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Theory of shot noise in hydrodynamic electron systems

Develop a theoretical treatment of shot noise in electron fluids operating in the hydrodynamic regime, specifying how current-fluctuation statistics depend on hydrodynamic parameters, geometry, and boundary conditions.

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Background

In hydrodynamic flow, carrier motion is strongly correlated, so the usual Poissonian picture of shot noise breaks down. Preliminary data suggest suppression of the Fano factor as systems approach the hydrodynamic regime, and quantum-critical cases have been analyzed, but a theory specifically for hydrodynamic electron fluids is missing. Such a framework would enable interpreting experiments and distinguishing hydrodynamic effects from ballistic or diffusive limits.

References

However, to our knowledge there is still no theoretical treatment of shot noise in hydrodynamic electron systems.

— Hydrodynamics of the electronic Fermi liquid: a pedagogical overview (2504.01249 - Hui et al., 1 Apr 2025) in Section “Current noise of hydrodynamic electrons”