Formulation of time-resolved counting statistics based on a positive-operator-valued measure

Area of Science:

• Quantum electronics
• Statistical mechanics
• Mesoscopic physics

Background:

• Full counting statistics (FCS) are crucial for understanding electron transport.
• Existing models often simplify noise correlations, particularly at high frequencies.
• Levitov-Lesovik formula provides a theoretical framework for current noise.

Purpose of the Study:

• To derive the full counting statistics of electronic current using a positive-operator-valued measure (POVM).
• To generalize existing theoretical frameworks to include finite-frequency noise correlations.
• To investigate the implications of quantum mechanics on high-frequency current noise.

Main Methods:

• Development of a theoretical framework based on positive-operator-valued measures.
• Analysis of the long-time limit to justify the Levitov-Lesovik formula.
• Incorporation of the projection postulate and quantum noise formulas for high-frequency analysis.

Main Results:

• A novel derivation of the full counting statistics of electronic current.
• Justification of the Levitov-Lesovik formula in the long-time limit.
• Identification of an additional white noise component at high frequencies, consistent with experimental data.

Conclusions:

• The proposed POVM approach offers a robust method for analyzing electronic current statistics.
• The study predicts an additional white noise component, suggesting new avenues for experimental verification.
• A simultaneous measurement of high- and low-frequency noise is proposed as a definitive experimental test.