Related papers: Exponential propagators for the Schr\"odinger equa…
The quasistatic electric current density of fermions in the presence of an external electric field is determined through the utilization of a time-ordered Schwinger propagator. The study encompasses the necessary conditions for establishing…
We prove the optimal endpoint Strichartz estimates for Schr\"{o}dinger equation with charge transfer potentials and a general source term in $\mathbb{R}^n$ for $n\geq3$. The proof is based on using the projection on the scattering states…
This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…
We present an exact integral formula for the multi-particle propagator of the one-dimensional Fermi--Hubbard model on an infinite lattice. The proof is based on the nested Bethe ansatz without relying on the string hypothesis. Our formula…
Given the extreme accuracy of modern space astrometry, a precise relativistic modeling of observations is required. Concerning light propagation, the standard procedure is the solution of the null-geodesic equations. However, another…
A method for computing all-point quark propagators is applied to a variety of processes of physical interest in lattice QCD. The method allows, for example, efficient calculation of disconnected parts and full momentum-space 2 and 3 point…
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…
We study the gauge dependence of the fermion propagator in quenched QED3 with and without dynamical symmetry breaking in the light of its Landau-Khalatnikov-Fradkin Transformation (LKFT). In the former case, starting with the massive bare…
We apply the exponential operator method to derive the propagator for a fermion immersed within a rigidly rotating environment with cylindrical geometry. Given that the rotation axis provides a preferred direction, Lorentz symmetry is lost…
We consider a class of linear Schroedinger equations in R^d, with analytic symbols. We prove a global-in-time integral representation for the corresponding propagator as a generalized Gabor multiplier with a window analytic and decaying…
We study the Schr\"odinger flow for the SSH model, a class of self-adjoint discrete dimer lattice Hamiltonians on the half-line. Using oscillatory integral techniques, we prove dispersive time-decay estimates, which quantify the spreading…
The integrating factor technique is widely used to solve numerically (in particular) the Schr\"odinger equation in the context of spectral methods. Here, we present an improvement of this method exploiting the freedom provided by the gauge…
Efficient and accurate numerical propagation of the time dependent Schroedinger equation is a problem with applications across a wide range of physics. This paper develops an efficient, trivially parallelizeable method for relaxing a trial…
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schr\"odinger equation. The method is based on: i) the definition of a linearly independent working…
We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although…
We show how to use the input-output formalism compute the propagator for an open quantum system, i.e. quantum networks with a low dimensional quantum system coupled to one or more loss channels. The total propagator is expressed entirely in…
In the Euclidean-space formulation of integral equations for the structure of quantum chromodynamics (QCD) bound states, the quark propagators with complex-valued momentum are densely sampled. We therefore propose an accurate and efficient…
The vector electric-field Helmholtz equation, containing cross-polarization terms, is factored to produce both pseudo-differential and exponential operator forms of a three-dimensional, one-way, vector, wave equation for propagation through…
The multiple-quantum operator algebra formalism has been exploited to construct generally an unsorted quantum search algorithm. The exponential propagator and its corresponding effective Hamiltonian are constructed explicitly that describe…