Related papers: Large deviations and adiabatic transitions for dyn…
This paper presents description of time evolution of averages of Markov process in wide range of noise intensity. Exact expression of time scale of average evolution has been obtained. It has been demonstrated numerically that for purely…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
We study a zero-range process with system-size dependent jump rates, which is known to exhibit a discontinuous condensation transition. Metastable homogeneous phases and condensed phases coexist in extended phase regions around the…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
In dynamical systems with distinct time scales the time evolution in phase space may be influenced strongly by the fixed points of the fast subsystem. Orbits then typically follow these points, performing in addition rapid transitions…
We study the disruption process of hierarchical 3-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with 3-body numerical…
We solve a simple model that supports a dynamic phase transition and show conditions for the existence of the transition. Using methods of large deviation theory we analytically compute the probability distribution for activity and entropy…
We prove a large deviation principle on path space for a class of discrete time Markov processes whose state space is the intersection of a regular domain $\L\subset \R^d$ with some lattice of spacing $\e$. Transitions from $x$ to $y$ are…
Using random matrices, we study the reduced dynamics of a two level system interacting with a generic environment. In the weak coupling limit, the result can be obtained directly from known results for purity decay, and result in Markovian…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…
In this paper, we investigate a special class of stochastic Markov processes, known as Glauber dynamics. Markov processes are importance, for example, in the study of complex systems. For this, we present the basic theory of Glauber…
We present an investigation of stochastic evolution in which a family of evolution equations in $L^1$ are driven by continuous-time Markov processes. These are examples of so-called piecewise deterministic Markov processes (PDMP's) on the…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field…
The state of an open quantum system undergoing an adiabatic process evolves by following the instantaneous stationary state of its time-dependent generator. This observation allows one to characterize, for a generic adiabatic evolution, the…
Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…