Energy Transitions-Flip-Rate of Half Spin Particle by Magnetic Impurity in One Dimension

In this article, we considered the dependence of the rate of energy transition on various parameters and how the energy-transition -rate changes as a function of radius R. We observed that with increasing radius R, the energy-flip-rate decreases, which is perfectly consistent with a system approaching ferromagnetic order. Also the energy-transition-rate for different choices of the amplitude of the impurities, for a purely static potential scatter, no energy transition occurs, but for magnetic impurities, we observed a high peak in the energy-transition-rate for one particular amplitude of order 5 ？. Different profiles of energy-transition-rate (ETR) against frequencies and amplitude are drawn respectively, for angle , θ , with μBB0=0.5 and ？？？？x = R2 = 100 and different values of frequencies and amplitude