Related papers: Scattering and perturbation theory for discrete-ti…
Scattering processes are fundamental for understanding the structure of matter, yet simulating their real-time dynamics remains challenging for classical computers. Quantum computing and quantum-inspired methods offer a promising avenue for…
Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasi-potential…
A scalar quantum field theory defined on a discrete spatial coordinate is examined. The renormalization of the lattice propagator is discussed with an emphasis on the periodic nature of the associated momentum coordinate. The analytic…
We study a time-dependent scattering theory for Schr\"{o}dinger operators on a manifold with asymptotically polynomially growing ends. We use the Mourre theory to show the spectral properties of self-adjoint second-order elliptic operators.…
Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in…
We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinite-dimensional…
We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affecting the particle's speed and the other its direction. These…
We propose an effectively nonperturbative approach to calculating scattering amplitudes in the perturbative regime. We do this in a discretized momentum space by using the QSE method to calculate all the contributions (to all orders in…
This paper treats the dynamics and scattering of a model of coupled oscillating systems, a finite dimensional one and a wave field on the half line. The coupling is realized producing the family of selfadjoint extensions of the suitably…
In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.
The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…
The discrete one-dimensional Schr\"odinger operator is studied in the finite interval of length $N=2 M$ with the Dirichlet boundary conditions and an arbitrary potential even with respect to the spacial reflections. It is shown, that the…
We study the Klein paradox for the semi-classical Dirac operator on $\R$ with potentials having constant limits, not necessarily the same at infinity. Using the complex WKB method, the time-independent scattering theory in terms of incoming…
In this paper we investigate the spectral and the scattering theory of Schr\"odinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
A scattering event in a quantum field theory is a coherent superposition of all processes consistent with its symmetries and kinematics. While real-time simulations have progressed toward resolving individual channels, existing approaches…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…