Field-Theory Approaches to Nonequilibrium Dynamics

Gert Aarts A

S. M. Alamoudi

Philip R. Johnson

Christian Gramsch, Karsten Balzer, Martin Eckstein +1 more

We derive an exact mapping from the action of nonequilibrium dynamical mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with time-dependent parameters, which can be solved numerically by exact diagonalization. The representability of the nonequilibrium DMFT action by a SIAM is established as a rather general property of nonequilibrium Green functions. We also obtain the nonequilibrium DMFT equations using the cavity method alone. We show how to numerically obtain the SIAM parameters using Cholesky or eigenvector matrix decompositions. As an application, we use a Krylov-based time propagation method to investigate the Hubbard model in which the hopping is switched on, starting from the atomic limit. Possible future developments are discussed.

Hugo U. R. Strand, Martin Eckstein, Philipp Werner

We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambureal-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory andstrong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory capturesnot only dynamical transitions but also damping and thermalization effects at finite temperature. We applythe formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamicalproperties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well aslong-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium“phase diagrams” that map out the different dynamical regimes.

知司 山田, Takao Ohta, Kyozi Kawasaki