Related papers: Perturbation theory for dispersion relations of sp…
Band formation in periodic media is a central topic in undergraduate solid-state physics, typically introduced through Bloch's theorem as an eigenvalue problem in reciprocal space for infinitely periodic systems. While mathematically…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
Field pattern materials (FP-materials) are space-time composites with PT-symmetry in which the one-dimensional- spatial distribution of the constituents changes in time in such a special manner to give rise to a new type of waves, which we…
Using the time periodic ABCD parameters, an expression for the dispersion relation of space-time modulated structures is obtained. The relation is valid for general structures even when the spatial granularity is comparable to the operating…
We present an effective theory for the Bloch functions of a two-dimensional square lattice near a quadratic degeneracy point. The degeneracy is protected by the symmetries of the crystal, and breaking these symmetries can either open a…
For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…
The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary…
In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed. What is assumed is, firstly, that the perturbed Hamiltonians $H=H_0+\lambda V$ are non-Hermitian and lie…
We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At…
We present a procedure for the systematic estimation of the dispersion properties of linear discrete systems with periodic time-varying coefficients. The approach relies on the analysis of a single unit cell, making use of Bloch theorem…
We consider in this work a model conservative system subject to dissipation and Gaussian-type stochastic perturbations. The original conservative system possesses a continuous set of steady states, and is thus degenerate. We characterize…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
This paper concerns the homogenization of Schrodinger equations for non-crystalline matter, that is to say the coefficients are given by the composition of stationary functions with stochastic deformations. Two rigorous results of so-called…
A new scheme of the iterative perturbation theory is proposed for the strongly correlated electron systems with orbital degeneracy. The method is based on the modified self-energy of Yeyati, et al. which interpolates between the weak and…
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…
In this work, we introduce a degenerating PDE system with a time-depending domain for complete damage processes under time-varying Dirichlet boundary conditions. The evolution of the system is described by a doubly nonlinear differential…
We investigate the impact of asymmetric perturbations on the perfect transmission resonances (PTRs) of one-dimensional finite periodic systems. With no perturbations, the scattering region consists of $N$ identical cells, and the…
The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals. Considering…
The dynamic behaviour of periodic thermodiffusive multi-layered media excited by harmonic oscillations is studied. In the framework of linear thermodiffusive elasticity, periodic laminates, whose elementary cell is composed by an arbitrary…