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A coupled quantum-classical model describing the transport of electrons confined in nanoscale semiconductor devices is considered. Using the subband decomposition approach allows to separate the transport directions from the confinement…

Analysis of PDEs · Mathematics 2012-07-02 Paola Pietra , Nicolas Vauchelet

Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in {[Qiu and…

Numerical Analysis · Mathematics 2015-06-17 Andrew Christlieb , Wei Guo , Maureen Morton , Jing-Mei Qiu

We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured…

Numerical Analysis · Mathematics 2021-05-19 Daniel Fortunato , Nicholas Hale , Alex Townsend

Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. High-order operator splitting is an attractive approach for simulating…

Quantum Physics · Physics 2026-02-17 Peter Brearley , Philipp Pfeffer

Numerical solving the Schr\"odinger equation with incommensurate potentials presents a great challenge since its solutions could be space-filling quasiperiodic structures without translational symmetry nor decay. In this paper, we propose…

Numerical Analysis · Mathematics 2023-12-29 Kai Jiang , Shifeng Li , Juan Zhang

We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical…

Quantum Physics · Physics 2018-07-12 David Leiner , Steffen J. Glaser

Precise modeling of extended sources is a central challenge in modern optical engineering, laser physics, and computational lithography. Unlike ideal point sources or completely incoherent thermal radiation sources, real-world light sources…

Optics · Physics 2025-12-09 Rongqi Shang , Donglin Ma

This work develops simulation methods that enable the application of the variational quantum linear solver (VQLS) to simulate quantum transport in nanoscale semiconductor devices. Most previous work on VQLS applications in semiconductor…

Quantum Physics · Physics 2025-09-10 Qimao Yang , Jing Guo

We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…

Numerical Analysis · Mathematics 2015-07-14 Kui Du

The analysis of wave-packet dynamics may be greatly simplified when viewed in phase-space. While harmonic oscillators are often used as a convenient platform to study wave-packets, arbitrary state preparation in these systems is more…

Quantum Physics · Physics 2015-06-11 Yoni Shalibo , Roy Resh , Ofer Fogel , David Shwa , Radoslaw Bialczak , John M. Martinis , Nadav Katz

Solving partial differential equations is crucial to analysing and predicting complex, large-scale physical systems but pushes conventional high-performance computers to their limits. Application specific photonic processors are an exciting…

Computational Physics · Physics 2025-11-04 Timoteo Lee , Frank Brückerhoff-Plückelmann , Jelle Dijkstra , Jan M. Pawlowski , Wolfram Pernice

The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr\"{o}dinger equations. However, when applied to certain nonlinear time-dependent Schr\"{o}dinger equations, this algorithm loses…

Chemical Physics · Physics 2024-09-26 Julien Roulet , Jiří Vaníček

In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation. The relevant scale which characterizes this kind of problems is the diffusive scaling. This means that,…

Numerical Analysis · Mathematics 2016-08-24 G. Dimarco , L. Pareschi , V. Rispoli

In this brief report we present a feasible scheme to split quantum information in the realm of traveling waves. An oversimplified scheme is also proposed for the generation of a class of W states useful for perfect teleportation and…

Quantum Physics · Physics 2009-09-03 W. B. Cardoso , N. G. de Almeida , A. T. Avelar , B. Baseia

By taking the Weyl equation with external electro-magnetic potentials as the simplest representative for a system of PDOs, we give a new method of treating non-commutativity of coefficients matrices. More precisely, we construct a Fourier…

Mathematical Physics · Physics 2007-05-23 Atsushi Inoue

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. One such strategy is multigrid. To realize the potential of…

Numerical Analysis · Mathematics 2023-02-27 Malachi Phillips , Paul Fischer

In this paper, we develop two energy-preserving splitting methods for solving three-dimensional stochastic Maxwell equations driven by multiplicative noise. We use operator splitting methods to decouple stochastic Maxwell equations into…

Numerical Analysis · Mathematics 2025-12-30 Liying Zhang , Xinyue Kang , Lihai Ji

We report on a high-fidelity digital quantum simulation of Wigner localisation in a quasi-one-dimensional (quasi-1D) electron system using a 6-qubit segment of the state-of-the-art \textbf{IBM\,Heron\,2} quantum processor. By mapping the…

Quantum Physics · Physics 2026-01-06 Airat Kiiamov , Dmitrii Tayurskii

We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the…

Computational Physics · Physics 2020-08-19 Robert Arslanbekov , Vladimir Kolobov

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we…

Computational Physics · Physics 2015-06-15 Ch. Skokos , E. Gerlach , J. D. Bodyfelt , G. Papamikos , S. Eggl