Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion

Free energy fluxes and the Kubo–Martin–Schwinger relation

“…In other words, for every spatial component α, the charge vector g α • must lie on a plane perpendicular to β • . Equation (26), and its corollaries ( 27)-( 29) below, are our main results. As ( 26) is a consequence of the KMS equation as applied to the currents, which are the crucial ingredients for Eulerscale hydrodynamics, we will refer to it as the EKMS relation.…”

Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems

“…Consequently, the fluctuations of the time-integrated current depend on the whole trajectories of the quasiparticles, as expressed by Eqs. (46) and (47).…”

“…(6). ∂ /∂ s is specified by the flow equation (46) and (47). The second cumulant is related to the Gaussianity of the distribution close to the mean value and, from Eqs.…”

“…( 29), therefore providing an important consistency check of Eqs. (43) and (46). The expression of the third cumulant c 3 is related to the asymmetry or skewness of the distribution.…”

“…[14,15,[17][18][19][20][21][22][23][24][25], has been to the study of ballistic transport from the partitioning protocol initial inhomogeneous state, but the versatility of GHD allows to study various inhomogeneous setups such as the effect of confining potentials [26,27], bump-release protocols [28,29], correlation functions [30][31][32] and entanglement spreading [33][34][35][36][37]. Remarkably, the formalism can also be used to study nonintegrable systems, provided the integrability breaking is weak enough so that on large enough length and time scales, the conserved charges may be assumed not to be broken [26,[38][39][40][41][42][43][44][45][46][47].…”