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

Fluctuations of Conductance Peak Spacings in the Coulomb Blockade Regime: Role of Electron-Electron Interaction

We study influence of electron-electron interaction on statistics of Coulomb blockade peak spacings in disordered quantum dots. It is shown that the interaction combined with fluctuations of eigenfunctions of the Fermi sea, enhances the peak spacing fluctuations, in accordance with recent experiments. In addition, account of the spin degrees of freedom leads to a pronounced odd-even structure for weak interaction ($e^2/\epsilon \ll v_F$); in the opposite case ($e^2/\epsilon \gtrsim v_F$) this structure is washed out.Comment: REVTEX 4 pages, some changes made, 1 figure adde

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

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

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

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 $\ell$ larger than the system size, there are two distinct regimes of behaviour depending on the relative magnitudes of $\ell$ and an inelastic scattering length.Comment: 7 pages, Latex-type, EuroMacr, 4 Postscript figures, to appear in Europhys. Lett. 199

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 $\mu = tr U -1$ 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 $\mu \to 0$. 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 $\mu$. 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

Full Counting Statistics in Quantum Contacts

Full counting statistics is a fundamentally new concept in quantum transport. After a review of basic statistics theory, we introduce the powerful Green's function approach to full counting statistics. To illustrate the concept we consider a number of examples. For generic two-terminal contacts we show how counting statistics elucidates the common (and different) features of transport between normal and superconducting contacts. Finally, we demonstrate how correlations in multi-terminal structures are naturally included in the formalism.Comment: 20 pages, proceedings of Summer School/Conference on Functional Nanostructures, Karlsruhe (2003

Shot noise measurements in NS junctions and the semiclassical theory

We present a new analysis of shot noise measurements in normal metal-superconductor (NS) junctions [X. Jehl et al., Nature 405, 50 (2000)], based on a recent semiclassical theory. The first calculations at zero temperature assuming quantum coherence predicted shot noise in NS contacts to be doubled with respect to normal contacts. The semiclassical approach gives the first opportunity to compare data and theory quantitatively at finite voltage and temperature. The doubling of shot noise is predicted up to the superconducting gap, as already observed, confirming that phase coherence is not necessary. An excellent agreement is also found above the gap where the noise follows the normal case.Comment: 2 pages, revtex, 2 eps figures, to appear in Phys. Rev.