Multilevel interference of a neutron wave

We present an analytical and numerical analysis of neutron multilevel interference phenomena generated when a neutron passes through a series of N resonant coils operated at the successive conditions ({Dirac_h}/2{pi})({omega}{sub 0}+n{delta}{omega})=2{mu}{sub n}(B{sub 0}+n{delta}B) with n=0,1,...,N-1. Each coil produces spin flip with probability {rho} between 0 and 1; thus the number of waves for the neutron is doubled after each coil, finally giving 2{sup N} interfering neutron waves. The phase difference between any pair is a multiple of a time dependent 'phase quantum' {delta}{phi}(t). The analysis predicts for each number N a highly regular pattern for the quantum mechanical probability to find the neutron spin in one specific state as a function of {rho} and {delta}{phi}. These patterns evolve in time and show revivals after a time T determined by the step {delta}{omega} according to T=2{pi}/{delta}{omega}. For some adjustments of the system an analytical solution is obtained. Application of multilevel interference in high-resolution neutron modulated-intensity-by-zero-effort-type spectrometers is discussed.