Dissipative quantum mechanics beyond Bloch-Redfield: A consistent weak-coupling expansion of the ohmic spin boson model at arbitrary bias

We study the time dynamics of the ohmic spin boson model at arbitrary bias $\epsilon$ and small coupling $\alpha$ to the bosonic bath. Using perturbation theory and the real-time renormalization group (RG) method we present a consistent zero-temperature weak-coupling expansion for the time evolution of the reduced density matrix one order beyond the Bloch-Redfield solution. We develop a renormalized perturbation theory and present an analytical solution covering the whole range from small to large times, including further results for exponentially small or large times. Resumming all secular terms in all orders of perturbation theory we find exponential decay for all terms of the time evolution. We determine the preexponential functions and find slowly varying logarithmic terms with the renormalized Rabi frequency $\Omega$ as energy scale together with strongly varying parts falling off asymptocially as $1/t$ in leading order, in contrast to the unbiased case. Resumming all logarithmic terms in all orders of perturbation theory via real-time RG we find the correct renormalized tunneling and a power-law behaviour for the oscillating modes with exponent crossing over from $2\alpha$ for exponentially small times to a bias-dependent value $2\alpha \epsilon^2/\Omega^2$ for exponentially large times. Furthermore, we present a degenerate perturbation theory to calculate consistently the purely decaying mode one order beyond Bloch-Redfield.Comment: 27 pages, 2 figure

Mechanism of temperature dependence of the magnetic anisotropy energy in ultrathin Cobalt and Nickel films

Temperature dependent FMR-measurements of Ni and Co films are analysed using a microscopic theory for ultrathin metallic systems. The mechanism governing the temperature dependence of the magnetic anisotropy energy is identified and discussed. It is reduced with increasing temperature. This behavior is found to be solely caused by magnon excitations.Comment: 3 pages, 4 figures III Joint European Magnetic Symposia, San Sebastian, Spai

Testing quantum superpositions of the gravitational field with Bose-Einstein condensates

We consider the gravity field of a Bose-Einstein condensate in a quantum superposition. The gravity field then is also in a quantum superposition which is in principle observable. Hence we have ``quantum gravity'' far away from the so-called Planck scale

A Continuous Time GARCH Process of Higher Order

A continuous time GARCH model of order (p,q) is introduced, which is driven by a single Lévy process. It extends many of the features of discrete time GARCH(p,q) processes to a continuous time setting. When p=q=1, the process thus defined reduces to the COGARCH(1,1) process of Klüppelberg, Lindner and Maller (2004). We give sufficient conditions for the existence of stationary solutions and show that the volatility process has the same autocorrelation structure as a continuous time ARMA process. The autocorrelation of the squared increments of the process is also investigated, and conditions ensuring a positive volatility are discussed