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Quantization and fractional quantization of currents in periodically driven stochastic systems. II. Full counting
Vladimir Y Chernyak1, John R Klein, Nikolai A Sinitsyn
1Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA.
The Journal of Chemical Physics
|April 24, 2012
Summary
Quantized currents in Markovian stochastic motion are linked to topological invariants in current counting statistics. This reveals robust quantization properties persisting to finite temperatures.
Area of Science:
- Statistical Physics
- Condensed Matter Physics
- Quantum Mechanics
Background:
- Markovian stochastic motion describes systems evolving randomly over time.
- Adiabatic driving involves slow changes in system parameters, preserving quantum states.
- Quantized currents are phenomena observed in systems with discrete, conserved quantities.
Purpose of the Study:
- To investigate the origin of quantized currents in driven stochastic systems.
- To establish a connection between quantized currents and topological invariants.
- To explore the temperature dependence of these topological properties.
Main Methods:
- Analysis of Markovian stochastic motion on finite graphs.
- Application of adiabatic and periodic driving to transition rates.
- Examination of current counting statistics and topological invariants.
Main Results:
- Quantized currents at low temperatures are shown to be manifestations of topological invariants.
- A framework for classifying topological properties of current counting statistics is proposed.
- Robust quantization of currents is extended to finite temperatures.
Conclusions:
- Topological invariants in current counting statistics explain quantized currents.
- The findings offer a new perspective on topological phenomena in driven systems.
- The research extends the understanding of robust current quantization to higher temperatures.
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