Related papers: Uniform stationary phase estimate with limited smo…
We present approximate analytical method of analysis of stationary states of nonlinear quantum systems with the noise. As an example we consider quantum nonlinear oscillator excited by fluctuating force and found parameter regions with more…
Given its well known spectral decomposition profile, the $1$-dim harmonic oscillator potential modified by an inverse square ($1$-dim angular momentum-like) contribution works as an efficient platform for probing classical and quantum…
We obtain sharp $L^p$ bounds for oscillatory integral operators with generic homogeneous polynomial phases in several variables. The phases considered in this paper satisfy the rank one condition which is an important notion introduced by…
We propose an analytical model for the accurate calculation of size and density dependent quantum oscillations in thermodynamic and transport properties of confined and degenerate non-interacting Fermi gases. We provide a universal,…
We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…
We introduce a higher order phase averaging method for nonlinear oscillatory systems. Phase averaging is a technique to filter fast motions from the dynamics whilst still accounting for their effect on the slow dynamics. Phase averaging is…
We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the…
The purpose of this note is to prove a stationary phase estimate well adapted to parameter dependent phases. In particular, no discussion is made on the positions (and behaviour) of critical points, no lower or upper bound on the gradient…
The problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations of the sequence with noise is considered. In the case of spectral certainty,…
The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of…
A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…
It is shown that an aberrated wavefront incident upon a Fabry-Perot optical cavity excites higher order spatial modes in the cavity, and that the spectral width and distribution of these modes is indicative of the type and magnitude of the…
Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction…
Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduction technique based on isochrons, can be unsuitable for…
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…
In this paper, we present new proofs for both the sharp $L^p$ estimate and the decoupling theorem for the H\"ormander oscillatory integral operator. The sharp $L^p$ estimate was previously obtained by Stein\;\cite{stein1} and Bourgain-Guth…
Many real-life signals, such as gravitational wave measurements, biomedical signals, or geophysical data, are strongly non-stationary but can be decomposed into mono-component signals that contain only one active frequency over time. This…
We study phase segregation in a model alloy undergoing both ordering and decomposition, using computer simulations of Kawasaki exchange dynamics on a square lattice. Following a quench into the miscibility gap we observe an early stage in…
We give an overview of basic methods that can be used for obtaining asymptotic expansions of integrals: Watson's lemma, Laplace's method, the saddle point method, and the method of stationary phase. Certain developments in the field of…
We consider a generalization of the notion of spaces of homogeneous type, inspired by recent work of Street [21] on the multi-parameter Carnot-Caratheodory geometry, which imbues such spaces with differentiability structure. The setting…