Generalized hydrodynamics with dephasing noise

Abstract

We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the system based on a hydrodynamic formulation. This results in an additional term to the standard generalized hydrodynamics theory describing diffusive dynamics in the momentum space of the quasiparticles of the system, with a time-and momentum-dependent diffusion constant. Our analytical predictions are then benchmarked in the classical limit by comparison with a microscopic simulation of the nonlinear Schrödinger equation, showing perfect agreement. In the quantum case, our predictions agree with state-of-the-art numerical simulations of the anisotropic Heisenberg spin in the accessible regime of times and with bosonization predictions in the limit of small dephasing times and temperatures.

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

“…Generalizations of Eq. (17) to account for the presence of trapping potentials [26], diffusive corrections [43,[86][87][88][89], space-time variations of the interaction terms of the Hamiltonian [38] and Markovian coupling to an external bath [40] have been further developed.…”

“…[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].…”

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

“…In parallel, recent progress in the study of integrability applied to nonequilibrium systems has led to the formulation of 'generalized hydrodynamics' (GHD) [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66]. This is a systematic framework for treating the effective longwavelength fluctuations of integrable models, which is a convenient route to access their far-from-equilibrium transport and response properties [67,68].…”

Anisotropic Landau-Lifshitz model in discrete space-time

“…Concurrently, we have seen an increased theoretical interest in various facets of nonequilibrium physcis. Integrable systems have been in the spotlight lately [13][14][15][16][16][17][18][19][20][21][22], largely due to their inherent non-ergodic features [23][24][25][26] and anomalous transport properties [5,[27][28][29][30][31][32][33][34][35][36][37] as recently covered in a compilation of review articles [38][39][40][41][42][43]. The study of nonequilibrium properties in classical integrable dynamical systems of interacting particles or fields has received comparatively less attention [44][45][46][47][48][49][50][51].…”