Open Systems & Information Dynamics

We consider the most general Gaussian quantum Markov semigroup on a one-mode Fock space, discuss its construction from the generalized GKSL representation of the generator. We prove the known explicit formula on Weyl operators, characterize irreducibility and its equivalence to a Hörmander type condition on commutators and establish necessary and sufficient conditions for existence and uniqueness of normal invariant states. We illustrate these results by applications to the open quantum oscillator and the quantum Fokker-Planck model.

The appearance of decoherence-recoherence events is analyzed in a dephasing model of a qubit which interacts with a bosonic environment. The initial condition is prepared from the thermal state of the whole system by performing a nonselective measurement on the qubit. Decoherence-recoherence events appear in the reduced dynamics of the qubit uniquely if special nonselective preparation measurements are adopted and the spectral density of the system fulfills determined conditions. General lower bounds are found for the number of decoherence-recoherence events in terms of the properties of the measurement scheme and of the spectral density. The number is finite for canonical spectral densities which are super-ohmic, perturbed super-ohmic, or ohmic at low frequencies and are arbitrarily tailored at high frequencies. The number is infinite in the sub-ohmic regime and for perturbations of the sub-ohmic or ohmic regime. Decoherence-recoherence times are evaluated, analytically and numerically, for ohmic-like spectral densities with exponential high-frequency cutoffs.

A Hamiltonian $H$, with locally smeared Ising-type s-d exchange between s-electrons and magnetic impurities, in a dilute magnetic alloy, is investigated. The Feynman-Kac theorem, Laplace expansion and Bogolyubov inequality are applied to obtain a lower and upper bound (lb and ub) on the system’s free energy per conducting electron $f(H,\beta )$. The two bounds differ, in the infinite-volume limit by a term $\mathrm{\text{lt}}>0$, linear in impurity concentration: lb$=f(h,\beta )-\mathrm{\text{lt}}$, ub$=f(h,\beta )$, $h$ denoting the Hamiltonian of the approximating mean-field s-d system. $h$ represents randomly positioned impurities interacting with a mean field implemented by the gas of conduction s-electrons, the latter interacting with the field of barriers and wells (according to the s-electron’s spin orientation) localized at the impurity sites. The inequality $f(h,\beta )-\mathrm{\text{lt}}\le f(H,\beta )\le f(h,\beta )$ demonstrates increasing accuracy of the mean-field $h$-theory, with decreasing impurity concentration.

A new class of forward quantum Markov fields (FQMFs) is introduced. The structure of these quantum Markov fields is investigated in the finer structure of a quasi-local algebra of observable over a tree-like graph. We provide an effective construction of a class of FQMCs. Moreover, we show the existence of three FMRFs associated with an Ising type model on a Husimi tree.