Ballistic macroscopic fluctuation theory

Abstract

We introduce a new universal framework describing fluctuations and correlations in quantum and classical many-body systems, at the Euler hydrodynamic scale of space and time. The framework adapts the ideas of the conventional macroscopic fluctuation theory (MFT) to systems that support ballistic transport. The resulting “ballistic MFT” (BMFT) is solely based on the Euler hydrodynamics data of the many-body system. Within this framework, mesoscopic observables are classical random variables depending only on the fluctuating conserved densities, and Euler-scale fluctuations are obtained by deterministically transporting thermodynamic fluctuations via the Euler hydrodynamics. Using the BMFT, we show that long-range correlations in space generically develop over time from long-wavelength inhomogeneous initial states in interacting models. This result, which we verify by numerical calculations, challenges the long-held paradigm that at the Euler scale, fluid cells may be considered uncorrelated. We also show that the Gallavotti-Cohen fluctuation theorem for non-equilibrium ballistic transport follows purely from time-reversal invariance of the Euler hydrodynamics. We check the validity of the BMFT by applying it to integrable systems, and in particular the hard-rod gas, with extensive simulations that confirm our analytical results.

Entanglement Rényi entropies from ballistic fluctuation theory: The free fermionic case

“…But rather, it is based on the study of long-range correlations that such pairs give rise to after quenches. It has not been appreciated until now that quenches give rise to long-range spatial correlations , of the type found recently in non-equilibrium, longwavelength states [35,38]. These long-range correlations are generically seen by observables supported on regions of space that are large enough; specifically, with a ballistic scaling of the region's length x with respect to the time t since the quench.…”

“…It applies to generic systems with space-translation invariant dynamics and interaction range that is short enough. It has been developed originally for states that are spacetime stationary and clustering in space, but many of the ideas have been extended to more general situations [34,35].…”

“…We will explain how simple ideas based on the principles explained in [24] allow us to nevertheless use the BFT. We mention that long-range correlations can also, in principle, be accounted for directly by using the more sophisticated ballistic macroscopic fluctuation theory (BMFT) [35], which we leave for further studies.…”

“…A precise description of states with long-range correlations is more involved, see e.g. [35,38]. But the concept of MES is still useful in these situations, as, nevertheless, averages of all local observables, or observables supported on regions smaller than the correlation range, still are described by (5).…”

Mesoscopic impurities in generalized hydrodynamics

“…To perform the microscopic hard-rod simulation with an external potential, a standard molecular dynamics algorithm was used (see, for instance, [60]). (For simulating hard rods without external potential, there is a more efficient algorithm [58,[61][62][63]). For a given L, the hard rods were distributed randomly according to their initial distribution ρ(0, x macro , λ) = 1 2π 1 dr (x macro )n(0, x macro , λ), and then they were evolved time step by time step with ∆t micro = 0.01.…”