相关论文: A noisy system with a flattened Hamiltonian and mu…
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier…
In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white noise…
In a noisy environment, oscillations loose their coherence which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional…
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and…
In this paper, we study one dimensional Markov processes with spatial delay. Since the seminal work of Feller, we know that virtually any one dimensional, strong, homogeneous, continuous Markov process can be uniquely characterized via its…
In this paper, we study averaging principles for a class of time-inhomogeneous stochastic differential equations (SDEs) with slow and fast time-scales, where the drift term in the fast component is time-dependent and only partially…
We study the dynamics of a dissipative two-level, system driven by a monochromatic ac field, starting from the usual spin-boson Hamiltonian. The quantum Langevin equations for the spin variables are obtained. The amplitude of the coherent…
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…
Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures.…
Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…
Dynamical systems driven by a general L\'evy stable noise are considered. The inertia is included and the noise, represented by a generalised Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive…
A stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes where they receive service according to the Processor-Sharing policy. Once their service requirement is…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
We derive explicit results for the asymptotic probability density and drift velocity in systems driven by dichotomous Markov noise, including the situation in which the asymptotic dynamics crosses {\em unstable} fixed points. The results…
We study the spatial structure of a granular material, N particles subject to inelastic mutual collisions, when it is stirred by a bidimensional smooth chaotic flow. A simple dynamical model is introduced where four different time scales…
We study the breakdown of fluctuation-dissipation relations between time dependent density-density correlations and associated responses following a quench in chemical potential in the Frustrated Ising Lattice Gas. The corresponding slow…
We study the nonequilibrium dynamics of a many-body bosonic system on a lattice, subject to driving and dissipation. The time-evolution is described by a master equation, which we treat within a generalized Gutzwiller mean field…
An investigation of the mesoscopic dynamics of chemical systems whose mass action equation gives rise to a deterministic chaotic attractor is carried out. A reactive lattice-gas model for the three-variable autocatalator is used to provide…
We study a system of spins (qubits) coupled to a common noisy environment, each precessing at its own frequency. The correlated noise experienced by the spins implies long-lived correlations that relax only due to the differing frequencies.…
We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time.…