Related papers: The split-operator technique for the study of spin…
We use the Dirac continuum model to study the propagation of electronic wave packets in graphene with periodically arranged circular potential steps. The time propagation of the wave packets are calculated using the split-operator method…
A wave-packet time evolution method, based on the split-operator technique, is developed to investigate the scattering of quasi-particles at a normal-superconductor interface of arbitrary profile and shape. As a practical application, we…
We present a program to simulate the dynamics of a wave packet interacting with a time-dependent potential. The time-dependent Schr\"odinger equation is solved on a one-, two-, or three-dimensional spatial grid using the split operator…
We present a simple method to expedite simulation of quantum wave-packet dynamics by more than a factor of $2$ with the Strang split-operator propagation. Dynamics of quantum wave-packets are often evaluated using the the \emph{Strang}…
Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent papers, including pseudodifferential, Fourier integral and metaplectic operators, with applications to time-frequency…
In this study, using the Dirac continuum model combined with the split-operator technique, we investigate the propagation dynamics of wave packets in graphene in the presence of circular potential barriers arranged in square and triangular…
The free-particle propagator, a key operator in various algorithms for simulating the time evolution of the Schr\"odinger equation, is studied. A multiscale approximation of this propagator is constructed, representing the semigroup…
An analytical approach to quantum mechanical wave packet dynamics of laser-driven particles is presented. The time-dependent Schroedinger equation is solved for an electron exposed to a linearly polarized plane wave of arbitrary shape. The…
In this article, we study wave dynamics in the fractional nonlinear Schr\"odinger equation with a modulated honeycomb potential. This problem arises from recent research interests in the interplay between topological materials and nonlocal…
We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and…
An explicit formula for the wave operators associated with Schroedinger operators on the discrete half-line is deduced from their stationary expressions. The formula enables us to understand the wave operators as one dimensional…
Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we…
We review some recent results obtained for the time evolution of wave packets for systems of equations of pseudo-differential type, including Schr{\"o}dinger ones, and discuss their application to the approximation of the associated unitary…
We consider the expansion of wave packets governed by the free Schr\"odinger equation. This seemingly simple task plays an important role in simulations of various quantum experiments and in particular in the field of matter-wave…
Scattering of electrons from chiral spin textures such as the skyrmions is an emerging research area due to its richness in topological quantum transport, which is significant for spintronic devices. We study the dynamical process of…
An alternative triplet-wave expansion formalism for dimerized spin systems is presented, a modification of the 'bond operator' formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace,…
An approach to analyzing the spinor wave functions that appear in the electronic structure calculations when taking the spin-orbit interaction into account is developed. It is based on the projection analysis of angular parts of wave…
The article discusses the properties of time evolution of wave packets in a few systems. Dynamics of wave packet motion for Rydberg atoms with the hierarchy of collapses and revivals is briefly reviewed. The main part of the paper focuses…
We consider singular self-adjoint extensions for one-dimensional Schr\"{o}dinger operator for two-component wave function within the framework of the distribution theory for discontinuous test functions…
We introduce the construction of a orthogonal wavepacket basis set, using the concept of stroboscopic time propagation, tailored to the efficient description of non-equilibrium extended electronic systems. Thanks to three desirable…