Geometrical Pumping in Quantum Transport: Quantum Master Equation Approach

Abstract

For an open quantum system, we investigate the pumped current induced by a slow modulation of control parameters on the basis of the quantum master equation and full counting statistics. We find that the average and the cumulant generating function of the pumped quantity are characterized by the geometrical Berry-phase-like quantities in the parameter space, which is associated with the generator of the master equation. From our formulation, we can discuss the geometrical pumping under the control of the chemical potentials and temperatures of reservoirs. We demonstrate the formulation by spinless electrons in coupled quantum dots. We show that the geometrical pumping is prohibited for the case of non-interacting electrons if we modulate only temperatures and chemical potentials of reservoirs, while the geometrical pumping occurs in the presence of an interaction between electrons.

References in corpus (47)

• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Scattering approach to parametric pumping
• An Adiabatic Quantum Electron Pump
• Experimental Realization of a Quantum Spin Pump
• Modeling heat transport through completely positive maps
• Berry-Phase induced Heat Pumping and its Impact on the Fluctuation Theorem
• An Adiabatic Quantum Pump of Spin Polarized Current
• Dissipation and noise in adiabatic quantum pumps
• Adiabatic charge pumping in almost open dots
• Adiabatic transport in nanostructures
• Geometry, Statistics and Asymptotics of Quantum Pumps
• Counting statistics for arbitrary cycles in quantum pumps
• AC-driven double quantum dots as spin pumps and spin filters
• Pumping spin with electrical fields
• Adiabatic pumping through interacting quantum dots
• Directed flow in non-adiabatic stochastic pumps
• Adiabatic quantum pump in the presence of external ac voltages
• Adiabatic Transfer of Electrons in Coupled Quantum Dots
• A Josephson Quantum Electron Pump
• The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets
• Adiabatic pumping through a quantum dot with coulomb interactions: A perturbation expansion in the tunnel coupling
• Effect of inelastic scattering on parametric pumping
• Robust single-parameter quantized charge pumping
• Counting Statistics of an Adiabatic Pump
• Geometrical Expression of Excess Entropy Production
• Pumping in an interacting quantum wire
• Nonequilibrium theory of Coulomb blockade in open quantum dots
• Resonance approximation and charge loading/unloading in adiabatic quantum pumping
• Charge pumping in carbon nanotube quantum dots
• Adiabatic charge and spin pumping through quantum dots with ferromagnetic leads
• Charge transport through quantum dots via time-varying tunnel couplings
• Adiabatic Pumping in Interacting Systems
• Dephasing in a quantum pump
• Adiabatic pumping in the mixed-valence and Kondo regimes
• Phase coherence, inelastic scattering, and interaction corrections in pumping through quantum dots
• Interaction-induced adiabatic non-linear transport
• Charge and spin pumping through a double quantum dot
• Adiabatic Charge Pumping through Quantum Dots in the Coulomb Blockade Regime
• Nonlinear adiabatic response of interacting quantum dots
• Current and fluctuation in a two-state stochastic system under non-adiabatic periodic perturbation
• Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents
• Noise-assisted classical adiabatic pumping in a symmetric periodic potential
• Quantized Charge Pumping through a Carbon Nanotube Double Quantum Dot
• Charge pumping and noise in a one-dimensional wire with weak electron-electron interactions
• Adiabatic pumping through a quantum dot in the Kondo regime: Exact results at the Toulouse limit
• Interference and interaction effects in adiabatic pumping through quantum dots
• Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems II: Full Counting Statistics

Cited by in corpus (43)

• Nonequilibrium Energy Transfer at Nanoscale: A Unified Theory from Weak to Strong Coupling
• Shortcuts to Adiabatic Pumping in Classical Stochastic Systems
• Nonadiabatic Control of Geometric Pumping
• Negative differential thermal conductance and heat amplification in a nonequilibrium triangle-coupled spin-boson system at strong coupling
• Geometric thermodynamic uncertainty relation in periodically driven thermoelectric heat engine
• A many-body approach to transport in quantum systems: From the transient regime to the stationary state
• Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems
• Electron pumping in the strong coupling and non-Markovian regime: A reaction coordinate mapping approach
• Non-adiabatic effect on the quantum heat flux control
• Interaction effect on adiabatic pump of charge and spin in quantum dot
• Geometrical Formulation of Adiabatic Pumping as a Heat Engine
• Real-time diagrammatic approach to current-induced forces: Application to quantum-dot based nanomotors
• Time-dependent Landauer-Büttiker approach to charge pumping in AC-driven graphene nanoribbons
• Gauge freedom in observables and Landsbergs nonadiabatic geometric phase: pumping spectroscopy of interacting open quantum systems
• Optimal tunneling enhances quantum photovoltaic effect in double quantum dots
• Geometric Thermoelectric Pump: Energy Harvesting beyond Seebeck and Pyroelectric Effects
• Geometric Fluctuation Theorem
• Geometric energy transport and refrigeration with driven quantum dots
• Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas
• Geometric phaselike effects in a quantum heat engine
• Geometric effects in non-equilibrium electron transfer statistics in adiabatically driven quantum junctions
• Full Counting Statistics of a Non-adiabatic Electron Pump
• Excess entropy production in quantum system: Quantum master equation approach
• Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport
• Energy pumping in electrical circuits under avalanche noise
• Statistics of an adiabatic charge pump
• Fluctuation Relations For Adiabatic Pumping
• Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics
• Temperature-driven and electrochemical-potential-driven adiabatic pumping via a quantum dot
• Nonequilibrium fluctuations of a driven quantum heat engine via machine learning
• A perturbative method for nonequilibrium steady state of open quantum systems
• Work statistics in slow thermodynamic processes
• Quantum-to-Classical Reduction of Quantum Master Equations
• Nonadiabaticity in spin pumping under relaxation
• Asymptotic expansion of the solution of the master equation and its application to the speed limit
• Quantum adiabatic pumping by modulating tunnel phase in quantum dots
• Quantum transport phenomena induced by time-dependent fields
• Pumped heat and charge statistics from Majorana braiding
• Demon driven by geometric phase
• Non-adiabatic quantum pumping by a randomly moving quantum dot
• Pumping current in a non-Markovian $N$-state model
• Optimal control over the full counting statistics in a non-adiabatic pump
• Geometric pumping induced by shear flow in dilute liquid crystalline polymer solutions