Transport fluctuations in integrable models out of equilibrium

The physics of many-body systems out of equilibrium poses some of the most challenging questions in modern science. Particularly novel behaviour occurs in one dimension, where integrability often strongly affects the non-equilibrium physics, and numerous conservation laws constrain the natural relaxation to stationary states. For such integrable systems, a generalised hydro-dynamics (GHD) has recently been developed, which accounts for interacting ballistic currents. And yet, full characterisation of non-equilibrium states must go beyond relaxation processes and hydrodynamics to provide stronger organising principles.

For equilibrium systems, deep insights emerge from the analysis of fluctuations of thermodynamic quantities through statistical ensembles and free energies. Efforts to follow a similar approach out of equilibrium have employed large deviation theory and focused on the so-called large-deviation function, describing the rate of occurrence of rare, large fluctuations, which plays the role of an entropy. The related scaled cumulant generating function (SCGF) for full counting statistics plays the role of a free energy. Exact results for such functions in transport setups of truly interacting many-body models would provide a deeper understanding of non-equilibrium physics.

Exact transport SCGFs are known in non-equilibrium steady states (NESSs) of some stochastic classical gases such as exclusion processes, and can be understood within macroscopic fluctuation theory based on diffusive hydrodynamics. In a new pre-print, LML Fellow Rosemary Harris and colleagues report exact expressions for transport SCGFs in homogeneous stationary states of interacting one-dimensional integrable systems, including current-carrying NESSs. The expression applies to all models with large-scale dynamics governed by generalised hydro-dynamics, and to transport of all local conserved quantities they admit. This includes the Lieb-Liniger model which describes cold atomic gases  and many other quantum field theories, as well as integrable quantum chains, classical field theories, and classical gases such as the hard rod gas and soliton gases. The analytical approach they use involves a general new framework based on large deviation theory and Euler-scale linear fluctuating hydrodynamics, which gives access to exact SCGFs for ballistic transport. This approach is developed in a companion paper by two of the authors.

A pre-print of the paper is available at


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