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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Understanding charge transport in quantum systems is crucial for developing quantum technologies.
  • Random unitary circuits provide a powerful framework for studying complex quantum dynamics.
  • Full counting statistics offer a detailed probe of charge transfer fluctuations.

Purpose of the Study:

  • To investigate the full counting statistics of charge transport in U(1)-symmetric random unitary circuits.
  • To analyze charge transfer fluctuations in systems with initial chemical potential imbalance.
  • To explore the connection between quantum transport and classical stochastic processes.

Main Methods:

  • Employing an effective replica statistical mechanics model.
  • Mapping the quantum circuit to an emergent classical stochastic process.
  • Utilizing matrix-product state calculations for validation.

Main Results:

  • Charge transfer fluctuations in random unitary circuits approach those of the symmetric exclusion process at long times.
  • Subleading $t^{-1/2}$ quantum corrections to charge transfer fluctuations were identified.
  • The emergent classical stochastic process is valid for large on-site Hilbert space dimensions.

Conclusions:

  • Quantum charge transport in these circuits exhibits classical-like behavior at long times.
  • The findings connect quantum dynamics to classical nonequilibrium statistical mechanics.
  • The study provides a theoretical framework and computational validation for charge transport in quantum circuits.