Quantum generalized hydrodynamics of the tonks-girardeau gas: density fluctuations and entanglement entropy

We apply the theory of Quantum Generalized Hydrodynamics (QGHD) introduced in [Phys. Rev. Lett. 124, 140603 (2020)] to derive asymptotically exact results for the density fluctuations and the entanglement entropy of a one-dimensional trapped Bose gas in the Tonks-Girardeau (TG) or hard- core limit, after a trap quench from a double well to a single well. On the analytical side, the quadratic nature of the theory of QGHD is complemented with the emerging conformal invariance at the TG point to fix the universal part of those quantities. Moreover, the well-known mapping of hard-core bosons to free fermions, allows to use a generalized form of the Fisher-Hartwig conjecture to fix the non-trivial spacetime dependence of the ultraviolet cutoff in the entanglement entropy. The free nature of the TG gas also allows for more accurate results on the numerical side, where a higher number of particles as compared to the interacting case can be simulated. The agreement between analytical and numerical predictions is extremely good. For the density fluctuations, however, one has to average out large Friedel oscillations present in the numerics to recover such agreement.

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

We derive an exact formula for the scaled cumulant generating function of the time-integrated current associated to an arbitrary ballistically transported conserved charge. Our results rely on the Euler-scale description of interacting, many-body, integrable models out of equilibrium given by the generalized hydrodynamics, and on the large deviation theory. Crucially, our findings extend previous studies by accounting for inhomogeneous and dynamical initial states in interacting systems. We present exact expressions for the first three cumulants of the time-integrated current. Considering the non-interacting limit of our general expression for the scaled cumulant generating function, we further show that for the partitioning protocol initial state our result coincides with previous results of the literature. Given the universality of the generalized hydrodynamics, the expression obtained for the scaled cumulant generating function is applicable to any interacting integrable model obeying the hydrodynamic equations, both classical and quantum.

Thermodynamic Theory of Irreversible Processes and Generalized Hydrodynamics of Fluids

In this article, a review is presented of the thermodynamic theory of irreversible processes, based on the Clausius inequality representative of the literal forms of the second law of thermodynamics as stated by Kelvin and Clausius. Generalized hydrodynamic equations in conformation to the law are presented for transport processes in fluids removed far from equilibrium. They generalize the Navier--Stokes--Fourier hydrodynamics to flows of nonlinear irreversible processes. Keywords: thermodynamics of nonlinear irreversible processes; thermodynamic theory of nonlinear transport processes; generalized hydrodynamics; Boltzmann kinetic theory of nonlinear transport professes

Generalized hydrodynamics in complete box-ball system for $U_q(\widehat{sl}_n)$

We introduce the complete box-ball system (cBBS), which is an integrable cellular automaton on 1D lattice associated with the quantum group U_q(\widehat{sl}_n)Uq(sl̂n). Compared with the conventional (n-1)(n−1)-color BBS, it enjoys a remarkable simplification that scattering of solitons is totally diagonal. We also submit the cBBS to randomized initial conditions and study its non-equilibrium behavior by thermodynamic Bethe ansatz and generalized hydrodynamics. Excellent agreement is demonstrated between theoretical predictions and numerical simulation on the density plateaux generated from domain wall initial conditions including their diffusive broadening.