Evolution of escape processes with a time-varying load

We study an escape process of a noisy particle with a time varying load. We present an effective nonperturbative method which works even when the time varying load amplitude is comparable to other parameters. It is based on the idea that for every instant of time, we know the quasiadiabatic eigenspectrum and the quasiadiabatic eigenfunctions of the instantaneous system. We show that when two time-varying quasiadiabatic eigenvalues in the spectrum get close to each other, the amplitudes of the quasiadiabatic eigenfuntions show an abrupt change; therefore, the escape rate is highly affected.