Binary mixtures of chiral gases

A possible solution of the well known paradox of chiral molecules is based on the idea of spontaneous symmetry breaking. At low pressure the molecules are delocalized between the two minima of a given molecular potential while at higher pressure they become localized in one minimum due to the intermolecular dipole-dipole interactions. Evidence for such a phase transition is provided by measurements of the inversion spectrum of ammonia and deuterated ammonia at different pressures. In particular, at pressure greater than a critical value no inversion line is observed. These data are well accounted for by a model previously developed and recently extended to mixtures. In the present paper, we discuss the variation of the critical pressure in binary mixtures as a function of the fractions of the constituents.Comment: 5 pages, 1 figure, text substantially based on arXiv:1501.02099 to be presented in Progress in Electromagnetics Research Symposium (PIERS) 201

An equilibrium state with macroscopic correlations

In this paper we show that the equilibrium macroscopic entropy of a generic non reversible Kawasaki+Glauber dynamics is a non local functional of the density. This implies that equilibrium correlations extend to macroscopic distances.Comment: 8 page

Spontaneous symmetry breaking and inversion-line spectroscopy in gas mixtures

According to quantum mechanics chiral molecules, that is molecules that rotate the polarization of light, should not exist. The simplest molecules which can be chiral have four or more atoms with two arrangements of minimal potential energy that are equivalent up to a parity operation. Chiral molecules correspond to states localized in one potential energy minimum and can not be stationary states of the Schr\"odinger equation. A possible solution of the paradox can be founded on the idea of spontaneous symmetry breaking. This idea was behind work we did previously involving a localization phase transition: at low pressure the molecules are delocalized between the two minima of the potential energy while at higher pressure they become localized in one minimum due to the intermolecular dipole-dipole interactions. Evidence for such a transition is provided by measurements of the inversion spectrum of ammonia and deuterated ammonia at different pressures. A previously proposed model gives a satisfactory account of the empirical results without free parameters. In this paper, we extend this model to gas mixtures. We find that also in these systems a phase transition takes place at a critical pressure which depends on the composition of the mixture. Moreover, we derive formulas giving the dependence of the inversion frequencies on the pressure. These predictions are susceptible to experimental test.Comment: 15 pages, 11 figure

On Schroedinger Equations with Concentrated Nonlinearities

Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to separate the relevant degrees of freedom by noticing that in the regions where the nonlinearities are effective all states are suppressed but the metastable ones (resonances). In this way the description of the nonlinear regions is reduced to ordinary differential equations weakly coupled to standard Schr\"odinger equations valid in the linear regions. The idea is illustrated through the study of a prototype equation recently proposed for resonant tunneling of electrons through a double barrier heterostructure and for which nonlinear oscillations have been numerically predicted.Comment: 24 pages with figures, compressed and uuencoded ps fil

Evolution of fermionic systems as an expectation over Poisson processes

We derive an exact probabilistic representation for the evolution of a Hubbard model with site- and spin-dependent hopping coefficients and site-dependent interactions in terms of an associated stochastic dynamics of a collection of Poisson processes.Comment: 4 pages, contribution to the proceedings of tenth International Conference on Recent Progress in Many-Body Theories, Seattle, 199