相关论文: A Matrix Kato-Bloch Perturbation Method for Hamilt…
This article considers the $\mathcal{H}_\infty$ static output-feedback control for linear time-invariant uncertain systems with polynomial dependence on probabilistic time-invariant parametric uncertainties. By applying polynomial chaos…
We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can…
We propose a new approach to the Rayleigh-Schr\"{o}dinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard…
In a recent paper, wavelet analysis was used to perturb the coupling matrix in an array of identical chaotic systems in order to improve its synchronization. As the synchronization criterion is determined by the second smallest eigenvalue…
Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…
The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains the non-interacting sector and the diagonal elements of Fock space from the interacting terms. The…
The effect of multiplicative stochastic perturbations on Hamiltonian systems on the plane is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
I present a different approach to Rayleigh-Schr\"odinger perturbation theory, based on Laplace transforms and polynomial theory, yielding an iterative expression for the perturbative expansion of the energy of the non-degenerate ground…
Many problems in physics, chemistry and other fields are perturbative in nature, i.e. differ only slightly from related problems with known solutions. Prominent among these is the eigenvalue perturbation problem, wherein one seeks the…
A new method is developed to extend the histogram method to lattices with any type of disorder. The Monte Carlo single- and multiple-histogram methods were developed to get the most out of only a few simulations, but are restricted to…
The influence of multiplicative stochastic perturbations on the class of asymptotically Hamiltonian systems on the plane is investigated. It is assumed that disturbances do not preserve the equilibrium of the corresponding limiting system…
We propose a perturbative improvement of the hierarchical approximation for gaussian models. The procedure is based on a relabeling of the momenta which allows one to express the symmetries of the hierarchical model using a simple…
We consider a Hamiltonian $H=H^{0}(p)+\kappa H^{1}(p,q,t)$, $(p,q)\in {\mathbb{R}}^{n} \times {\mathbb{T}}^n$, $t\in{\mathbb{R}}$ where $\kappa \in {\mathbb{R}}$ is a small perturbation parameter and $p$, $q$ are the action and angle…
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…
The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak…
We find that localised perturbations in a chaotic classical many-body system-- the classical Heisenberg We find that the effects of a localised perturbation in a chaotic classical many-body system--the classical Heisenberg chain at infinite…
The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…