Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A finite difference scheme for the numerical treatment of the von Neumann equation for the (2+1)D Dirac Hamiltonian is presented. It is based on a sequential left–right (ket–bra) application of a staggered space–time scheme for the pure-state Dirac equation and offers a numerical treatment of the general mixed-state dynamics of an isolated quantum system within the von Neumann equation. Thereby this direct scheme inherits all the favorable features of the finite-difference scheme for the pure-state Dirac equation, such as the single-cone energy–momentum dispersion, convergence conditions, and scaling behavior. A conserved functional is identified. Moreover this scheme is shown to conserve both Hermiticity and positivity. Numerical tests comprise a numerical analysis of stability, as ll as the simulation of a mixed-state time-evolution of Gaussian wave functions, illustrating Zitterbegung and transverse current oscillations. Imaginary-potential absorbing boundary conditions and parameters which pertain to topological insulator surface states re used in the numerical simulations.
['Magdalena Schreilechner', 'W. Pötz']
I am writing a research paper on a idea Real-space finite difference scheme for the von Neumann equation with the Dirac Hamiltonian
[{"from": "human", "value": "I am writing a research paper on a idea Real-space finite difference scheme for the von Neumann equation with the Dirac Hamiltonian"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A finite difference scheme for the numerical treatment of the von Neumann equation for the (2+1)D Dirac Hamiltonian is presented. It is based on a sequential left\u2013right (ket\u2013bra) application of a staggered space\u2013time scheme for the pure-state Dirac equation and offers a numerical treatment of the general mixed-state dynamics of an isolated quantum system within the von Neumann equation. Thereby this direct scheme inherits all the favorable features of the finite-difference scheme for the pure-state Dirac equation, such as the single-cone energy\u2013momentum dispersion, convergence conditions, and scaling behavior. A conserved functional is identified. Moreover this scheme is shown to conserve both Hermiticity and positivity. Numerical tests comprise a numerical analysis of stability, as ll as the simulation of a mixed-state time-evolution of Gaussian wave functions, illustrating Zitterbegung and transverse current oscillations. Imaginary-potential absorbing boundary conditions and parameters which pertain to topological insulator surface states re used in the numerical simulations."}]