Effective fluctuation theorems for electron transport in a double quantum dot coupled to a quantum point contact

Abstract

A theoretical study is reported of electron transport at finite temperature in a double quantum dot (DQD) capacitively coupled to a quantum point contact (QPC). Starting from a Hamiltonian model, a master equation is obtained for the stochastic process taking place in the DQD while the QPC is at or away from equilibrium, allowing us to study the backaction of the QPC onto the DQD. The QPC is treated non-perturbatively in our analysis. Effective fluctuation theorems are established for the full counting statistics of the DQD current under different limiting conditions. These fluctuation theorems hold with respect to an effective affinity characterizing the nonequilibrium environment of the DQD and differing from the applied voltage if the QPC is out of equilibrium. The effective affinity may even change its sign if the Coulomb drag of the QPC reverses the DQD current. The thermodynamic implications of the effective fluctuation theorems are discussed.

References in corpus (16)

• The large deviation approach to statistical mechanics
• Stochastic thermodynamics under coarse-graining
• Thermodynamics of a physical model implementing a Maxwell demon
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field
• Frequency-selective single photon detection using a double quantum dot
• Measurement of finite-frequency current statistics in a single-electron transistor
• Electron counting in quantum dots
• Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula
• Scattering matrix approach to the description of quantum electron transport
• Fluctuation relations and coarse-graining
• Inelastic Interaction Corrections and Universal Relations for Full Counting Statistics
• Coulomb drag in quantum circuits
• Incomplete current fluctuation theorems for a four-terminal model
• A low-dimensional detector model for full counting statistics: Trajectories, Back-Action, and Fidelity
• Fluctuation Relations for Current Components in Mesoscopic Electric Circuits

Cited by in corpus (19)

• Coulomb drag
• Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
• Effective thermodynamics for a marginal observer
• An electronic Maxwell demon in the coherent strong-coupling regime
• Effective fluctuation and response theory
• Universal anomalous fluctuations in charged single-file systems
• Extreme reductions of entropy in an electronic double dot
• Double quantum dot coupled to a quantum point contact: A stochastic thermodynamics approach
• Quantum transport, master equations, and exchange fluctuations
• Stochastic thermodynamics based on incomplete information: Generalized Jarzynski equality with measurement errors with or without feedback
• On entropy production in nonequilibrium systems
• Monitoring quantum transport: Backaction and measurement correlations
• Transmission from reverse reaction coordinate mappings
• Capacitively coupled nano conductors: Ratchet currents and exchange fluctuation relations
• Non-equilibrium version of the Einstein relation
• Controlling quantum flux through measurement: an idealised example
• Distinguishing coherent from incoherent charge transport in linear triple quantum dots
• Effective Affinity for Generic Currents in Markov Processes
• Fluctuation theorem for quantum electron transport in mesoscopic circuits