Inhomogeneous stationary states in the Heisenberg model

Valter L. Líbero, F A O de Souza

Jiadong Shi, Wenchao Ma, Xue‐Ke Song +2 more

Assa Auerbach

Marko Medenjak

The primary area, on which we focus in the thesis, are the out-of-equilibrium properties of quantum and classical systems. The playground we use to study those properties, are interacting integrable and solitonic systems, whose structure enables us to perform analytical calculations. In the context of the out-of-equilibrium physics we focus on two questions. The first problem is related to the set of stationary states in quantum systems. The question is especially important in the context of the homogeneous quantum quenches, since it makes possible the calculations of expectation values of local observables. The building blocks of stationary states are quasilocal conserved quantities which constitute the information that is preserved under the time evolution. In the first part of the thesis we deal with the construction of quasilocal conserved quantities in one dimensional anisotropic Heisenberg model and bosonic models. Quasilocal charges are put in the context of the standard theory of integrability, which in turn allows for the calculation of physical quantities. The second question we deal with are the transport properties of one dimensional systems. The connection between the local integrals of motion and ideal transport was established in 90's. Here we extend the connection to the diffusive transport. This enables us to obtain explicit lower bound on diffusion constant in Heisenberg model, which proves that the Heisenberg model is not an insulator at finite temperatures. In the last chapter we deal with the transport properties of classical celular automata. The first example we consider is the gas of charged hard core interacting particles, and the second one the gas of interacting solitons. Explicit solution of the dynamics of local observables allows for the explicit calculation of transport coeffcients, and the solution of the inhomogeneous quench problem. Despite their simplicity, the models exhibit wide range of transport phenomena ranging from insulating, through diffusive to ballistic transport.

Jay D. Mancini, Vassilios Fessatidis, Robert K. Murawski +2 more

Maurizio Fagotti

Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including ``quantum corrections'').