4,002 research outputs found
Open system dynamics with non-Markovian quantum jumps
We discuss in detail how non-Markovian open system dynamics can be described
in terms of quantum jumps [J. Piilo et al., Phys. Rev. Lett. 100, 180402
(2008)]. Our results demonstrate that it is possible to have a jump description
contained in the physical Hilbert space of the reduced system. The developed
non-Markovian quantum jump (NMQJ) approach is a generalization of the Markovian
Monte Carlo Wave Function (MCWF) method into the non-Markovian regime. The
method conserves both the probabilities in the density matrix and the norms of
the state vectors exactly, and sheds new light on non-Markovian dynamics. The
dynamics of the pure state ensemble illustrates how local-in-time master
equation can describe memory effects and how the current state of the system
carries information on its earlier state. Our approach solves the problem of
negative jump probabilities of the Markovian MCWF method in the non-Markovian
regime by defining the corresponding jump process with positive probability.
The results demonstrate that in the theoretical description of non-Markovian
open systems, there occurs quantum jumps which recreate seemingly lost
superpositions due to the memory.Comment: 19 pages, 10 figures. V2: Published version. Discussion section
shortened and some other minor changes according to the referee's suggestion
Stabilizing Randomly Switched Systems
This article is concerned with stability analysis and stabilization of
randomly switched systems under a class of switching signals. The switching
signal is modeled as a jump stochastic (not necessarily Markovian) process
independent of the system state; it selects, at each instant of time, the
active subsystem from a family of systems. Sufficient conditions for stochastic
stability (almost sure, in the mean, and in probability) of the switched system
are established when the subsystems do not possess control inputs, and not
every subsystem is required to be stable. These conditions are employed to
design stabilizing feedback controllers when the subsystems are affine in
control. The analysis is carried out with the aid of multiple Lyapunov-like
functions, and the analysis results together with universal formulae for
feedback stabilization of nonlinear systems constitute our primary tools for
control designComment: 22 pages. Submitte
Postprocessed integrators for the high order integration of ergodic SDEs
The concept of effective order is a popular methodology in the deterministic
literature for the construction of efficient and accurate integrators for
differential equations over long times. The idea is to enhance the accuracy of
a numerical method by using an appropriate change of variables called the
processor. We show that this technique can be extended to the stochastic
context for the construction of new high order integrators for the sampling of
the invariant measure of ergodic systems. The approach is illustrated with
modifications of the stochastic -method applied to Brownian dynamics,
where postprocessors achieving order two are introduced. Numerical experiments,
including stiff ergodic systems, illustrate the efficiency and versatility of
the approach.Comment: 21 pages, to appear in SIAM J. Sci. Compu
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