Parity-violating macroscopic force between chiral molecules and source mass

A theory concerning non-zero macroscopic chirality-dependent force between a source mass and homochiral molecules due to the exchange of light particles is presented in this paper. This force is proposed to have opposite sign for molecules with opposite chirality. Using the central field approximation, we calculate this force between a copper block and a vessel of chiral molecules (methyl phenyl carbinol nitrite). The magnitude of force is estimated with the published limits of the scalar and pseudo-scalar coupling constants. Based on our theoretical model, this force may violate the equivalence principle when the homochiral molecules are used to be the test masses.Comment: 10 pages, 1 figur

Continuous symmetry reduction and return maps for high-dimensional flows

We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetry-equivalent points is represented by a single point. In either approach, numerical computations can be performed in the original state-space representation, and the solutions are then projected onto the symmetry-reduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a 5-dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for high-dimensional flows, symmetry reduction by the method of moving frames offers hope.Comment: 32 pages, 7 figure

Chiral Polymerization in Open Systems From Chiral-Selective Reaction Rates

We investigate the possibility that prebiotic homochirality can be achieved exclusively through chiral-selective reaction rate parameters without any other explicit mechanism for chiral bias. Specifically, we examine an open network of polymerization reactions, where the reaction rates can have chiral-selective values. The reactions are neither autocatalytic nor do they contain explicit enantiomeric cross-inhibition terms. We are thus investigating how rare a set of chiral-selective reaction rates needs to be in order to generate a reasonable amount of chiral bias. We quantify our results adopting a statistical approach: varying both the mean value and the rms dispersion of the relevant reaction rates, we show that moderate to high levels of chiral excess can be achieved with fairly small chiral bias, below 10%. Considering the various unknowns related to prebiotic chemical networks in early Earth and the dependence of reaction rates to environmental properties such as temperature and pressure variations, we argue that homochirality could have been achieved from moderate amounts of chiral selectivity in the reaction rates.Comment: 15 pages, 6 figures, accepted for publication in Origins of Life and Evolution of Biosphere

Punctuated Chirality

Most biomolecules occur in mirror, or chiral, images of each other. However, life is homochiral: proteins contain almost exclusively levorotatory (L) amino acids, while only dextrorotatory (R) sugars appear in RNA and DNA. The mechanism behind this fundamental asymmetry of life remains an open problem. Coupling the spatiotemporal evolution of a general autocatalytic polymerization reaction network to external environmental effects, we show through a detailed statistical analysis that high intensity and long duration events may drive achiral initial conditions towards chirality. We argue that life's homochirality resulted from sequential chiral symmetry breaking triggered by environmental events, thus extending the theory of punctuated equilibrium to the prebiotic realm. Applying our arguments to other potentially life-bearing planetary platforms, we predict that a statistically representative sampling will be racemic on average.Comment: 13 pages, 4 color figures. Final version published in Origins of Life and Evolution of Biospheres. Typos corrected, figures improved, and a few definitions and word usage clarifie

Decoherence Effects on Superpositions of Chiral States in a Chiral Molecule

The superposition of chiral states of chiral molecules, as delocalized quantum states of a many-particle system, can be used for the experimental investigations of decoherence theory. In this regard, a great challenge is the precise quantification of the robustness of these superpositions against environmental effects. The methods so far proposed need the detailed specification of the internal states of the molecule, usually requiring heavy numerical calculations. Here, by using the linearized quantum Boltzmann equation and by borrowing ideas employed for analyzing other quantum systems, we present a general and simple approach, of large applicability, which can be used to compute the dominant contribution to the decoherence rate for the superpositions of chiral states of chiral molecules, due to environmental scattering.Comment: 6 pages, 1 Figur

Gauge symmetry, chirality and parity violation in four-particle systems: Coulomb's law as a universal molecular function

Following recent work in search of a universal function (Van Hooydonk, Eur J Inorg Chem, 1999, 1617), we test symmetric potentials for reproducing molecular potential energy curves (PECs). For a bond, a four-particle system, charge inversion is the key to explain this shape generically. A parity adapted Hamiltonian reduces from ten to two terms. The analytical perturbed Coulomb function scales attractive and repulsive branches of 13 PECs (HH, HF, LiH, KH, AuH, LiLi, LiF, KLi, NaCs, RbRb,RbCs, CsCs and II) in a single straight line. Turning points are reproduced with a deviation of 0.3 % (0.007 angstrom). At the repulsive side, the deviation is 0.2 % (0.003 angstrom). The ab initio zero molecular parameter function gives PECs of acceptable quality, just using atomic ionisation energies. The function can be used as a model potential for inverting energy levels. The theory may be tested with femtochemistry. Reactions between hydrogen and anti-hydrogen, feasible in the near future, will probably produce normal HH.Comment: 90 p., 5 tables, 35 figure

Stability of dynamic squeezed state in four-wave mixing

One of the realistic models of the squeezed state generation in the four-wave mixing has been discussed. An asymptotic stability of the generation regime of the light dynamic squeezing is strictly shown. The absence of the periodic bifurcation for the experimental parameter values reveals that the multifrequency generation of the squeezed light has not taken place