The mechanism analysis for the fractional quantum dynamics on a comb structure with the absorbing boundary conditions

The paper contributes to investigating the quantum transport on a comb structure, whose feature of quantum motion is geometrically constrained such that the quantum motion is exclusively restricted to the backbone along the x -direction. Instead of substituting with the fractional derivative directly, the one-dimensional (1D) time fractional Schrödinger equation (TFSE) is formulated, which is derived by mathematical derivation from the 2D Schrödinger equation with the wave operator (SEWO). The infinite boundaries are replaced with the absorbing boundary conditions (ABCs). The finite difference method (FDM) is formulated, followed by theoretical analysis to establish stability and convergence. A fast scheme is employed to enhance computational efficiency. The contrast of the numerical and exact solutions is analyzed by innovating a source term. In addition, the contrast of the distributions for the ABCs and zero boundary conditions is analyzed. Results show that ABCs provide a more accurate numerical solution compared to zero boundary conditions. Finally, the evolutions of the modules and the phasic pictures with different parameters are given.