Quantum Dynamics in a Fluctuating Environment

We theoretically investigate the dynamics of a quantum system which is coupled to a fluctuating environment based on the framework of Kubo-Anderson spectral diffusion. By employing the projection operator technique, we derive two types of dynamical equations, namely, time-convolution and time-convolutionless quantum master equations, respectively. We derive the exact quantum master equations of a qubit system with both diagonal splitting and tunneling coupling when the environmental noise is subject to a random telegraph process and a Ornstein-Uhlenbeck process, respectively. For the pure decoherence case with no tunneling coupling, the expressions of the decoherence factor we obtained are consistent with the well-known existing ones. The results are significant to quantum information processing and helpful for further understanding the quantum dynamics of open quantum systems.

Gauss-Seidel type algorithms for a class of variational inequalities

In this paper, we consider a new system of extended general quasi variational inequalities involving six nonlinear operators. Using projection operator technique, we show that system of extended general quasi variational inequalities is equivalent to a system of fixed point problems. Using this alternative equivalent formulation, we propose and analyze Gauss-Seidel type algorithms for solving a system of extended general quasi variational inequalities. Convergence of new method is discussed under some suitable conditions. Several special cases are discussed. Results obtained in this paper continue to hold for these problems.

Memory function approach to correlated electron transport: A comprehensive review

Memory function formalism or projection operator technique is an extremely useful method to study the transport and optical properties of various condensed matter systems. A recent revival of its uses in various correlated electronic systems is being observed. It is being used and discussed in various contexts, ranging from nonequilibrium dynamics to the optical properties of various strongly correlated systems such as high temperature superconductors. However, a detailed discussion on this method, starting from its origin to its present day applications at one place is lacking. In this paper, we attempt a comprehensive review of the memory function approach focusing on its uses in studying the dynamics and the transport properties of correlated electronic systems.

Magnetic Response of Pr1-xLaCexCuO4 in Comparison with Hole-Doped Cuprates

The magnetic susceptibility of the optimally doped Pr1-xLaCexCuO4in the superconducting state is calculated using thet-Jmodel of Cu-O planes, the Mori projection operator technique, and the dispersion of electron bands derived from photoemission experiments. The electron band folding across the antiferromagnetic Brillouin zone border, which is inherent in the crystal, leads to a commensurate low-frequency response. The same band folding causes the appearance of a supplementary spin-excitation branch, which coexists with usual spin excitations. This coexistence can explain two maxima observed in the frequency dependence of the susceptibility. The two nested spin-excitation branches lead to a comb of closely spaced peaks in momentum cuts, which presumably are not resolved in experiment, being seen as a broad commensurate peak up to 100 meV. Reasons for differences in magnetic responses of electron- and hole-doped cuprates are discussed.

MAGNETIC RESPONSE OF Pr1-xLaCexCuO4 IN COMPARISON WITH HOLE-DOPED CUPRATES

The origin of differences in the magnetic responses of Pr 1-x LaCe x CuO 4 with x = 0.11–0.12 and moderately doped p-type cuprates is investigated using the t–J model, the Mori projection operator technique and dispersions of charge carriers derived from photoemission experiments. These differences are related to the proximity of the former crystal to the boundary of the antiferromagnetic (AF) phase and to the remoteness of p-type compounds from it. This leads to different nesting vectors of the low-frequency equi-energy contours of carrier dispersions in these crystals. The strong nesting with the AF momentum as the nesting vector produces the commensurate low-frequency response and the coexistence of two spin-excitation branches in Pr 1-x LaCe x CuO 4, while incommensurate nesting vectors in p-type crystals lead to the incommensurate low-frequency response and the hourglass dispersion of susceptibility maxima.

MAGNETIC INCOMMENSURABILITY IN p-TYPE CUPRATE PEROVSKITES

For the superconducting phase with a d-wave order parameter and zero temperature, the magnetic susceptibility of the t–J model is calculated using the Mori projection operator technique. Conditions for the appearance of an incommensurate magnetic response below the resonance frequency are identified. A fast decay of the tails of the hole coherent peaks and a weak intensity of the hole incoherent continuum near the Fermi level are enough to produce an incommensurate response using different hole dispersions established for p-type cuprates, in which such response was observed. In this case, the nesting of the itinerant-electron theory or the charge modulation of the stripe theory is unnecessary for the incommensurability. The theory reproduces the hourglass dispersion of the susceptibility maxima with their location in the momentum space similar to that observed experimentally. The upper branch of the dispersion stems from the excitations of localized spins, while the lower one is due to the incommensurate maxima of their damping. The narrow and intensive resonance peak arises if the frequency of these excitations at the antiferromagnetic momentum lies below the edge of the two-fermion continuum; otherwise the maximum is broad and less intensive.