A mathematical model for the Fermi weak interactions

We consider a mathematical model of the Fermi theory of weak interactions as patterned according to the well-known current-current coupling of quantum electrodynamics. We focuss on the example of the decay of the muons into electrons, positrons and neutrinos but other examples are considered in the same way. We prove that the Hamiltonian describing this model has a ground state in the fermionic Fock space for a sufficiently small coupling constant. Furthermore we determine the absolutely continuous spectrum of the Hamiltonian and by commutator estimates we prove that the spectrum is absolutely continuous away from a small neighborhood of the thresholds of the free Hamiltonian. For all these results we do not use any infrared cutoff or infrared regularization even if fermions with zero mass are involved

The vibrational dynamics of vitreous silica: Classical force fields vs. first-principles

We compare the vibrational properties of model SiO_2 glasses generated by molecular-dynamics simulations using the effective force field of van Beest et al. (BKS) with those obtained when the BKS structure is relaxed using an ab initio calculation in the framework of the density functional theory. We find that this relaxation significantly improves the agreement of the density of states with the experimental result. For frequencies between 14 and 26 THz the nature of the vibrational modes as determined from the BKS model is very different from the one from the ab initio calculation, showing that the interpretation of the vibrational spectra in terms of calculations using effective potentials can be very misleading.Comment: 7 pages of Latex, 4 figure

On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field

We consider a non-relativistic electron interacting with a classical magnetic field pointing along the $x_3$-axis and with a quantized electromagnetic field. The system is translation invariant in the $x_3$-direction and we consider the reduced Hamiltonian $H(P_3)$ associated with the total momentum $P_3$ along the $x_3$-axis. For a fixed momentum $P_3$ sufficiently small, we prove that $H(P_3)$ has a ground state in the Fock representation if and only if $E'(P_3)=0$, where $P_3 \mapsto E'(P_3)$ is the derivative of the map $P_3 \mapsto E(P_3) = \inf \sigma (H(P_3))$. If $E'(P_3) \neq 0$, we obtain the existence of a ground state in a non-Fock representation. This result holds for sufficiently small values of the coupling constant

Universal electric-field-driven resistive transition in narrow-gap Mott insulators

One of today's most exciting research frontier and challenge in condensed matter physics is known as Mottronics, whose goal is to incorporate strong correlation effects into the realm of electronics. In fact, taming the Mott insulator-to-metal transition (IMT), which is driven by strong electronic correlation effects, holds the promise of a commutation speed set by a quantum transition, and with negligible power dissipation. In this context, one possible route to control the Mott transition is to electrostatically dope the systems using strong dielectrics, in FET-like devices. Another possibility is through resistive switching, that is, to induce the insulator-to-metal transition by strong electric pulsing. This action brings the correlated system far from equilibrium, rendering the exact treatment of the problem a difficult challenge. Here, we show that existing theoretical predictions of the off-equilibrium manybody problem err by orders of magnitudes, when compared to experiments that we performed on three prototypical narrow gap Mott systems V2-xCrxO3, NiS2-xSex and GaTa4Se8, and which also demonstrate a striking universality of this Mott resistive transition (MRT). We then introduce and numerically study a model based on key theoretically known physical features of the Mott phenomenon in the Hubbard model. We find that our model predictions are in very good agreement with the observed universal MRT and with a non-trivial timedelay electric pulsing experiment, which we also report. Our study demonstrates that the MRT can be associated to a dynamically directed avalanche

Dissolution–precipitation processes governing the carbonation and silicification of the serpentinite sole of the New Caledonia ophiolite

International audienceThe weathering of mantle peridotite tectoni-cally exposed to the atmosphere leads commonly to natural carbonation processes. Extensive cryptocrystalline mag-nesite veins and stock-work are widespread in the ser-pentinite sole of the New Caledonia ophiolite. Silica is systematically associated with magnesite. It is commonly admitted that Mg and Si are released during the laterization of overlying peridotites. Thus, the occurrence of these veins is generally attributed to a per descensum mechanism that involves the infiltration of meteoric waters enriched in dissolved atmospheric CO 2. In this study, we investigate serpentinite carbonation processes, and related silicifica-tion, based on a detailed petrographic and crystal chemical study of serpentinites. The relationships between serpen-tine and alteration products are described using an original method for the analysis of micro-X-ray fluorescence images performed at the centimeter scale. Our investigations highlight a carbonation mechanism, together with precipitation of amorphous silica and sepiolite, based on a dis-solution–precipitation process. In contrast with the per descensum Mg/Si-enrichment model that is mainly concentrated in rock fractures, dissolution–precipitation process is much more pervasive. Thus, although the texture of rocks remains relatively preserved, this process extends more widely into the rock and may represent a major part of total carbonation of the ophiolite

A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices

Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. For the antiferromagnetic chain we recover the Haldane decomposition. This order parameter interacts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natural manner. In fact this merely corresponds to a novel extension of the spin group by a local gauge field. This analysis based on the real division algebras applies to low dimensional lattices.Comment: 5 pages; REVTeX

Electronic redistribution around oxygen atoms in silicate melts by ab initio molecular dynamics simulation

The structure around oxygen atoms of four silicate liquids (silica, rhyolite, a model basalt and enstatite) is evaluated by ab initio molecular dynamics simulation. Thanks to the use of maximally localized Wannier orbitals to represent the electronic ground state of the simulated system, one is able to quantify the redistribution of electronic density around oxygen atoms as a function of the cationic environment and melt composition. It is shown that the structure of the melt in the immediate vicinity of the oxygen atoms modulates the distribution of the Wannier orbitals associated with oxygen atoms. In particular the evaluation of the distances between the oxygen-core and the orbital Wannier centers and their evolution with the nature of the cation indicates that the Al-O bond in silicate melts is certainly less covalent than the Si-O bond while for the series Mg-O, Ca-O, Na-O and K-O the covalent character of the M-O bond diminishes rapidly to the benefit of the ionic character. Furthermore it is found that the distribution of the oxygen dipole moment coming from the electronic polarization is only weakly dependent on the melt composition, a finding which could explain why some empirical force fields can exhibit a high degree of transferability with melt composition.Comment: 27 pages, 7 figures. To be published in Journal of Non-Crystalline Solid

Coupling between magnetic field and curvature in Heisenberg spins on surfaces with rotational symmetry

We study the nonlinear $\sigma$-model in an external magnetic field applied on curved surfaces with rotational symmetry. The Euler-Lagrange equations derived from the Hamiltonian yield the double sine-Gordon equation (DSG) provided the magnetic field is tuned with the curvature of the surface. A $2\pi$ skyrmion appears like a solution for this model and surface deformations are predicted at the sector where the spins point in the opposite direction to the magnetic field. We also study some specific examples by applying the model on three rotationally symmetric surfaces: the cylinder, the catenoid and the hyperboloid. The coupling between a magnetic field and the curvature of the substract is an interesting result and we believe that this issue may be relevant to be applied in condensed matter systems, e.g., superconductors, nematic liquid crystals, graphene and topological insulators.Comment: To be published in Physics Letters