Existence of resonant tunnelling in multicomponent superfluid 3He

Determine whether resonant tunnelling can occur for the multicomponent spin-triplet p-wave order parameter of superfluid 3He, i.e., whether the A–B transition dynamics in superfluid 3He admits resonant tunnelling enabled by classically allowed intermediate states of equal energy.

Background

The paper reviews proposed explanations for the unexpectedly fast A–B transition in superfluid 3He, where classical homogeneous nucleation theory predicts astronomically long lifetimes of the metastable A phase. Among various hypotheses, resonant tunnelling has been suggested as a mechanism that could enhance transition rates.

In quantum field theory with a single scalar field, classically allowed intermediate states necessary for resonant tunnelling were shown not to exist, which rules out the mechanism in that context. Superfluid 3He, however, has a multicomponent (18-component) order parameter, leaving open whether resonant tunnelling might operate in this more complex setting. Clarifying this would help assess whether resonant tunnelling can explain A–B nucleation in ultra-pure superfluid 3He.

References

It has also been proposed that resonant tunnelling, a quantum-mechanical phenomenon where quantum tunnelling can proceed via a classically allowed intermediate state of the same energy, could be at play in superfluid $3$He as well . However, such classically allowed states were shown not to exist in the quantum field theory of a single scalar field , so the existence of resonant tunnelling for the multicomponent order parameter of $3$He is not clear.

— A-B transition in superfluid $^3$He and cosmological phase transitions  (2401.07878 - Hindmarsh et al., 2024) in Section 4 (Explanations for the nucleation puzzle)