Abstract
We develop a theory that incorporates the relaxation properties of a condensed medium into the quantum decay of a metastable liquid near the liquid-gas spinodal line at low temperatures. We find that both the regime and the rate of quantum nucleation strongly depend on the relaxation time and its temperature behavior. The quantum nucleation rate slows down with decreasing relaxation time. We also discuss the low-temperature experiments on cavitation in normal $^{3}\mathrm{He}$ and superfluid $^{4}\mathrm{He}$ at negative pressures. It is the drastic distinctions in the properties of the high-frequency sound mode and in the temperature behavior of the relaxation time that make the quantum cavitation kinetics in $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ completely different.
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