Spontaneous symmetry breaking and inversion-line spectroscopy in gas mixtures

TL;DR

This paper extends a model of spontaneous symmetry breaking in chiral molecules to gas mixtures, predicting a pressure-dependent phase transition and inversion frequencies, supported by experimental evidence and offering testable formulas.

Contribution

It introduces a generalized model for symmetry breaking in gas mixtures, linking phase transition pressure to mixture composition and deriving pressure-dependent inversion frequency formulas.

Findings

Phase transition occurs at a critical pressure depending on mixture composition.

Inversion frequencies vary with pressure according to derived formulas.

Model aligns with empirical data from ammonia and deuterated ammonia spectra.

Abstract

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.