Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems II: Full Counting Statistics

Abstract

We study Markovian stochastic motion on a graph with finite number of nodes and adiabatically periodically driven transition rates. We show that, under general conditions, the quantized currents that appear at low temperatures are a manifestation of topological invariants in the counting statistics of currents. This observation provides an approach for classification of topological properties of the counting statistics, as well as for extensions of the phenomenon of the robust quantization of currents at low temperatures to the properties of the counting statistics which persist to finite temperatures.

18 pages, 5 figures

References in corpus (14)

• Artificial Brownian motors: Controlling transport on the nanoscale
• Berry-Phase induced Heat Pumping and its Impact on the Fluctuation Theorem
• Distributions of Waiting Times of Dynamic Single-Electron Emitters
• Conditional statistics of electron transport in interacting nanoscale conductors
• Geometrical Expression of Excess Entropy Production
• Towards Classification of Phase Transitions in Reaction--Diffusion Models
• Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
• The stochastic pump current and the non-adiabatic geometrical phase
• Phase transitions in full counting statistics for periodic pumping
• Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents
• Supersymmetry and fluctuation relations for currents in closed networks
• Fluctuation Relations for Current Components in Mesoscopic Electric Circuits
• Stochastic approach and fluctuation theorem for ion transport
• Geometric Universality of Currents

Cited by in corpus (11)

• Geometrical Pumping in Quantum Transport: Quantum Master Equation Approach
• Nonadiabatic Control of Geometric Pumping
• Geometrical Formulation of Adiabatic Pumping as a Heat Engine
• Gauge freedom in observables and Landsbergs nonadiabatic geometric phase: pumping spectroscopy of interacting open quantum systems
• Geometric Fluctuation Theorem
• Non-adiabatic effect in quantum pumping for a spin-boson system
• Unification and new extensions of the no-pumping theorems of stochastic pumps
• Fluctuation Relations For Adiabatic Pumping
• Hybrid models of molecular machines and the no-pumping theorem
• Stochastic Dynamics of Extended Objects in Driven Systems: I. Higher-Dimensional Currents in the Continuous Setting
• Geometric pumping induced by shear flow in dilute liquid crystalline polymer solutions