We develop a formalism to describe the scattering of dark matter (DM) particles by electrons bound in crystals for a general form of the underlying DM-electron interaction. Such a description is relevant for direct-detection experiments of DM particles lighter than a nucleon, which might be observed in operating DM experiments via electron excitations in semiconductor crystal detectors. Our formalism is based on an effective theory approach to general non-relativistic DM-electron interactions, including the anapole, and magnetic and electric dipole couplings, combined with crystal response functions defined in terms of electron wave function overlap integrals. Our main finding is that, for the usual simplification of the velocity integral, the rate of DM-induced electronic transitions in a semiconductor material depends on at most five independent crystal response functions, four of which were not known previously. We identify these crystal responses, and evaluate them using density functional theory for crystalline silicon and germanium, which are used in operating DM direct detection experiments. Our calculations allow us to set 90% confidence level limits on the strength of DM-electron interactions from data reported by the SENSEI and EDELWEISS experiments. The novel crystal response functions discovered in this work encode properties of crystalline solids that do not interact with conventional experimental probes, suggesting the use of the DM wind as a probe to reveal new kinds of hidden order in materials.

In the context of a microscopic model of string-inspired foam, in which foamy structures are provided by brany point-like defects (D-particles) in space-time, we discuss flavour mixing as a result of flavour non-preserving interactions of (low-energy) fermionic stringy matter excitations with the defects. Such interactions involve splitting and capture of the matter string state by the defect, and subsequent re-emission. As a result of charge conservation, only electrically neutral matter can interact with the D-particles. Quantum fluctuations of the D-particles induce a nontrivial space-time background; in some circumstances this could be akin to a cosmological Friedman-Robertson Walker expanding-Universe, with weak (but non-zero) particle production. Furthermore the D-particle medium can induce an MSW type effect. We have argued previously, in the context of bosons, that the so-called flavour vacuum is the appropriate state to be used, at least for lowenergy excitations, with energies/momenta up to a dynamically determined cutoff scale. Given the intriguing mass scale provided by neutrino flavour mass differences from the point of view of dark energy, we evaluate the flavour-vacuum expectation value (condensate) of the stress-energy tensor of the 1/2-spin fields with mixing in an effective low-energy Quantum Field Theory in this foaminduced curved space-time. We demonstrate, at late epochs of the Universe, that the fermionic vacuum condensate behaves as a fluid with negative pressure and positive energy; however the equation of state has w fermion > −1/3 and so the contribution of the fermion-fluid flavour vacuum alone could not yield accelerating Universes. Such contributions to the vacuum energy should be considered as (algebraically) additive to the flavoured boson contributions, evaluated in our previous works; this should be considered as natural from (broken) target-space supersymmetry that characterises realistic superstring/supermembrane models of space-time foam. The boson fluid is also characterised by positive energy and negative pressure, but its equation of state is, for late eras, close to w boson → −1, and hence overall the D-foam universe appears accelerating at late eras.

Perturbation theory using self-consistent Green's functions is one of the most widely used approaches to study many-body effects in condensed matter. On the basis of general considerations and by performing analytical calculations for the specific example of the Hubbard atom, we discuss some key features of this approach. We show that when the domain of the functionals that are used to realize the map between the non-interacting and the interacting Green's functions is properly defined, there exists a class of self-energy functionals for which the self-consistent Dyson equation has only one solution, which is the physical one. We also show that manipulation of the perturbative expansion of the interacting Green's function may lead to a wrong self-energy as functional of the interacting Green's function, at least for some regions of the parameter space. These findings confirm and explain numerical results of Kozik et al. for the widely used skeleton series of Luttinger and Ward [Phys. Rev. Lett. 114, 156402]. Our study shows that it is important to distinguish between the maps between sets of functions and the functionals that realize those maps. We demonstrate that the self-consistent Green's functions approach itself is not problematic, whereas the functionals that are widely used may have a limited range of validity.