125 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
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
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
Bosonization for disordered and chaotic systems
Using a supersymmetry formalism, we reduce exactly the problem of electron
motion in an external potential to a new supermatrix model valid at all
distances. All approximate nonlinear sigma models obtained previously for
disordered systems can be derived from our exact model using a coarse-graining
procedure. As an example, we consider a model for a smooth disorder and
demonstrate that using our approach does not lead to a 'mode-locking' problem.
As a new application, we consider scattering on strong impurities for which the
Born approximation cannot be used. Our method provides a new calculational
scheme for disordered and chaotic systems.Comment: 4 pages, no figure, REVTeX4; title changed, revision for publicatio
A minimal approach for the local statistical properties of a one-dimensional disordered wire
We consider a one-dimensional wire in gaussian random potential. By treating
the spatial direction as imaginary time, we construct a `minimal'
zero-dimensional quantum system such that the local statistical properties of
the wire are given as products of statistically independent matrix elements of
the evolution operator of the system. The space of states of this quantum
system is found to be a particular non-unitary, infinite dimensional
representation of the pseudo-unitary group, U(1,1). We show that our
construction is minimal in a well defined sense, and compare it to the
supersymmetry and Berezinskii techniques.Comment: 10 pages, 0 figure
Field Theory of Mesoscopic Fluctuations in Superconductor/Normal-Metal Systems
Thermodynamic and transport properties of normal disordered conductors are
strongly influenced by the proximity of a superconductor. A cooperation between
mesoscopic coherence and Andreev scattering of particles from the
superconductor generates new types of interference phenomena. We introduce a
field theoretic approach capable of exploring both averaged properties and
mesoscopic fluctuations of superconductor/normal-metal systems.
As an example the method is applied to the study of the level statistics of a
SNS-junction.Comment: 4 pages, REVTEX, two eps-figures included; submitted to JETP letter
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