Abstract: The decomplexification procedure allows one to show mathematically (stricto sensu) the equivalence (isomorphism) between the quantum dynamics of a system with a finite number of basis states and a classical dynamics system. This unique way of connecting different dynamics was used in the past to analyze the relationship between the well-known geometric phase present in the quantum evolution discovered by Berry and its generalizations, with their analogs, the Hannay phases, in the classical domain. In here, this analysis is carried out for several quantum hermitian and non-hermitian PT-symmetric Hamiltonians and compared with the Hannay phase analysis in their classical isomorphic equivalent systems. As the equivalence ends in the classical domain with oscillator dynamics, we exploit the analogy to propose resonant electric circuits coupled with a gyrator, to reproduce the geometric phase coming from the theoretical solutions, in simulated laboratory experiments.

Abstract: The concordance of the ACDM cosmological model in light of current observations has been the subject of an intense debate in recent months. The 2018 Planck Cosmic Microwave Background (CMB) temperature anisotropy power spectrum measurements appear at face value to favour a spatially closed Universe with curvature parameter Omega(K) < 0. This preference disappears if Baryon Acoustic Oscillation (BAO) measurements are combined with Planck data to break the geometrical degeneracy, although the reliability of this combination has been questioned due to the strong tension present between the two datasets when assuming a curved Universe. Here, we approach this issue from yet another point of view, using measurements of the full-shape (FS) galaxy power spectrum, P(k), from the Baryon Oscillation Spectroscopic Survey DR12 CMASS sample. By combining Planck data with FS measurements, we break the geometrical degeneracy and find Omega(K) = 0.0023 +/- 0.0028. This constrains the Universe to be spatially flat to sub-percent precision, in excellent agreement with results obtained using BAO measurements. However, as with BAO, the overall increase in the best-fit chi(2) suggests a similar level of tension between Planck and P(k) under the assumption of a curved Universe. While the debate on spatial curvature and the concordance between cosmological datasets remains open, our results provide new perspectives on the issue, highlighting the crucial role of FS measurements in the era of precision cosmology.

Abstract: The impact of dark matter-neutrino interactions on the measurement of the cosmological parameters has been investigated in the past in the context of massless neutrinos exclusively. Here we revisit the role of a neutrino-dark matter coupling in light of ongoing cosmological tensions by implementing the full Boltzmann hierarchy for three massive neutrinos. Our tightest 95% CL upper limit on the strength of the interactions, parameterized via u(chi) = sigma(0)/sigma(Th) (m(chi)/100GeV)(-1), is u(chi) <= 3.34 . 10(-4), arising from a combination of Planck TTTEEE data, Planck lensing data and SDSS BAO data. This upper bound is, as expected, slightly higher than previous results for interacting massless neutrinos, due to the correction factor associated with neutrino masses. We find that these interactions significantly relax the lower bounds on the value of sigma 8 that is inferred in the context of Lambda CDM from the Planck data, leading to agreement within 1-2 sigma with weak lensing estimates of sigma 8, as those from KiDS1000. However, the presence of these interactions barely affects the value of the Hubble constant H-0.