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Emergence of Navier-Stokes Hydrodynamics in Chaotic Quantum Circuits
Hansveer Singh1,2, Ewan McCulloch3, Sarang Gopalakrishnan3
1University of Massachusetts, Department of Physics, Amherst, Massachusetts 01003, USA.
Physical Review Letters
|June 27, 2025
Summary
We developed chaotic quantum circuits with conserved particle current to efficiently compute viscosity. This method bypasses complex simulations for strongly interacting 2D quantum systems.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Nonintegrable quantum circuits exhibit chaotic behavior.
- Conserved particle current leads to finite Drude weight.
- Long-wavelength hydrodynamics are described by Navier-Stokes equations.
Purpose of the Study:
- To construct an ensemble of 2D nonintegrable quantum circuits.
- To investigate transport coefficients, specifically viscosity, in these systems.
- To develop an efficient method for computing viscosity in strongly interacting quantum systems.
Main Methods:
- Ensemble construction of 2D nonintegrable quantum circuits.
- Analysis of circuit-to-circuit fluctuations.
- Mapping circuit-averaged transport coefficients to a classical Markov process.
Main Results:
- Demonstrated negligible circuit-to-circuit fluctuations.
- Showed that ensemble-averaged transport coefficients represent typical circuit values.
- Established an efficient computational method for viscosity.
Conclusions:
- The proposed construction allows for efficient viscosity computation in strongly interacting chaotic 2D quantum systems.
- The mapping to classical Markov processes simplifies the analysis of quantum transport.
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