Related papers: Perturbative Scattering Phase Shifts in One-Dimens…
The scattering problem can be implemented in a square-integrable basis via the so-called $J$-matrix method. While methods to compute the phase shift in the $J$-matrix approach are known, we introduce a novel formula in square-integrable…
It will be shown that transformations of order one on the Wiener space give rise to quadratic forms as exponents of change of variables formulas, and conversely every exponentially integrable quadratic form has a transformation of order one…
The transitions in disordered substances are discussed briefly: liquid--liquid phase transitions, liquid--glass transition and the transformations of one amorphous form to another amorphous form of the same substances. A description of…
The scattering phase shift encodes a good amount of physical information which can be used to study resonances from scattering data. Among others, it can be used to calculate the continuum density of states and the collision time in a…
The scattering transform is a non-linear signal representation method based on cascaded wavelet transform magnitudes. In this paper we introduce phase scattering, a novel approach where we use phase derivatives in a scattering procedure. We…
Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain. The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.
An integral equation method for scalar scattering in Schwarzschild spacetime is constructed. The zeroth-order and first-order scattering phase shift is obtained.
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…
We consider the one-dimensional Schr\"odinger equation with a potential satisfying the standard assumptions of the inverse scattering theory and supported on the half-line $x\ge 0$. For this equation at fixed positive energy we give…
The classification of structural phase transitions as displacive or order-disorder in character is usually based on spectroscopic data above the transition. We use single crystal x-ray diffraction to investigate structural correlations in…
The J-matrix method of scattering is used to obtain analytic expressions for the phase shift of two classes of relativistic exponential-type separable potentials whose radial component is either of the general form r^(n-1)exp(-r) or…
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
Scattering of an electron in quasi-one dimensional quantum wires have many unusual features, not found in one, two or three dimensions. In this work we analyze the scattering phase shifts due to an impurity in a multi-channel quantum wire…
We investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in Ref.~\cite{Guo:2023ecc} that relates the…
A phase diagram, defined by the amplitude square and phase of scattering coefficients for absorption cross-section in each individual channel, is introduced as a universal map on the electromagnetic properties for passive scatterers.…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…
General dynamical transport of classical particles in disordered quasi-1D samples is viewed in the framework of scattering approach. Simple equation for the transfer-matrix is obtained within this unified picture. In the case of diffusive…
We consider a singularly perturbed fourth-order problem with third-order terms on the unit square. With a formal power series approach, we decompose the solution into solutions of reduced (third-order) problems and various layer parts. The…