Effective quantum Hamiltonian for a two-mesh LC circuit with discrete charge: Managing of currents and voltages

In this paper, we study the dynamics of a quantum two-mesh LC circuit with discrete charge subject to rapidly oscillating voltage sources. A time-independent effective Hamiltonian for this system is derived in a high-frequency series expansion upto ω-2 whose dominant behavior indicates the possibility of observing two physical phenomena: first, the controlled manipulation and suppression of the mesh currents by setting specific values of the voltage source amplitudes and, second, the onset of a DC regime (in the single-mesh case) which could be inferred by interpreting the quasi-degenerate quantum states.