Abstract:
A fast algorithm is used to study the transient behavior due to the step-like pulse. This algorithm consists of two parts: The algorithm I reduces the computational complexity to T 0 N 3 for large systems as long as T 0 N 3 whenever T 2 beyond which it becomes T log 2 N for even longer time. Hence it is of order O(1) if T 2 . Benchmark calculation has been done on graphene nanoribbons with N=10 4 and T=10 8 . This new algorithm allows many large scale transient problems to be solved, including magnetic tunneling junctions and ferroelectric tunneling junctions that could not be achieved before.