41,452 research outputs found
Quantum Semi-Markov Processes
We construct a large class of non-Markovian master equations that describe
the dynamics of open quantum systems featuring strong memory effects, which
relies on a quantum generalization of the concept of classical semi-Markov
processes. General conditions for the complete positivity of the corresponding
quantum dynamical maps are formulated. The resulting non-Markovian quantum
processes allow the treatment of a variety of physical systems, as is
illustrated by means of various examples and applications, including quantum
optical systems and models of quantum transport.Comment: 4 pages, revtex, no figures, to appear in Phys. Rev. Let
Metastability in Markov processes
We present a formalism to describe slowly decaying systems in the context of
finite Markov chains obeying detailed balance. We show that phase space can be
partitioned into approximately decoupled regions, in which one may introduce
restricted Markov chains which are close to the original process but do not
leave these regions. Within this context, we identify the conditions under
which the decaying system can be considered to be in a metastable state.
Furthermore, we show that such metastable states can be described in
thermodynamic terms and define their free energy. This is accomplished showing
that the probability distribution describing the metastable state is indeed
proportional to the equilibrium distribution, as is commonly assumed. We test
the formalism numerically in the case of the two-dimensional kinetic Ising
model, using the Wang--Landau algorithm to show this proportionality
explicitly, and confirm that the proportionality constant is as derived in the
theory. Finally, we extend the formalism to situations in which a system can
have several metastable states.Comment: 30 pages, 5 figures; version with one higher quality figure available
at http://www.fis.unam.mx/~dsanders
The Heckman-Opdam Markov processes
We introduce and study the natural counterpart of the Dunkl Markov processes
in a negatively curved setting. We give a semimartingale decomposition of the
radial part, and some properties of the jumps. We prove also a law of large
numbers, a central limit theorem, and the convergence of the normalized process
to the Dunkl process. Eventually we describe the asymptotic behavior of the
infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric
spaces setting in \cite{ABJ}
Consistency of Feature Markov Processes
We are studying long term sequence prediction (forecasting). We approach this
by investigating criteria for choosing a compact useful state representation.
The state is supposed to summarize useful information from the history. We want
a method that is asymptotically consistent in the sense it will provably
eventually only choose between alternatives that satisfy an optimality property
related to the used criterion. We extend our work to the case where there is
side information that one can take advantage of and, furthermore, we briefly
discuss the active setting where an agent takes actions to achieve desirable
outcomes.Comment: 16 LaTeX page
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