Quantization of the Smoluchowski equation and the problem of quantum tunneling at zero temperature

In this article we address the problem of quantum tunneling of a non-Markovian Brownian particle away from thermal equilibrium. We calculate the Kramers escape rate at low temperature (including the zero temperature case) in the Smoluchowski limit (strong friction regime). Our main findings are: (i) our quantum escape rate is valid far from the thermal equilibrium and is non-Markovian, but it becomes Markovian as the correlation time vanishes; (ii) at thermodynamic equilibrium we obtain a non-Markovian quantum rate that predicts a superfluidity phenomenon in the Markovian limit at low and zero temperatures.