A splitting approach for the magnetic Schr\"odinger equation

The Schr\"odinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics. It also provides a nice example of a differential equation whose flow can be split with benefit into three parts. After presenting a splitting approach for three operators with two of them being unbounded, we exemplarily prove first-order convergence of Lie splitting in this framework. The result is then applied to the magnetic Schr\"odinger equation, which is split into its potential, kinetic and advective parts. The latter requires special treatment in order not to lose the conservation properties of the scheme. We discuss several options. Numerical examples in one, two and three space dimensions show that the method of characteristics coupled with a nonequispaced fast Fourier transform (NFFT) provides a fast and reliable technique for achieving mass conservation at the discrete level

A splitting approach for the magnetic Schr\uf6dinger equation

The Schr\uf6dinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics. It also provides a nice example of a differential equation whose flow can be split with benefit into three parts. After presenting a splitting approach for three operators with two of them being unbounded, we exemplarily prove first-order convergence of Lie splitting in this framework. The result is then applied to the magnetic Schr\uf6dinger equation, which is split into its potential, kinetic and advective parts. The latter requires special treatment in order not to lose the conservation properties of the scheme. We discuss several options. Numerical examples in one, two and three space dimensions show that the method of characteristics coupled with a nonequispaced fast Fourier transform (NFFT) provides a fast and reliable technique for achieving mass conservation at the discrete level

Towards a Modular Architecture for eXtended Reality Systems

For full-fledged social acceptance of eXtended Reality (XR) systems, emphasis should be on design prototypes to allow frictionless, context-aware, and secure interaction with non-specialized users. This necessitates a modular architecture to ensure that the system is versatile and applicable across applications, and is open to the integration of interaction modalities. We discuss our proposal for (and prototypical implementation of) a modular architecture for XR systems that relies on cloud infrastructure resources and edge computing frameworks with shared communication protocols for scalability. The modules are abstracted from both functional and non-functional requirements, including security