Evolution of energy and magnetic moment of a quantum charged particle in power-decaying magnetic fields

Abstract

We consider a quantum spinless nonrelativistic charged particle moving in the xy plane under the action of a homogeneous time-dependent magnetic field B(t)=B0(1+t/t0)−1−g, directed along the z-axis and described by means of the vector potential A(t)=B(t)[−y,x]/2. Assuming that the particle was initially in the thermal equilibrium state with a negligible coupling to a reservoir, we obtain exact formulas for the time-dependent mean values of the energy and magnetic moment in terms of the Bessel functions. Different regimes of the evolution are discovered and illustrated in several figures. The energy goes asymptotically to a finite value if g>0 (“fast” decay), while it goes asymptotically to zero if g≤0 (“slow” decay). The dependence on parameter t0 practically disappears when 1+g is close to zero value (“superslow” decay). The mean magnetic moment goes to zero for g>1, while it grows unlimitedly if g<1.