Full counting statistics of a general quantum mechanical variable

We present here a quantum mechanical framework for defining the statistics of measurements of time integrals of A(t), A(t) being a quantum mechanical variable. This is a generalization of the so-called full counting statistics proposed earlier for DC electric currents. We develop an influence functional formalism that allows us to study the quantum system along with the measuring device thus fully accounting for the action of the detector on the system to be measured. We define the full counting statistics of an arbitrary variable by means of an evolution operator that relates initial and final density matrices of the measuring device. In this way we are able to resolve inconsistencies that occur in earlier definitions. We suggest two schemes whereby the so defined full statistics can be observed experimentally.Comment: 11 page

Fully Overheated Single-Electron Transistor

We consider the fully overheated single-electron transistor, where the heat balance is determined entirely by electron transfers. We find three distinct transport regimes corresponding to cotunneling, single-electron tunneling, and a competition between the two. We find an anomalous sensitivity to temperature fluctuations at the crossover between the two latter regimes that manifests in an exceptionally large Fano factor of current noise.Comment: 6 pages, 3 figures, includes Appendi

Coulomb Blockade due to Quantum Phase-Slips Illustrated with Devices

In order to illustrate the emergence of Coulomb blockade from coherent quantum phase-slip processes in thin superconducting wires, we propose and theoretically investigate two elementary setups, or "devices". The setups are derived from Cooper-pair box and Cooper-pair transistor, so we refer to them as QPS-box and QPS-transistor, respectively. We demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. Experimental realization of these devices will unambiguously prove the Coulomb blockade as an effect of coherence of phase-slip processes. We analyze the emergence of discrete charging in the limit strong phase-slips. We have found and investigated six distinct regimes that are realized depending on the relation between three characteristic energy scales: inductive and charging energy, and phase-slip amplitude. For completeness, we include a brief discussion of dual Josephson-junction devices

Current fluctuations in composite conductors: Beyond the second cumulant

Employing the non-linear $\sigma$-model we analyze current fluctuations in coherent composite conductors which contain a diffusive element in-between two tunnel barriers. For such systems we explicitly evaluate the frequency-dependent third current cumulant which also determines the leading Coulomb interaction correction to shot noise. Our predictions can be directly tested in future experiments.Comment: 6 pages, 1 figur

Inelastic Interaction Corrections and Universal Relations for Full Counting Statistics

We analyze in detail the interaction correction to Full Counting Statistics (FCS) of electron transfer in a quantum contact originating from the electromagnetic environment surrounding the contact. The correction can be presented as a sum of two terms, corresponding to elastic/inelastic electron transfer. Here we primarily focus on the inelastic correction. For our analysis, it is important to understand more general -- universal -- relations imposed on FCS only by quantum mechanics and statistics with no regard for a concrete realization of a contact. So we derive and analyze these relations. We reveal that for FCS the universal relations can be presented in a form of detailed balance. We also present several useful formulas for the cumulants. To facilitate the experimental observation of the effect, we evaluate cumulants of FCS at finite voltage and temperature. Several analytical results obtained are supplemented by numerical calculations for the first three cumulants at various transmission eigenvalues.Comment: 10 pages, 3 figure