Related papers: First-order perturbation theory of eigenmodes for …

First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…

When studying a general system of delay differential equation with a single constant delay, we encounter a certain lack of uniqueness in determining the coefficient of one of the third order terms of the series defining the center manifold.…

Spontaneous time-reversal symmetry breaking in superconductors with competing non-degenerate pairing channels is an exotic quantum phase transition that could give rise to robust topological superconductivity and unusual magnetism. It is…

The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…

Here, we present an overview of a first principles homogenization theory of periodic metamaterials. It is shown that in a rather general context it is possible to formally introduce effective parameters that describe the time evolution of…

We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…

The classic example of the destruction of interference fringes in a ``which-way'' experiment, caused by an environmental interaction, may be viewed as the destruction of first-order coherence as defined by Glauber many years ago (Glauber).…

We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling $\tilde{U}$. Though the presence of…

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…

Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…

In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…

We present a theoretical framework for electromagnetic scattering by particles with a permittivity that is periodically varying in time, based on a perturbative approach. Within this framework, we derive explicit expressions for the…

The hadronic decay rate of the tau lepton serves as one of the most precise determinations of the QCD coupling alpha_s. The dominant theoretical source of uncertainty at present resides in the seeming disparity of two approaches to…

The deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of…

Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of…

The effect of inclusion of higher-order interactions in the {\it XY} model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape…

In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these…

Using a regularization with the properties of dimensional regularization, higher order local consistency conditions on one loop anomalies and divergent counterterms are given. They are derived without any a priori assumption on the form of…

By applying effective medium-style calculations to random spring networks, we demonstrate that internal stresses fundamentally alter the nature of the rigidity transition in disordered materials, changing it from continuous to first-order…

We deal with first-order definability in the substructure ordering $(\mathcal{D}; \sqsubseteq)$ of finite directed graphs. In two papers, the author has already investigated the first-order language of the embeddability ordering $(…