The Landau-Zener Transition and the Surface Hopping Method for the 2D Dirac Equation for Graphene

DOI10.4208/cicp.020515.250716azbMath1488.35458arXiv1505.05988OpenAlexW2964335219MaRDI QIDQ5158730

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Publication date: 26 October 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.05988

zbMATH Keywords

Dirac equationsemiclassical modelspectral methodsWigner transformLandau-Zener formulaband crossingsurface hopping algorithm

Mathematics Subject Classification ID

Computational methods for problems pertaining to quantum theory (81-08) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Applications of quantum theory to specific physical systems (81V99) Simulation of dynamical systems (37M05) Applications to the sciences (65Z05) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (3)

A Micro-Macro Method for a Kinetic Graphene Model in One Space Dimension ⋮ Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations ⋮ Global geometrical optics method for vector-valued Schrödinger problems

Uses Software

• NanoTCAD ViDES

Cites Work

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• Regularized semiclassical limits: linear flows with infinite Lyapunov exponents
• A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene
• Single-cone real-space finite difference scheme for the time-dependent Dirac equation
• A hybrid Schrödinger/Gaussian beam solver for quantum barriers and surface hopping
• Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps
• A coherent semiclassical transport model for pure-state quantum scattering
• A Landau-Zener formula for non-degenerated involutive codimension 3 crossings
• A kinetic model for the transport of electrons in a graphene layer
• Basics of surface hopping in mixed quantum/classical simulations
• Destruction of the beating effect for a nonlinear Schrödinger equation
• Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
• Construction and validation of a rigorous surface hopping algorithm for conical crossing
• A time-splitting spectral scheme for the Maxwell-Dirac system
• PLANE WAVE STABILITY OF THE SPLIT-STEP FOURIER METHOD FOR THE NONLINEAR SCHRÖDINGER EQUATION
• An Eulerian Surface Hopping Method for the Schrödinger Equation with Conical Crossings
• Wigner model for quantum transport in graphene
• Mathematical and computational methods for semiclassical Schrödinger equations
• Mesures semi-classiques et croisement de modes
• Homogenization limits and Wigner transforms
• Non-adiabatic crossing of energy levels
• Central Differencing Based Numerical Schemes for Hyperbolic Conservation Laws with Relaxation Terms
• Finite Volume Methods for Hyperbolic Problems
• Semiclassical asymptotics for the Maxwell–Dirac system
• Propagation through conical crossings: An asymptotic semigroup

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