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In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic…
We present the numerical estimation of noise parameter induced in the dynamics of the variables by random particle interactions involved in the stochastic chemical oscillator and use it as order parameter to detect the transition from…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently…
The exact stochastic decomposition of non-Markovian dissipative quantum dynamics is combined with the time-dependent semiclassical initial value formalism. It is shown that even in the challenging regime of moderate friction and low…
Growth models with internal habit formation have been studied in various settings under the assumption of deterministic dynamics. The purpose of this paper is to explore a stochastic version of the model in Carroll et al. [1997, 2000], one…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
Different models are described where non-interacting particles generate dissipative effective forces by the mixing of infinitely many soft normal modes. The effective action is calculated for these models within the Closed Time Path…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
We consider the micro-canonical ensemble of a classical Hamiltonian dynamical system, the Hamiltonian being parameter dependent and in the possible presence of other first integrals. We describe a thermodynamic formalism in which a 1st law…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
This article sets up a formalism to describe stochastic thermodynamics for driven out-of-equilibrium open quantum systems. A stochastic Schr\"odinger equation allows to construct quantum trajectories describing the dynamics of the system…
We shall show that the abstract and formal rules which govern the quantum kinematic and dynamics can be derived from a law of change of the information content or the degree of uncertainty that the system has a certain configuration in a…
Using the formalism of stochastic embedding developed by [J. Cresson, D. Darses, J. Math. Phys. 48, 072703 (2007)], we study how the dynamics of the classical Newton equation for a force deriving from a potential is deformed under the…
As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's approach of Hamiltonian formalism for…
We address the dynamics of nonclassicality for a quantum system interacting with a noisy fluctuating environment described by a classical stochastic field. As a paradigmatic example, we consider a harmonic oscillator initially prepared in a…
Semiclassical methods are extremely valuable in the study of transport and thermodynamical properties of ballistic microstructures. By expressing the conductance in terms of classical trajectories, we demonstrate that quantum interference…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…