Exact time-correlation functions of quantum Ising chain in a kicking transversal magnetic field

Spectral analysis of the {\em adjoint} propagator in a suitable Hilbert space (and Lie algebra) of quantum observables in Heisenberg picture is discussed as an alternative approach to characterize infinite temperature dynamics of non-linear quantum many-body systems or quantum fields, and to provide a bridge between ergodic properties of such systems and the results of classical ergodic theory. We begin by reviewing some recent analytic and numerical results along this lines. In some cases the Heisenberg dynamics inside the subalgebra of the relevant quantum observables can be mapped explicitly into the (conceptually much simpler) Schr\" odinger dynamics of a single one-(or few)-dimensional quantum particle. The main body of the paper is concerned with an application of the proposed method in order to work out explicitly the general spectral measures and the time correlation functions in {\em a quantum Ising spin 1/2 chain in a periodically kicking transversal magnetic field}, including the results for the simpler autonomous case of a static magnetic field in the appropriate limit. The main result, being a consequence of a purely continuous non-trivial part of the spectrum, is that the general time-correlation functions decay to their saturation values as $t^{-3/2}$.Comment: 12 pages with 4 eps-figure

Quantum invariants of motion in a generic many-body system

Dynamical Lie-algebraic method for the construction of local quantum invariants of motion in non-integrable many-body systems is proposed and applied to a simple but generic toy model, namely an infinite kicked $t-V$ chain of spinless fermions. Transition from integrable via {pseudo-integrable (\em intermediate}) to quantum ergodic (quantum mixing) regime in parameter space is investigated. Dynamical phase transition between ergodic and intermediate (neither ergodic nor completely integrable) regime in thermodynamic limit is proposed. Existence or non-existence of local conservation laws corresponds to intermediate or ergodic regime, respectively. The computation of time-correlation functions of typical observables by means of local conservation laws is found fully consistent with direct calculations on finite systems.Comment: 4 pages in REVTeX with 5 eps figures include

Charge and spin current statistics of the open Hubbard model with weak coupling to the environment

Based on generalization and extension of previous work [Phys. Rev. Lett. {\bf 112}, 067201 (2014)] to multiple independent markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. The physical results are related to those for the $XXZ$ model in the analogous setup implying a certain universality which potentially holds in this class of nonequilibrium models.Comment: 10 pages, 1 figur

Generation of entanglement in regular systems

We study dynamical generation of entanglement in bipartite quantum systems, characterized by purity (or linear entropy), and caused by the coupling between the two subsystems. Explicit semiclassical theory of purity decay is derived for integrable classical dynamics of the uncoupled system, and for localized (general Gaussian wave-packet) initial states. Purity decays as an algebraic function of time times strength of perturbation, independently of the Planck's constant.Comment: 4 pages, 3 figure