Related papers: Stochastic Dynamics of Einstein Matter-Radiation M…
A system's internal dynamics and its interaction with the environment can be determined by tracking how external perturbations affect its transition rates between states. Quantitative measurements of these rates are crucial for optimizing…
In his celebrated 1916-17 papers in which he proposed the A and B coefficients for the spontaneous and stimulated emission of energy quanta from excited atoms, Einstein conjectured that stimulated emission involves the release of individual…
Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A…
The derivation of a quantum Markovian model for an opto-mechanical system consisting of a quantum mechanical mirror interacting with quantum optical input fields via radiation pressure is difficult problem which ultimately involves the…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
The stimulated emission from an atom interacting with radiation in non-equilibrium state is considered. The stochastic limit, applied to the non-relativistic Hamiltonian describing the interaction, shows that the state of atoms, driven by…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
We study in this paper the effect of an unique initial stimulation on random recurrent networks of leaky integrate and fire neurons. Indeed given a stochastic connectivity this so-called spontaneous mode exhibits various non trivial…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
Over the last few decades, the predominant strategies for controlling spontaneous emission have involved tailoring the spatial surroundings of quantum emitters or atoms to create resonant or spatially periodic photonic structures. However,…
We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…
The paradigm of stochastic resonance (SR)---the idea that signal detection and transmission may benefit from noise---has met with great interest in both physics and the neurosciences. We investigate here the consequences of reducing the…
One of the paradigms of a small quantum system in a dissipative environment is the decay of an excited atom undergoing spontaneous photon emission into the fluctuating quantum electrodynamic vacuum. Recent experiments have demonstrated that…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…
We investigate toy dynamical models of energy-level repulsion in quantum eigenvalue sequences. We focus on parametric (with respect to a running coupling or "complexity" parameter) stochastic processes that are capable of relaxing towards a…
Mean field approximation treats only coherent aspects of the evolution of a Bose Einstein condensate. However, in many experiments some atoms scatter out of the condensate. We study an analytic model of two counter-propagating atomic…
The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…