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Full counting statistics for noninteracting fermions: joint probability distributions.
1Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany.
Summary
This study simplifies calculating full counting statistics (FCS) for noninteracting electrons by presenting a new method for long-time contributions. New results for scattering matrices and charge distributions in Y junctions and quantum dots are derived.
Area of Science:
- Quantum transport phenomena
- Statistical mechanics of electrons
Background:
- Full counting statistics (FCS) is crucial for understanding electron transport.
- Calculating FCS for interacting subsystems is complex.
Purpose of the Study:
- To develop a simplified method for calculating the long-time contribution to the logarithm of the characteristic function in FCS.
- To derive new explicit results for determinants involving scattering matrices.
- To analyze the joint probability distribution of charges in specific electronic systems.
Main Methods:
- Analysis of joint probability distribution for noninteracting electrons.
- Development of a simplified method for leading-order long-time contributions.
- Calculation of determinants involving scattering matrices.
Main Results:
- A simplified method for calculating the long-time contribution to the logarithm of the characteristic function is presented.
- New explicit results for determinants involving scattering matrices are obtained.
- The joint probability distribution for charges in Y junctions and dots connected to four leads is discussed.
Conclusions:
- The new method simplifies previous approaches to FCS calculations.
- The findings provide explicit results for charge distributions in complex electronic systems.
- This work advances the understanding of quantum transport statistics.
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