201 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
Momentum noise in a quantum point contact
Ballistic electrons flowing through a constriction can transfer momentum to
the lattice and excite a vibration of a free-standing conductor. We show (both
numerically and analytically) that the electromechanical noise power P does not
vanish on the plateaus of quantized conductance -- in contrast to the current
noise. The dependence of on the constriction width can be oscillatory or
stepwise, depending on the geometry. The stepwise increase amounts to an
approximate quantization of momentum noise.Comment: 4 pages including 4 figure
Clauser-Horne inequality and decoherence in mesoscopic conductors
We analyze the effect of decoherence on the violation of the Clauser-Horne
(CH) inequality for the full electron counting statistics in a mesoscopic
multiterminal conductor. Our setup consists of an entangler that emits a flux
of entangled electrons into two conductors characterized by a scattering matrix
and subject to decoherence. Loss of phase memory is modeled phenomenologically
by introducing fictitious extra leads. The outgoing electrons are detected
using spin-sensitive electron counters. Given a certain average number of
incoming entangled electrons, the CH inequality is evaluated as a function of
the numbers of detected particles and on the various quantities characterizing
the scattering matrix. When decoherence is turned on, we show that the amount
of violation of the CH inequality is effectively reduced. Interestingly we find
that, by adjusting the parameters of the system, there exists a protected
region of values for which violation holds for arbitrary strong
decoherence.Comment: 14 pages, 10 figures. Published versio
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
Correlations and fluctuations of a confined electron gas
The grand potential and the response of a phase-coherent confined noninteracting electron gas depend
sensitively on chemical potential or external parameter . We compute
their autocorrelation as a function of , and temperature. The result
is related to the short-time dynamics of the corresponding classical system,
implying in general the absence of a universal regime. Chaotic, diffusive and
integrable motions are investigated, and illustrated numerically. The
autocorrelation of the persistent current of a disordered mesoscopic ring is
also computed.Comment: 12 pages, 1 figure, to appear in Phys. Rev.
Orthogonality Catastrophe in Parametric Random Matrices
We study the orthogonality catastrophe due to a parametric change of the
single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian
is modeled by a suitable random matrix ensemble. We show that the overlap
between the original and the parametrically modified many-body ground states,
, taken as Slater determinants, decreases like , where is
the number of electrons in the systems, is a numerical constant of the
order of one, and is the deformation measured in units of the typical
distance between anticrossings. We show that the statistical fluctuations of
are largely due to properties of the levels near the Fermi energy.Comment: 12 pages, 8 figure
Effect of deconfinement on resonant transport in quantum wires
The effect of deconfinement due to finite band offsets on transport through
quantum wires with two constrictions is investigated. It is shown that the
increase in resonance linewidth becomes increasingly important as the size is
reduced and ultimately places an upper limit on the energy (temperature) scale
for which resonances may be observed.Comment: 6 pages, 6 postscript files with figures; uses REVTe
Universal parametric correlations in the transmission eigenvalue spectra of disordered conductors
We study the response of the transmission eigenvalue spectrum of disordered
metallic conductors to an arbitrary external perturbation. For systems without
time-reversal symmetry we find an exact non-perturbative solution for the
two-point correlation function, which exhibits a new kind of universal behavior
characteristic of disordered conductors. Systems with orthogonal and symplectic
symmetries are studied in the hydrodynamic regime.Comment: 10 pages, written in plain TeX, Preprint OUTP-93-36S (University of
Oxford), to appear in Phys. Rev. B (Rapid Communication
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
Manifestation of Quantum Chaos in Electronic Band Structures
We use semiconductors as an example to show that quantum chaos manifests
itself in the energy spectrum of crystals. We analyze the {\it ab initio} band
structure of silicon and the tight-binding spectrum of the alloy
, and show that some of their statistical properties obey the
universal predictions of quantum chaos derived from the theory of random
matrices. Also, the Bloch momenta are interpreted as external, tunable,
parameters, acting on the reduced (unit cell) Hamiltonian, in close analogy to
Aharonov-Bohm fluxes threading a torus. They are used in the investigation of
the parametric autocorrelator of crystal velocities. We find that our results
are in good agreement with the universal curves recently proposed by Simons and
coworkers.Comment: 15 pages with 6 Postscript figures included, RevTex-3, CMT-ERM/940
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