Counting Statistics of Non-Markovian Quantum Stochastic Processes
arXiv:0801.0661 · doi:10.1103/PhysRevLett.100.150601
Abstract
We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.
4+ pages, 2 figures, final version as published in Phys. Rev. Lett
References in corpus (19)
- Shot Noise in Mesoscopic Conductors
- Quantum state engineering with Josephson-junction devices
- Counting statistics of single-electron transport in a quantum dot
- Full Counting Statistics of Charge Transfer in Coulomb Blockade Systems
- Microscopic derivation of rate equations for quantum transport
- Fluctuation Theorems
- Environmental effects in the third moment of voltage fluctuations in a tunnel junction
- Integral fluctuation theorem for the housekeeping heat
- Measurement of Counting Statistics of Electron Transport in a Tunnel Junction
- Full Counting Statistics in Strongly Interacting Systems: Non-Markovian Effects
- Full counting statistics of nano-electromechanical systems
- Shot Noise Spectrum of Open Dissipative Quantum Two-level Systems
- Noise enhancement due to quantum coherence in coupled quantum dots
- Current noise in a vibrating quantum dot array
- Non-equilibrium Entanglement and Noise in Coupled Qubits
- Asymmetric Quantum Shot Noise in Quantum Dots
- Wide-band detection of the third moment of shot noise by a hysteretic Josephson junction
- Current noise spectrum of a quantum shuttle
- Spectrum of qubit oscillations from Bloch equations
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