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Full-counting statistics of random transition-rate matrices.

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Area of Science:

  • Statistical mechanics
  • Quantum physics
  • Condensed matter physics

Background:

  • Understanding charge transport in mesoscopic systems is crucial.
  • Full-counting statistics provides detailed information about current fluctuations.
  • Random-matrix theory offers a powerful framework for analyzing complex systems.

Purpose of the Study:

  • To investigate the full-counting statistics of electric current in large open quantum systems.
  • To develop a theoretical method for calculating current-cumulant generating functions.
  • To explore the influence of system symmetries and counting schemes on transport properties.

Main Methods:

  • Application of random-matrix theory to transition-rate matrices.
  • Development of an expansion method based on inverse system size.
  • Ensemble averaging of current-cumulant generating functions.

Main Results:

  • A novel method for calculating ensemble-averaged current-cumulant generating functions was established.
  • The dependence of current statistics on system symmetries was elucidated.
  • The impact of different counting schemes on transport properties was analyzed.

Conclusions:

  • The developed method provides a robust framework for studying quantum transport in large systems.
  • Symmetry properties play a significant role in determining current fluctuations.
  • Further research can extend this approach to various quantum transport phenomena.