Continuous-Time Random Walks at All Times

Continuous-time random walks (CTRW) play important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on stationary-state dynamics. We present a new theoretical approach, based on generalized master equations picture, that allowed us to obtain explicit expressions for Laplace transforms for all dynamic quantities for different CTRW models. This theoretical method leads to the effective description of CTRW at all times. Specific calculations are performed for homogeneous, periodic models and for CTRW with irreversible detachments. The approach to stationary states for CTRW is analyzed. Our results are also used to analyze generalized fluctuations theorem

Spatial Resonator Solitons

Spatial solitons can exist in various kinds of nonlinear optical resonators with and without amplification. In the past years different types of these localized structures such as vortices, bright, dark solitons and phase solitons have been experimentally shown to exist. Many links appear to exist to fields different from optics, such as fluids, phase transitions or particle physics. These spatial resonator solitons are bistable and due to their mobility suggest schemes of information processing not possible with the fixed bistable elements forming the basic ingredient of traditional electronic processing. The recent demonstration of existence and manipulation of spatial solitons in emiconductor microresonators represents a step in the direction of such optical parallel processing applications. We review pattern formation and solitons in a general context, show some proof of principle soliton experiments on slow systems, and describe in more detail the experiments on semiconductor resonator solitons which are aimed at applications.Comment: 15 pages, 32 figure

Convergence of the state of a passive nonlinear plant with an L2 input

In this paper, we consider a strictly output passive nonlinear plant P with storage function H. We assume that P is zero-state detectable. Under some mild conditions on H, we show that the state x of the plant converges to zero for any L2 input. This implies the solvability for all t ≥ 0 of the system equations, for every input in L^2_{loc} We define a stability notion called L2 system-stable, a variant to the L2-stability concept, which has a nice interconnection properties

Strong coupling of a qubit to shot noise

We perform a nonperturbative analysis of a charge qubit in a double quantum dot structure coupled to its detector. We show that strong detector-dot interaction tends to slow down and halt coherent oscillations. The transitions to a classical and a low-temperature quantum overdamping (Zeno) regime are studied. In the latter, the physics of the dissipative phase transition competes with the effective shot noise.Comment: 5 pages, 4 figure