Full counting statistics for noninteracting fermions: Exact finite temperature results and generalized long time approximation

Exact numerical results for the full counting statistics (FCS) of a one-dimensional tight-binding model of noninteracting electrons are presented at finite temperatures using an identity recently presented by Abanov and Ivanov. A similar idea is used to derive a new expression for the cumulant generating function for a system consisting of two quasi-one-dimensional leads connected by a quantum dot in the long time limit. This provides a generalization of the Levitov-Lesovik formula for such systems.Comment: 17 pages, 6 figures, extended introduction, additional comment

Electrical transport through a single-electron transistor strongly coupled to an oscillator

We investigate electrical transport through a single-electron transistor coupled to a nanomechanical oscillator. Using a combination of a master-equation approach and a numerical Monte Carlo method, we calculate the average current and the current noise in the strong-coupling regime, studying deviations from previously derived analytic results valid in the limit of weak-coupling. After generalizing the weak-coupling theory to enable the calculation of higher cumulants of the current, we use our numerical approach to study how the third cumulant is affected in the strong-coupling regime. In this case, we find an interesting crossover between a weak-coupling transport regime where the third cumulant heavily depends on the frequency of the oscillator to one where it becomes practically independent of this parameter. Finally, we study the spectrum of the transport noise and show that the two peaks found in the weak-coupling limit merge on increasing the coupling strength. Our calculation of the frequency-dependence of the noise also allows to describe how transport-induced damping of the mechanical oscillations is affected in the strong-coupling regime.Comment: 11 pages, 9 figure

Full Current Statistics in Diffusive Normal-Superconductor Structures

We study the current statistics in normal diffusive conductors in contact with a superconductor. Using an extension of the Keldysh Green's function method we are able to find the full distribution of charge transfers for all temperatures and voltages. For the non-Gaussian regime, we show that the equilibrium current fluctuations are enhanced by the presence of the superconductor. We predict an enhancement of the nonequilibrium current noise for temperatures below and voltages of the order of the Thouless energy E_Th=D/L^2. Our calculation fully accounts for the proximity effect in the normal metal and agrees with experimental data. We demonstrate that the calculation of the full current statistics is in fact simpler than a concrete calculation of the noise.Comment: 4 pages, 2 figures (included

On a Factorization Formula for the Partition Function of Directed Polymers

We prove a factorization formula for the point-to-point partition function associated with a model of directed polymers on the space-time lattice Zd+1 . The polymers are subject to a random potential induced by independent identically distributed random variables and we consider the regime of weak disorder, where polymers behave diffusively. We show that when writing the quotient of the point-to-point partition function and the transition probability for the underlying random walk as the product of two point-to-line partition functions plus an error term, then, for large time intervals [0, t], the error term is small uniformly over starting points x and endpoints y in the sub-ballistic regime ‖ x- y‖ ≤ tσ , where σ< 1 can be arbitrarily close to 1. This extends a result of Sinai, who proved smallness of the error term in the diffusive regime ‖ x- y‖ ≤ t1 / 2 . We also derive asymptotics for spatial and temporal correlations of the field of limiting partition functions

On irreducibility of tensor products of evaluation modules for the quantum affine algebra

Every irreducible finite-dimensional representation of the quantized enveloping algebra U_q(gl_n) can be extended to the corresponding quantum affine algebra via the evaluation homomorphism. We give in explicit form the necessary and sufficient conditions for irreducibility of tensor products of such evaluation modules.Comment: 22 pages. Some references are adde

Ehrenfest-time dependence of counting statistics for chaotic ballistic systems

Transport properties of open chaotic ballistic systems and their statistics can be expressed in terms of the scattering matrix connecting incoming and outgoing wavefunctions. Here we calculate the dependence of correlation functions of arbitrarily many pairs of scattering matrices at different energies on the Ehrenfest time using trajectory based semiclassical methods. This enables us to verify the prediction from effective random matrix theory that one part of the correlation function obtains an exponential damping depending on the Ehrenfest time, while also allowing us to obtain the additional contribution which arises from bands of always correlated trajectories. The resulting Ehrenfest-time dependence, responsible e.g. for secondary gaps in the density of states of Andreev billiards, can also be seen to have strong effects on other transport quantities like the distribution of delay times.Comment: Refereed version. 15 pages, 14 figure

Quantum dot occupation and electron dwell time in the cotunneling regime

We present comparative measurements of the charge occupation and conductance of a GaAs/AlGaAs quantum dot. The dot charge is measured with a capacitively coupled quantum point contact sensor. In the single-level Coulomb blockade regime near equilibrium, charge and conductance signals are found to be proportional to each other. We conclude that in this regime, the two signals give equivalent information about the quantum dot system. Out of equilibrium, we study the inelastic-cotunneling regime. We compare the measured differential dot charge with an estimate assuming a dwell time of transmitted carriers on the dot given by h/E, where E is the blockade energy of first-order tunneling. The measured signal is of a similar magnitude as the estimate, compatible with a picture of cotunneling as transmission through a virtual intermediate state with a short lifetime

Two-dimensional array of diffusive SNS junctions with high-transparent interfaces

We report the first comparative study of the properties of two-dimensional arrays and single superconducting film - normal wire - superconducting film (SNS) junctions. The NS interfaces of our SNS junctions are really high transparent, for superconducting and normal metal parts are made from the same material (superconducting polycrystalline PtSi film). We have found that the two-dimensional arrays reveal some novel features: (i) the significant narrowing of the zero bias anomaly (ZBA) in comparison with single SNS junctions, (ii) the appearance of subharmonic energy gap structure (SGS), with up to n=16 (eV=\pm 2\Delta/n), with some numbers being lost, (iii) the transition from 2D logarithmic weak localization behavior to metallic one. Our experiments show that coherent phenomena governed by the Andreev reflection are not only maintained over the macroscopic scale but manifest novel pronounced effects as well. The behavior of the ZBA and SGS in 2D array of SNS junctions strongly suggests that the development of a novel theoretical approach is needed which would self-consistently take into account the distribution of the currents, the potentials, and the superconducting order parameter.Comment: RevTex, 5 pages, 5 figure

The Keldysh action of a multi-terminal time-dependent scatterer

We present a derivation of the Keldysh action of a general multi-channel time-dependent scatterer in the context of the Landauer-B\"uttiker approach. The action is a convenient building block in the theory of quantum transport. This action is shown to take a compact form that only involves the scattering matrix and reservoir Green functions. We derive two special cases of the general result, one valid when reservoirs are characterized by well-defined filling factors, the other when the scatterer connects two reservoirs. We illustrate its use by considering Full Counting Statistics and the Fermi Edge Singularity.Comment: 13 pages, 2 figures, submitted to PR

Finite-frequency counting statistics of electron transport: Markovian Theory

We present a theory of frequency-dependent counting statistics of electron transport through nanostructures within the framework of Markovian quantum master equations. Our method allows the calculation of finite-frequency current cumulants of arbitrary order, as we explicitly show for the second- and third-order cumulants. Our formulae generalize previous zero-frequency expressions in the literature and can be viewed as an extension of MacDonald's formula beyond shot noise. When combined with an appropriate treatment of tunneling, using, e.g. Liouvillian perturbation theory in Laplace space, our method can deal with arbitrary bias voltages and frequencies, as we illustrate with the paradigmatic example of transport through a single resonant level model. We discuss various interesting limits, including the recovery of the fluctuation-dissipation theorem near linear response, as well as some drawbacks inherent of the Markovian description arising from the neglect of quantum fluctuations.Comment: Accepted in New Journal of Physics. Updated tex