Two-dimensional ³He: A crucial system for understanding fermion dynamics

Neutron scattering measurements at the Institut Laue-Langevin off quasi-two-dimensional ³He have shown, for the first time, a situation where the collective mode crosses the particle-hole continuum and reappears, at a momentum transfer of q≈1.55 Å ^-1 as a well-defined collective excitation (Godfrin et al. in J. Low Temp. Phys., 2009, in press). The effect is well described by the Fermion generalization of multi-particle fluctuation theory of Jackson, Feenberg, and Campbell that has been so successful for bosonic quantum fluids. We describe the theory briefly and state that it can be mapped onto the form of time-dependent Hartree-Fock theory (TDHF) containing energy dependent effective interactions; these are obtained from microscopic ground state theory. Our theoretical result has far-reaching consequences: a popular paradigm in discussing the density-density response function of Fermi systems is the "random phase approximation" (RPA), most frequently applied with some static interaction and, perhaps, some effective mass. Such a "phenomenologically modified" RPA can be justified only under severe simplifying approximations and is unable to describe the experimental situation consistently. As soon as one goes beyond the RPA, intermediate states which cannot be described in terms of the quantum numbers of a single (quasi-)particle become essential for capturing the correct physics. In order to understand the above mentioned experiment, their appropriate inclusion, as presented in this work, is essential.