相关论文: Equivalence of the Siegert-pseudostate and Lagrang…

In this work, we investigate time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that is valid in the limit as…

The normalization of scattering states is more than a rote step necessary to calculate expectation values. This normalization actually contains important information regarding the density of the scattering spectrum (along with useful…

The S-matrix in the static limit of a dispersion relation has a finite order N and is a matrix of meromorfic functions of energy in the complex plane with cuts. In the elastic case it reduces to N functions connected by the crossing…

The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…

Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…

We give a definition of scattering matrices based on the asymptotic behaviors of generalized eigenfunctions and show that these scattering matrices are equivalent to the ones defined by wave-operator approach in long-range $N$-body…

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…

We show that the use of wavelet bases for solving the momentum-space scattering integral equation leads to sparse matrices which can simplify the solution. Wavelet bases are applied to calculate the K-matrix for nucleon-nucleon scattering…

General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial…

In coupled-channel models the poles of the scattering S-matrix are located on different Riemann sheets. Physical observables are affected mainly by poles closest to the physical region but sometimes shadow poles have considerable effect,…

The physical nature of pseudogap phase is one of the most important and intriguing problems towards understanding the key mechanism of high temperature superconductivity in cuprates. Theoretically, the square-lattice $t$-$J$ model is widely…

The computation of light scattering by the superposition T-matrix scheme has been so far restricted to systems made of particles that are either sparsely distributed or of near-spherical shape. In this work, we extend the range of…

The quantum mechanical description of the evolution of an unstable system defined initially as a state in a Hilbert space at a given time does not provide a semigroup (exponential) decay law. The Wigner-Weisskopf survival amplitude,…

Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…

The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…

We discuss "the plane wave approximation" to quantum mechanical scattering using simple one-dimensional examples. The central points of the paper are that (a) plane waves should be thought of as infinitely wide wave packets, and (b) the…

With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of…

In this paper, we correct a mistake we made in [Phys. Rev. Lett. $\textbf{122}$, 190402 (2019)] and [Phys. Rev. A $\textbf{103}$, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here…

We consider the nonrelativistic model of coupling bare discrete states with continuum states in which the continuum states can have interactions among themselves. By partial-wave decomposition and constraint to the conserved angular…

Within the class of Derezi{\'n}ski-Enss pair-potentials which includes Coulomb potentials and for which asymptotic completeness is known \cite{De}, we show that all entries of the $N$-body quantum scattering matrix have a well-defined…