单锥实空间有限差分方案用于Dirac von Neumann方程
Single-cone real-space finite difference schemes for the Dirac von Neumann equation
AI总结：
本文提出两种单锥交错时空网格方案用于求解(2+1)D Dirac哈密顿量的von Neumann方程，第一种基于密度算符的
摘要：
本文提出了两种有限差分方案用于处理(2+1)D Dirac哈密顿量的von Neumann方程。两种方案均采用单锥交错时空网格，以确保单锥能谱，从而在von Neumann方程中表征混合态动力学。第一种方案根据密度算符的
英文摘要：
Two finite difference schemes for the numerical treatment of the von Neumann equation for the (2+1)D Dirac Hamiltonian are presented. Both utilize a single-cone staggered space-time grid which ensures a single-cone energy dispersion to formulate a numerical treatment of the mixed-state dynamics within the von Neumann equation. The first scheme executes the time-derivative according to the product rule for "bra" and "ket" indices of the density operator. It therefore directly inherits all the favorable properties of the difference scheme for the pure-state Dirac equation and conserves positivity. The second scheme proposed here performs the time-derivative in one sweep. This direct scheme is investigated regarding stability and convergence. Both schemes are tested numerically for elementary simulations using parameters which pertain to topological insulator surface states. Application of the schemes to a Dirac Lindblad equation and real-space-time Green's function formulations are discussed.
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