Research output: Contribution to journal › Article

**Fluctuations in ballistic transport from Euler hydrodynamics.** / Doyon, Benjamin; Myers, Jason.

Research output: Contribution to journal › Article

Doyon, B & Myers, J 2020, 'Fluctuations in ballistic transport from Euler hydrodynamics', *Annales Henri Poincare*, vol. 21, no. 1, pp. 255-302. https://doi.org/10.1007/s00023-019-00860-w

Doyon, B., & Myers, J. (2020). Fluctuations in ballistic transport from Euler hydrodynamics. *Annales Henri Poincare*, *21*(1), 255-302. https://doi.org/10.1007/s00023-019-00860-w

Doyon B, Myers J. Fluctuations in ballistic transport from Euler hydrodynamics. Annales Henri Poincare. 2020 Jan 14;21(1):255-302. https://doi.org/10.1007/s00023-019-00860-w

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title = "Fluctuations in ballistic transport from Euler hydrodynamics",

abstract = "We propose a general formalism, within large-deviation theory, giving access to the exact statistics of fluctuations of ballistically transported conserved quantities in homogeneous, stationary states. The formalism is expected to apply to any system with an Euler hydrodynamic description, classical or quantum, integrable or not, in or out of equilibrium. We express the exact scaled cumulant generating function (or full counting statistics) for any (quasi-)local conserved quantity in terms of the flux Jacobian. We show that the “extended fluctuation relations” of Bernard and Doyon follow from the linearity of the hydrodynamic equations, forming a marker of “freeness” much like the absence of hydrodynamic diffusion does. We show how an extension of the formalism gives exact exponential behaviours of spatio-temporal two-point functions of twist fields, with applications to order-parameter dynamical correlations in arbitrary homogeneous, stationary state. We explain in what situations the large-deviation principle at the basis of the results fail, and discuss how this connects with nonlinear fluctuating hydrodynamics. Applying the formalism to conformal hydrodynamics, we evaluate the exact cumulants of energy transport in quantum critical systems of arbitrary dimension at low but nonzero temperatures, observing a phase transition for Lorentz boosts at the sound velocity.",

author = "Benjamin Doyon and Jason Myers",

year = "2020",

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doi = "10.1007/s00023-019-00860-w",

language = "English",

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journal = "Annales Henri Poincare",

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TY - JOUR

T1 - Fluctuations in ballistic transport from Euler hydrodynamics

AU - Doyon, Benjamin

AU - Myers, Jason

PY - 2020/1/14

Y1 - 2020/1/14

N2 - We propose a general formalism, within large-deviation theory, giving access to the exact statistics of fluctuations of ballistically transported conserved quantities in homogeneous, stationary states. The formalism is expected to apply to any system with an Euler hydrodynamic description, classical or quantum, integrable or not, in or out of equilibrium. We express the exact scaled cumulant generating function (or full counting statistics) for any (quasi-)local conserved quantity in terms of the flux Jacobian. We show that the “extended fluctuation relations” of Bernard and Doyon follow from the linearity of the hydrodynamic equations, forming a marker of “freeness” much like the absence of hydrodynamic diffusion does. We show how an extension of the formalism gives exact exponential behaviours of spatio-temporal two-point functions of twist fields, with applications to order-parameter dynamical correlations in arbitrary homogeneous, stationary state. We explain in what situations the large-deviation principle at the basis of the results fail, and discuss how this connects with nonlinear fluctuating hydrodynamics. Applying the formalism to conformal hydrodynamics, we evaluate the exact cumulants of energy transport in quantum critical systems of arbitrary dimension at low but nonzero temperatures, observing a phase transition for Lorentz boosts at the sound velocity.

AB - We propose a general formalism, within large-deviation theory, giving access to the exact statistics of fluctuations of ballistically transported conserved quantities in homogeneous, stationary states. The formalism is expected to apply to any system with an Euler hydrodynamic description, classical or quantum, integrable or not, in or out of equilibrium. We express the exact scaled cumulant generating function (or full counting statistics) for any (quasi-)local conserved quantity in terms of the flux Jacobian. We show that the “extended fluctuation relations” of Bernard and Doyon follow from the linearity of the hydrodynamic equations, forming a marker of “freeness” much like the absence of hydrodynamic diffusion does. We show how an extension of the formalism gives exact exponential behaviours of spatio-temporal two-point functions of twist fields, with applications to order-parameter dynamical correlations in arbitrary homogeneous, stationary state. We explain in what situations the large-deviation principle at the basis of the results fail, and discuss how this connects with nonlinear fluctuating hydrodynamics. Applying the formalism to conformal hydrodynamics, we evaluate the exact cumulants of energy transport in quantum critical systems of arbitrary dimension at low but nonzero temperatures, observing a phase transition for Lorentz boosts at the sound velocity.

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U2 - 10.1007/s00023-019-00860-w

DO - 10.1007/s00023-019-00860-w

M3 - Article

VL - 21

SP - 255

EP - 302

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 1

ER -

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