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 (16)

• Modeling heat transport through completely positive maps
• Berry-Phase induced Heat Pumping and its Impact on the Fluctuation Theorem
• Adiabatic pumping through interacting quantum dots
• Directed flow in non-adiabatic stochastic pumps
• The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets
• Robust single-parameter quantized charge pumping
• 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
• Adiabatic pumping in the mixed-valence and Kondo regimes
• Phase coherence, inelastic scattering, and interaction corrections in pumping through quantum dots
• Charge and spin pumping through a double quantum dot
• Adiabatic Charge Pumping through Quantum Dots in the Coulomb Blockade Regime
• 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