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Large deviations of density fluctuations in the boundary-driven quantum symmetric simple inclusion process
Denis Bernard1, Tony Jin2, Stefano Scopa1
1l'École Normale Superieure, Laboratoire de Physique de , CNRS, ENS & Université PSL, Sorbonne Université, Université Paris Cité, Paris 75005, France.
Physical Review. E
|October 21, 2025
Summary
We show that the dynamics of two-point functions in the Quantum Symmetric Simple Inclusion Process (QSSIP) and Quantum Symmetric Simple Exclusion Process (QSSEP) coincide, despite differences in particle statistics. Local density fluctuations in both systems exhibit classical behavior.
Area of Science:
- Statistical mechanics
- Quantum many-body systems
- Non-equilibrium physics
Background:
- The Quantum Symmetric Simple Inclusion Process (QSSIP) models bosonic particles with stochastic hopping and boundary-driven gain/loss.
- The Quantum Symmetric Simple Exclusion Process (QSSEP) is an analogous fermionic system.
- Classical models like SSEP and SSIP differ due to bosonic statistics allowing multiple particles per site.
Purpose of the Study:
- To investigate the dynamics and fluctuations of the boundary-driven QSSIP.
- To compare QSSIP dynamics with its fermionic counterpart, QSSEP.
- To derive the large deviation function for density fluctuations in QSSIP and classical SSIP.
Main Methods:
- Analysis of the boundary-driven QSSIP.
- Comparison of two-point function dynamics between QSSIP and QSSEP.
- Exact derivation of the large deviation function for density fluctuations using the quantum formulation.
- Investigation of cumulant generating functions for local densities.
Main Results:
- The dynamics of two-point functions and their fluctuations coincide for QSSIP and QSSEP, despite differing particle statistics.
- An exact derivation of the large deviation function for density fluctuations in QSSIP and classical SSIP is provided.
- Local density fluctuations in both QSSIP and QSSEP are shown to be typically classical, converging to those of classical SSEP and SSIP.
Conclusions:
- The study reveals a surprising coincidence in the dynamics of quantum bosonic and fermionic systems concerning two-point functions.
- The research provides a method for deriving large deviation functions in related classical systems.
- This work supports the conjecture of classical transport fluctuations in noisy diffusive quantum many-body systems.
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