52 research outputs found
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
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