality of
. However the cross-over near zero and
requires to study these correlations for finite N. For this purpose we use an
exact contour-integral representation of the two-level correlation function
which allows us to characterize these cross-over oscillatory properties. The
method is also extended to the time-dependent case.Comment: 36P, (+5 figures not included
Non-universal corrections to the level curvature distribution beyond random matrix theory
The level curvature distribution function is studied beyond the random matrix
theory for the case of T-breaking perturbations over the orthogonal ensemble.
The leading correction to the shape of the level curvature distribution is
calculated using the nonlinear sigma-model. The sign of the correction depends
on the presence or absence of the global gauge invariance and is different for
perturbations caused by the constant vector-potential and by the random
magnetic field. Scaling arguments are discussed that indicate on the
qualitative difference in the level statistics in the dirty metal phase for
space dimensionalities .Comment: 4 pages, Late
Universality of Parametric Spectral Correlations: Local versus Extended Perturbing Potentials
We explore the influence of an arbitrary external potential perturbation V on
the spectral properties of a weakly disordered conductor. In the framework of a
statistical field theory of a nonlinear sigma-model type we find, depending on
the range and the profile of the external perturbation, two qualitatively
different universal regimes of parametric spectral statistics (i.e.
cross-correlations between the spectra of Hamiltonians H and H+V). We identify
the translational invariance of the correlations in the space of Hamiltonians
as the key indicator of universality, and find the connection between the
coordinate system in this space which makes the translational invariance
manifest, and the physically measurable properties of the system. In
particular, in the case of localized perturbations, the latter turn out to be
the eigenphases of the scattering matrix for scattering off the perturbing
potential V. They also have a purely statistical interpretation in terms of the
moments of the level velocity distribution. Finally, on the basis of this
analysis, a set of results obtained recently by the authors using random matrix
theory methods is shown to be applicable to a much wider class of disordered
and chaotic structures.Comment: 16 pages, 7 eps figures (minor changes and reference [17] added
Sensitivity to perturbations in a quantum chaotic billiard
The Loschmidt echo (LE) measures the ability of a system to return to the
initial state after a forward quantum evolution followed by a backward
perturbed one. It has been conjectured that the echo of a classically chaotic
system decays exponentially, with a decay rate given by the minimum between the
width of the local density of states and the Lyapunov exponent. As the
perturbation strength is increased one obtains a cross-over between both
regimes. These predictions are based on situations where the Fermi Golden Rule
(FGR) is valid. By considering a paradigmatic fully chaotic system, the
Bunimovich stadium billiard, with a perturbation in a regime for which the FGR
manifestly does not work, we find a cross over from to Lyapunov decay.
We find that, challenging the analytic interpretation, these conjetures are
valid even beyond the expected range.Comment: Significantly revised version. To appear in Physical Review E Rapid
Communication
Environment-independent decoherence rate in classically chaotic systems
We study the decoherence of a one-particle system, whose classical
correpondent is chaotic, when it evolves coupled to a weak quenched
environment. This is done by analytical evaluation of the Loschmidt Echo, (i.e.
the revival of a localized density excitation upon reversal of its time
evolution), in presence of the perturbation. We predict an exponential decay
for the Loschmidt Echo with a (decoherence) rate which is asymptotically given
by the mean Lyapunov exponent of the classical system, and therefore
independent of the perturbation strength, within a given range of strengths.
Our results are consistent with recent experiments of Polarization Echoes in
nuclear magnetic resonance and preliminary numerical simulations.Comment: No figures. Typos corrected and minor modifications to the text and
references. Published versio
Measuring the Lyapunov exponent using quantum mechanics
We study the time evolution of two wave packets prepared at the same initial
state, but evolving under slightly different Hamiltonians. For chaotic systems,
we determine the circumstances that lead to an exponential decay with time of
the wave packet overlap function. We show that for sufficiently weak
perturbations, the exponential decay follows a Fermi golden rule, while by
making the difference between the two Hamiltonians larger, the characteristic
exponential decay time becomes the Lyapunov exponent of the classical system.
We illustrate our theoretical findings by investigating numerically the overlap
decay function of a two-dimensional dynamical system.Comment: 9 pages, 6 figure
Universality in quantum parametric correlations
We investigate the universality of correlation functions of chaotic and
disordered quantum systems as an external parameter is varied. A new, general
scaling procedure is introduced which makes the theory invariant under
reparametrizations. Under certain general conditions we show that this
procedure is unique. The approach is illustrated with the particular case of
the distribution of eigenvalue curvatures. We also derive a semiclassical
formula for the non-universal scaling factor, and give an explicit expression
valid for arbitrary deformations of a billiard system.Comment: LaTeX, 10 pages, 2 figures. Revised version, to appear in PR
- …