# Quantization and fractional quantization of currents in periodically driven stochastic systems. II. Full counting statistics.

@article{Chernyak2012QuantizationAF, title={Quantization and fractional quantization of currents in periodically driven stochastic systems. II. Full counting statistics.}, author={Vladimir Y. Chernyak and John R. Klein and Nikolai A. Sinitsyn}, journal={The Journal of chemical physics}, year={2012}, volume={136 15}, pages={ 154108 } }

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…

## 17 Citations

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## References

SHOWING 1-10 OF 38 REFERENCES

Quantization and fractional quantization of currents in periodically driven stochastic systems. I. Average currents.

- Physics, MedicineThe Journal of chemical physics
- 2012

It is shown that under general conditions, the currents in the system on average become quantized or fractionally quantized for adiabatic driving at sufficiently low temperature and the quantitative theory of this quantization is developed in terms of topological invariants.

Phase transitions in full counting statistics for periodic pumping

- Physics, Mathematics
- 2010

We discuss the problem of full counting statistics for periodic pumping. The probability generating function is usually defined on a circle of the "physical" values of the counting parameter, with…

Discrete changes of current statistics in periodically driven stochastic systems

- Mathematics, Physics
- 2010

We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the…

Non-Equilibrium Thermodynamics and Topology of Currents

- Mathematics, Physics
- 2009

In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of…

The geometric universality of currents

- Mathematics, Physics
- 2011

We discuss a non-equilibrium statistical system on a graph or network. Particles are injected, interact with each other, and traverse and leave the graph in a stochastic manner. We show that under…

Counting statistics of an adiabatic pump

- Physics, MedicinePhysical review letters
- 2000

We use the Schwinger-Keldysh formalism to derive the charge counting statistics of an adiabatic pump based on an open quantum dot. The distribution function of the transmitted charge in terms of the…

Current fluctuations and statistics during a large deviation event in an exactly solvable transport model

- Mathematics, Physics
- 2009

We study the distribution of the time-integrated current in an exactly solvable toy model of heat conduction, both analytically and numerically. The simplicity of the model allows us to derive the…

Robust quantization of a molecular motor motion in a stochastic environment.

- Physics, MedicineThe Journal of chemical physics
- 2009

The pumping-quantization theorem (PQT) is formulated that identifies the conditions for robust integer quantized behavior of a periodically driven molecular machine.

The Berry phase and the pump flux in stochastic chemical kinetics

- Physics
- 2007

We study a classical two-state stochastic system in a sea of substrates and products (absorbing states), which can be interpreted as a single Michaelis-Menten catalyzing enzyme or as a channel on a…

Fluctuation statistics in networks: A stochastic path integral approach

- Mathematics, Physics
- 2004

We investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors. The nodes carry generalized charge that may be randomly transferred from one node to…