Non-Markovian Dynamics in the Theory of Full Counting Statistics
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Full counting statistics (FCS) of charge transfer through mesoscopic devices has become a significant field of research, no longer only being of theoretical interest, but recently also encompassing a number of experimental studies probing the distribution of electrons transported through nanoscopic structures 1. In recent years, the question of how decoherence in coherently coupled quantum dot systems affects the FCS has been of particular interest 2. Conventionally, the FCS of transport through Coulomb-blockade devices is explained using Markovian equations of motion 3. This approach relies on finding the analytic dependence of an extremal eigenvalue on the counting field a task that might be highly non-trivial for systems with several states involved in the transport. We circumvented this technical problem by developing an abstract perturbation theory using super-operators which enables the calculation of the current cumulants for systems exhibiting Markovian dynamics with, in principle, any number of states 4.
Interactions with additional degrees of freedom, e.g. a heat bath, may, however, lead to non-Markovian dynamics with clear signatures in the higher-order moments of the FCS as was recently demonstrated in Ref. 5. We combine our perturbative method from Ref. 4 with the approach developed in Ref. 5 and present a general theory for the FCS of systems governed by non-Markovian equations of motion 6. The theory is again applicable to systems with any number of states, and we calculate the current cumulants of transport through coherently coupled quantum dots, where interactions with a heat bath introduce memory effects. We extend our discussions to quantum dot systems with coupling to a nanomechanical resonator or a nearby charge detector 7 and show how the experimental and/or theoretical results for the FCS of these very different systems can all be understood in terms of a new unified interpretation based on non-Markovian dynamics 6.
References:
1) S. Gustavsson et al., Counting Statistics of Single-Electron Transport in a Quantum Dot, Phys. Rev. Lett. 96, 076605 (2006). T. Fujisawa et al., Bidirectional Counting of Single Electrons, Science 312, 1634 (2006).\\
2) G. Kiesslich et al., Counting statistics and decoherence in coupled quantum dots, Phys. Rev. B 73, 033312 (2006). R. Aguado and T. Brandes, Shot Noise Spectrum of Open Dissipative Quantum Two-Level Systems, Phys. Rev. Lett. 92, 206601 (2004). \\
3) D. A. Bagrets and Yu. V. Nazarov, Full counting statistics of charge transfer in Coulomb blockade structures, Phys. Rev. B 67, 085316 (2003). \\
4) C. Flindt, T. Novotný, and A.-P. Jauho, Full counting statistics of nano-electromechanical systems, Europhys. Lett. 69, 475 (2005).\\
5) A. Braggio, J. Koenig, and R. Fazio, Full Counting Statistics in Strongly Interacting Systems: Non-markovian Effects, Phys. Rev. Lett. 96, 026805 (2006).\\
6) C. Flindt, A. Braggio, T. Novotný, M. Sassetti, and A.-P. Jauho, Full counting statistics of non-Markovian systems, in preparation (2007).\\
7) F. Haupt et al., Anomalous suppression of the shot noise in a nanoelectromechanical system, Phys. Rev. B 74, 205328 (2006). S. Gustavsson et al., Measurements of higher order noise correlations in a quantum dot with a finite bandwidth detector, cond-mat/0607192 (2006).