5,727 research outputs found
Piecewise deterministic Markov processes in biological models
We present a short introduction into the framework of piecewise deterministic
Markov processes. We illustrate the abstract mathematical setting with a series
of examples related to dispersal of biological systems, cell cycle models, gene
expression, physiologically structured populations, as well as neural activity.
General results concerning asymptotic properties of stochastic semigroups
induced by such Markov processes are applied to specific examples.Comment: in: Semigroup of Operators - Theory and Applications, J. Banasiak et
al. (eds.), Springer Proceedings in Mathematics & Statistics 113, (2015), pp.
235-25
Open Quantum Dynamics: Complete Positivity and Entanglement
We review the standard treatment of open quantum systems in relation to
quantum entanglement, analyzing, in particular, the behaviour of bipartite
systems immersed in a same environment. We first focus upon the notion of
complete positivity, a physically motivated algebraic constraint on the quantum
dynamics, in relation to quantum entanglement, i.e. the existence of
statistical correlations which can not be accounted for by classical
probability. We then study the entanglement power of heat baths versus their
decohering properties, a topic of increasing importance in the framework of the
fast developing fields of quantum information, communication and computation.
The presentation is self contained and, through several examples, it offers a
detailed survey of the physics and of the most relevant and used techniques
relative to both quantum open system dynamics and quantum entanglement.Comment: LaTex, 77 page
A singular limit for an age structured mutation problem
The spread of a particular trait in a cell population often is modelled by an
appropriate system of ordinary differential equations describing how the sizes
of subpopulations of the cells with the same genome change in time. On the
other hand, it is recognized that cells have their own vital dynamics and
mutations, leading to changes in their genome, mostly occurring during the cell
division at the end of its life cycle. In this context, the process is
described by a system of McKendrick type equations which resembles a network
transport problem. In this paper we show that, under an appropriate scaling of
the latter, these two descriptions are asymptotically equivalent
Coagulation and fragmentation processes with evolving size and shape profiles : a semigroup approach
We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators
Open Quantum Systems. An Introduction
We revise fundamental concepts in the dynamics of open quantum systems in the
light of modern developments in the field. Our aim is to present a unified
approach to the quantum evolution of open systems that incorporates the
concepts and methods traditionally employed by different communities. We
present in some detail the mathematical structure and the general properties of
the dynamical maps underlying open system dynamics. We also discuss the
microscopic derivation of dynamical equations, including both Markovian and
non-Markovian evolutions.Comment: 100 pages, 3 figures. Updated version with typos corrected. Preprint
version of the published boo
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