Ricci flow, quantum mechanics and gravity

It has been argued that, underlying any given quantum-mechanical model, there exists at least one deterministic system that reproduces, after prequantisation, the given quantum dynamics. For a quantum mechanics with a complex d-dimensional Hilbert space, the Lie group SU(d) represents classical canonical transformations on the projective space CP^{d-1} of quantum states. Let R stand for the Ricci flow of the manifold SU(d-1) down to one point, and let P denote the projection from the Hopf bundle onto its base CP^{d-1}. Then the underlying deterministic model we propose here is the Lie group SU(d), acted on by the operation PR. Finally we comment on some possible consequences that our model may have on a quantum theory of gravity.Comment: 8 page

Roper Excitation in Alpha-Proton Scattering

We study the Roper excitation in the $(\alpha,\alpha')$ reaction. We consider all processes which may be relevant in the Roper excitation region, namely, Roper excitation in the target, Roper excitation in the projectile, and double $\Delta$ excitation processes. The theoretical investigation shows that the Roper excitation in the proton target mediated by an isoscalar exchange is the dominant mechanism in the process. We determine an effective isoscalar interaction by means of which the experimental cross section is well reproduced. This should be useful to make predictions in related reactions and is a first step to construct eventually a microscopic $NN \rightarrow NN^*$ transition potential, for which the present reaction does not offer enough information.Comment: Latex 17 pages; figures available by request; Phys. Rev. C in prin

Neutrino masses and mixing parameters in a left-right model with mirror fermions

In this work we consider a left-right model containing mirror fermions with gauge group SU(3)$_{C} \otimes SU(2)_{L} \otimes SU(2)_{R} \otimes U(1)_{Y^\prime}$. The model has several free parameters which here we have calculated by using the recent values for the squared-neutrino mass differences. Lower bound for the mirror vacuum expectation value helped us to obtain crude estimations for some of these parameters. Also we estimate the order of magnitude of the masses of the standard and mirror neutrinos.Comment: 13 pages, version submitted to European Physical Journal

On Z2Z4-additive complementary dual codes and related LCD codes

Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space with mixed binary and quaternary alphabets. These codes are additive, in the sense that they are additive subgroups, rather than linear as they are not vector spaces over some finite field. We study the structure of these codes and we use the canonical Gray map from this space to the Hamming space to construct binary LCD codes in certain cases. We give examples of such binary LCD codes which are distance-optimal, i.e., they have the largest minimum distance among all binary LCD codes with the same length and dimension

Coherent pion production in neutrino nucleus collision in the 1 GeV region

We calculate cross sections for coherent pion production in nuclei induced by neutrinos and antineutrinos of the electron and muon type. The analogies and differences between this process and the related ones of coherent pion production induced by photons, or the (p,n) and $(^3 He, t)$ reactions are discussed. The process is one of the several ones occurring for intermediate energy neutrinos, to be considered when detecting atmospheric neutrinos. For this purpose the results shown here can be easily extrapolated to other energies and other nuclei.Comment: 13 pages, LaTex, 8 post-script figures available at [email protected]

Projectile Δ\Delta and target-Roper excitation in the p (d, d')X reaction

In this paper we compare a model that contains the mechanisms of $\Delta$ excitation in the projectile and Roper excitation in the target with experimental data from two (d, d') experiments on a proton target. The agreement of the theory with the experiment is fair for the data taken at T_d = 2.3 GeV. The $\Delta$ excitation in the projectile is predicted close to the observed energy with the correct width. The theory, however, underpredicts by about 40% the cross sections measured at T_d = 1.6 GeV at angles where the cross section has fallen by about two orders of magnitude. The analysis done here allows to extract an approximate strength for the excitation of the Roper [N^*(1440)] excitation and a qualitative agreement with the theoretical predictions is also found.Comment: 8 ps figure

Variability in low Mars atmosphere's H2_2O concentration stimulated by solar cycle activity

Mars' thin, CO$_2$-rich atmosphere poses a unique puzzle involving composition, climate history, and habitability. This work explores the intrincate relationship between Mars' atmospheric variations and dynamic solar activity patterns. We focus on periodic oscillations in H$_2$O vapor and the Pectinton solar flux index in the $\lambda$ = 10.7 cm radio band, around the characteristic 11-year solar cycle. Periodic Mars activity was studied using data from Mars Express' SPICAM instrument spanning 2004-2018. The Lomb-Scargle Periodogram method was applied to analyze the power spectra of both signals around this period, calibrated using peaks associated with the seasonal Martian cycle. This method was validated by analyzing power spectra of chemical species abundances in Earth's atmosphere, obtained from the NRLMSISE 00 empirical model provided by the National Oceanic and Atmospheric Administration (NOAA). Model executions reproduced chemical abundance data for various atmospheric species (N$_2$, O$_2$, N, H$_2$, Ar, and He) at two reference heights (upper mesosphere and low ionosphere) over a 1961-2021 time span. Results suggest a connection between variability in H$_2$O vapor concentration in Mars' atmosphere and fluctuations in the Pectinton solar flux index. We propose the Lomb-Scargle Periodogram method as a heuristic for studying oscillatory activity in planetary atmospheres with non-uniformly sampled data. While our results provide valuable insights, further analysis, cross-referencing with data from different orbiters, is required to deepen our understanding of these findings in the fields of planetary climatology and atmospheric physics.Comment: 25 pages, 24 figures. Submitted to MNRA

Roper excitation in p⃗+α→p⃗+α+X\vec{p}+\alpha \to \vec{p}+\alpha+X reactions

We calculate differential cross sections and the spin transfer coefficient $D_{nn}$ in the $\vec{p}+\alpha \to \vec{p}+\alpha+\pi^0$ reaction for proton bombarding energies from 1 to 10 GeV and $\pi^0 - p$ invariant masses spanning the region of the N$^*$(1440) Roper resonance. Two processes -- $\Delta$ excitation in the $\alpha$-particle and Roper excitation in the proton -- are included in an effective reaction model which was shown previously to reproduce existing inclusive spectra. The present calculations demonstrate that these two contributions can be clearly distinguished via $D_{nn}$, even under kinematic conditions where cross sections alone exhibit no clear peak structure due to the excitation of the Roper.Comment: 12 pages, 11 ps figures, Late

Ground states and formal duality relations in the Gaussian core model

We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core model in up to eight dimensions. The results include unexpected geometric structures, with surprising anisotropy as well as formal duality relations. These duality relations suggest that the Gaussian core model possesses unexplored symmetries, and they have implications for a broad range of soft-core potentials.Comment: 7 pages, 1 figure, appeared in Physical Review E (http://pre.aps.org