Three Dimensional Time Domain Simulation of the Quantum Magnetic Susceptibility

A way of using the Finite Difference Time Domain method is described to simulate the magnetic susceptibility of a quantum toroid. This simulation is based on the direct implementation of the time-dependent Schrödinger equation in three dimensions. First, the ground state eigenenergy and eigenstate are found. Next, the expectation value of the quantum magnetic dipole operator is calculated as a function of the applied magnetic field strength with a static magnetic field, and the results are compared with classical results. Then the magnetic dipole moment is calculated with a time-oscillating magnetic field applied. These expectation values are used to calculate the linear and nonlinear magnetic susceptibility of a torus, both without a grating and with a grating to increase irregularities in the shape, by repeating the calculations at various frequencies. The results are consistent with the expected results. This method can be used to calculate the quantum magnetic susceptibility of any structure in order to search for structures with better nonlinear properties.