170 research outputs found
Fermi gas response to time-dependent perturbations
We describe the Riemann-Hilbert (RH) approach to computing the long-time
response of a Fermi gas to a time-dependent perturbation. The approach maps the
problem onto a non-commuting RH problem. The method is non-perturbative, quite
general and can be used to compute the Fermi gas response in driven (out of
equilibrium) as well as equilibrium systems. We illustrate the power of the
method by rederiving standard results for the core-hole and open-line Greens
functions for the equilibrium Fermi edge singularity (FES) problem. We then
show that the case of the non-separable potential can be solved
non-perturbatively with no more effort than for the separable case. We compute
the corresponding results for a biased (non-equilibrium) model tunneling
device, similar to those used in single photon detectors, in which a photon
absorption process can significantly change the conductance of the barrier. For
times much larger than the inverse bias across the device, the response of the
Fermi gases in the two electrodes shows that the equilibrium Fermi edge
singularity is smoothed, shifted in frequency and becomes
polarity-dependent.These results have a simple interpretation in terms of known
results for the equilibrium case but with (in general complex-valued)
combinations of elements of the scattering matrix replacing the equilibrium
phase shifts. We also consider the shot noise spectrum of a tunnel junction
subject to a time-dependent bias and demonstrate that the calculation is
essentially the same as for the FES problem. For the case of a periodically
driven device we show that the noise spectrum for the Coherent States of
Alternating Current can be easily obtained using this approach.Comment: 15 page
Interface dependence of the Josephson-current fluctuations in short SNS junctions
We discuss the dependence of the Josephson current correlations in mesoscopic
superconductor/normal-conductor/superconductor (SNS) devices on the
transparency of the superconductor/normal-conductor (SN) interfaces. Focusing
on short junctions we apply the supersymmetry method to construct an effective
field theory for mesoscopic SNS devices which is evaluated in the limit of
highly and weakly transparent interfaces. We show that the two-point
Josephson-current correlator differs by an universal factor 2 in these two
cases.Comment: 5 pages, 1figure, version accepted by PR
From clean to diffusive mesoscopic systems: A semiclassical approach to the magnetic susceptibility
We study disorder-induced spectral correlations and their effect on the
magnetic susceptibility of mesoscopic quantum systems in the non-diffusive
regime. By combining a diagrammatic perturbative approach with semiclassical
techniques we perform impurity averaging for non-translational invariant
systems. This allows us to study the crossover from clean to diffusive systems.
As an application we consider the susceptibility of non-interacting electrons
in a ballistic microstructure in the presence of weak disorder. We present
numerical results for a square billiard and approximate analytic results for
generic chaotic geometries. We show that for the elastic mean free path
larger than the system size, there are two distinct regimes of behaviour
depending on the relative magnitudes of and an inelastic scattering
length.Comment: 7 pages, Latex-type, EuroMacr, 4 Postscript figures, to appear in
Europhys. Lett. 199
The effect of Fermi surface curvature on low-energy properties of fermions with singular interactions
We discuss the effect of Fermi surface curvature on long-distance/time
asymptotic behaviors of two-dimensional fermions interacting via a gapless mode
described by an effective gauge field-like propagator. By comparing the
predictions based on the idea of multi-dimensional bosonization with those of
the strong- coupling Eliashberg approach, we demonstrate that an agreement
between the two requires a further extension of the former technique.Comment: Latex, 4+ pages. Phys. Rev. Lett., to appea
Fermi edge singularity in a non-equilibrium system
We report exact results for the Fermi Edge Singularity in the absorption
spectrum of an out-of-equilibrium tunnel junction. We consider two metals with
chemical potential difference V separated by a tunneling barrier containing a
defect, which exists in one of two states. When it is in its excited state,
tunneling through the otherwise impermeable barrier is possible. We find that
the lineshape not only depends on the total scattering phase shift as in the
equilibrium case but also on the difference in the phase of the reflection
amplitudes on the two sides of the barrier. The out-of-equilibrium spectrum
extends below the original threshold as energy can be provided by the power
source driving current across the barrier. Our results have a surprisingly
simple interpretation in terms of known results for the equilibrium case but
with (in general complex-valued) combinations of elements of the scattering
matrix replacing the equilibrium phase shifts.Comment: 4 page
Role of divergence of classical trajectories in quantum chaos
We study logarithmical in effects in the statistical description of
quantum chaos. We found analytical expressions for the deviations from the
universality in the weak localization corrections and the level statistics and
showed that the characteristic scale for these deviations is the Ehrenfest
time, , where is the Lyapunov exponent
of the classical motion.Comment: 4 pages, no figure
Nonequilibrium kinetics of a disordered Luttinger liquid
We develop a kinetic theory for strongly correlated disordered
one-dimensional electron systems out of equilibrium, within the Luttinger
liquid model. In the absence of inhomogeneities, the model exhibits no
relaxation to equilibrium. We derive kinetic equations for electron and plasmon
distribution functions in the presence of impurities and calculate the
equilibration rate . Remarkably, for not too low temperature and bias
voltage, is given by the elastic backscattering rate, independent of
the strength of electron-electron interaction, temperature, and bias.Comment: 4 pages, 3 figures, revised versio
Quantum Chaos and Random Matrix Theory - Some New Results
New insight into the correspondence between Quantum Chaos and Random Matrix
Theory is gained by developing a semiclassical theory for the autocorrelation
function of spectral determinants. We study in particular the unitary operators
which are the quantum versions of area preserving maps. The relevant Random
Matrix ensembles are the Circular ensembles. The resulting semiclassical
expressions depend on the symmetry of the system with respect to time reversal,
and on a classical parameter where U is the classical 1-step
evolution operator. For system without time reversal symmetry, we are able to
reproduce the exact Random Matrix predictions in the limit . For
systems with time reversal symmetry we can reproduce only some of the features
of Random Matrix Theory. For both classes we obtain the leading corrections in
. The semiclassical theory for integrable systems is also developed,
resulting in expressions which reproduce the theory for the Poissonian ensemble
to leading order in the semiclassical limit.Comment: LaTeX, 16 pages, to appear in a special issue of Physica D with the
proceedings of the workshop on "Physics and Dynamics Between Chaos, Order,
and Noise", Berlin, 199
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