Related papers: Spectral formulation and WKB approximation for rar…
We calculate the probabilities to find systems of reacting particles in states which largely deviate from typical behavior. The rare event statistics is obtained from the master equation which describes the dynamics of the probability…
We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…
We study the statistics of extinction and blowup times in well-mixed systems of stochastically reacting particles. We focus on the short-time tail, $T \to 0$, of the extinction- or blowup-time distribution $\mathcal{P}_m(T)$, where $m$ is…
Using Wenzel-Kramers-Brillouin (WKB) approximation the scalar and tensor power spectra are obtained. Scale invariant spectra are obtained and the spectral indices come very close to the observed data from WMAP and Planck experiments. The…
Some commonly used approximations for complete fusion and breakup transmission coefficients in collisions of weakly bound projectiles at near barrier energies are assessed. We show that they strongly depend on the adopted classical…
A new method for predicting inflationary cosmological perturbations, based on the Wentzel-Kramers-Brillouin (WKB) approximation, is presented. A general expression for the WKB scalar and tensor power spectra is derived. The main advantage…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
We apply the spectral method, recently developed by the authors, to calculate the statistics of a reaction-limited multi-step birth-death process, or chemical reaction, that includes as elementary steps branching A->2A and annihilation…
This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the semiclassical limit in the highly oscillatory regime. A previous approach to this problem based on explicitly…
Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events E_{n}:=(f(X_{1})+...+f(X_{n}))\inA_{n} where the summands are i.i.d. and E_{n} is a…
Chemical reactions represent a class of quantum problems that challenge both the current theoretical understanding and computational capabilities. Reactions that occur at ultralow temperatures provide an ideal testing ground for quantum…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
We consider a switching rate of a meta-stable reaction scheme, which includes reactions with arbitrary steps, e.g. $kA\to(k+r)A$. Employing WKB approximation, controlled by a large system size, we evaluate both the exponent and the…
We numerically compute eigenvalues of the non-self-adjoint Zakharov--Shabat problem in the semiclassical regime. In particular, we compute the eigenvalues for a Gaussian potential and compare the results to the corresponding (formal) WKB…
The Bogoliubov transformation in cosmological particle production can be explained by the Stokes phenomena of the corresponding ordinary differential equation. The calculation becomes very simple as far as the solution is described by a…
The quasi-stationary method for black hole binary inspiral is an approximation for studying strong field effects while suppressing radiation reaction. In this paper we use a nonlinear scalar field toy model (i) to explain the underlying…
Although many computational methods for rare event sampling exist, this type of calculation is not usually practical for general nonequilibrium conditions, with macroscopically irreversible dynamics and away from both stationary and…
We present a unified formalism for describing chemical reaction rates of trapped, ultracold molecules. This formalism reduces the scattering to its essential features, namely, a propagation of the reactant molecules through a gauntlet of…
In this work, we consider the numerical estimation of the probability for a stochastic process to hit a set B before reaching another set A. This event is assumed to be rare. We consider reactive trajectories of the stochastic Allen-Cahn…
The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process,…