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The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
A non-statistical theory of continuous, but irreversible, evolution can be constructed in terms of the Cartan calculus. The fundamental postulate, for an evolutionary theory which admits irreversible processes, is that the topology of the…
The past few years have seen dramatic improvements in the scope and realism of star cluster simulations. Accurate treatments of stellar evolution, coupled with robust descriptions of all phases of binary evolution, have been incorporated…
We show how strongly continuous semigroups can be associated with evolutionary equations. For doing so, we need to define the space of admissible history functions and initial states. Moreover, the initial value problem has to be formulated…
We study some aspects of dynamical compactification scenario where stabilisation of extra dimensions occurs due to presence the Gauss-Bonnet term and non-zero spatial curvature. In the framework of the model under consideration there exists…
For nonuniform exponentially bounded evolution families defined on Banach spaces, we introduce a class of Banach function spaces, whose norms are completely determined by the nonuniform behaviour of the corresponding evolution family. We…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We study the dynamical evolution of a system with a phase space consisting of configurations with random energies. The dynamics we use is of Glauber type. It allows for some dynamical evolution ang aging even at very low temperatures,…
We present the Heisenberg-picture approach to the quantum evolution of the scalar fields in an expanding FRW universe which incorporates relatively simply the initial quantum conditions such as the vacuum state, the thermal equilibrium…
We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform…
With particular attention to the recently postulated introduction of a non-extensive generalization of Boltzmann-Gibbs statistics, we study the long-term stellar dynamical evolution of self-gravitating systems on timescales much longer than…
Loewner Theory, based on dynamical viewpoint, is a powerful tool in Complex Analysis, which plays a crucial role in such important achievements as the proof of famous Bieberbach's conjecture and well-celebrated Schramm's Stochastic Loewner…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic…
We obtain slow dynamics for self-adjoint semigroups and unitary evolution groups. For semigroups, the slow dynamics is for orbits, and for the average return probability in the case of unitary evolution groups. We present an application to…
We study the existence of the stochastic flow associated to a linear stochastic evolution equation $$d X= AX\,d t +\sum_{k} B_k X\,d W_k, $$ on a Hilbert space. Our first result covers the case where $A$ is the generator of a…
In recent work we developed a description of cosmic large scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works,…
The response of physical systems to external perturbations can be used to probe both their equilibrium and non-equilibrium dynamics. While response and correlation functions are related in equilibrium by fluctuation-dissipation theorems,…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…