Methanol as a tracer of fundamental constants

The methanol molecule CH3OH has a complex microwave spectrum with a large number of very strong lines. This spectrum includes purely rotational transitions as well as transitions with contributions of the internal degree of freedom associated with the hindered rotation of the OH group. The latter takes place due to the tunneling of hydrogen through the potential barriers between three equivalent potential minima. Such transitions are highly sensitive to changes in the electron-to-proton mass ratio, mu = m_e/m_p, and have different responses to mu-variations. The highest sensitivity is found for the mixed rotation-tunneling transitions at low frequencies. Observing methanol lines provides more stringent limits on the hypothetical variation of mu than ammonia observation with the same velocity resolution. We show that the best quality radio astronomical data on methanol maser lines constrain the variability of mu in the Milky Way at the level of |Delta mu/mu| < 28x10^{-9} (1sigma) which is in line with the previously obtained ammonia result, |Delta mu/mu| < 29x10^{-9} (1\sigma). This estimate can be further improved if the rest frequencies of the CH3OH microwave lines will be measured more accurately.Comment: 7 pages, 1 table, 1 figure. Accepted for publication in Ap

Combinatorial topology of the standard chromatic subdivision and Weak Symmetry Breaking for 6 processes

In this paper we study a family of discrete configuration spaces, the so-called protocol complexes, which are of utmost importance in theoretical distributed computing. Specifically, we consider questions of the existance of compliant binary labelings on the vertices of iterated standard chromatic subdivisions of an n-simplex. The existance of such labelings is equivalent to the existance of distributed protocols solving Weak Symmetry Breaking task in the standard computational model. As a part of our formal model, we introduce function sb(n), defined for natural numbers n, called the symmetry breaking function. From the geometric point of view sb(n) denotes the minimal number of iterations of the standard chromatic subdivision of an (n-1)-simplex, which is needed for the compliant binary labeling to exist. From the point of distributed computing, the function sb(n) measures the minimal number of rounds in a protocol solving the Weak Symmetry Breaking task. In addition to the development of combinatorial topology, which is applicable in a broader context, our main contribution is the proof of new bounds for the function sb(n). Accordingly, the bulk of the paper is taken up by in-depth analysis of the structure of adjacency graph on the set of n-simplices in iterated standard chromatic subdivision of an n-simplex. On the algorithmic side, we provide the first distributed protocol solving Weak Symmetry Breaking task in the layered immediate snapshot computational model for some number of processes. It is well known, that the smallest number of processes for which Weak Symmetry Breaking task is solvable is 6. Based on our analysis, we are able to find a very fast explicit protocol, solving the Weak Symmetry Breaking for 6 processes using only 3 rounds. Furthermore, we show that no protocol can solve Weak Symmetry Breaking in fewer than 2 rounds.Comment: updated references, in Configuration Spaces, Springer INdAM series 14, F. Callegaro et al. (eds.), Springer International Publishing Switzerland, 201

Sensitivity of the isotopologues of hydronium to variation of the electron-to-proton mass ratio

We study the sensitivity of the microwave and submillimeter transitions of the isotopologues of hydronium to the variation of the electron-to-proton mass ratio mu. These sensitivities are enhanced for the low frequency mixed inversion-rotational transitions. The lowest frequency transition (6.6 GHz) takes place for isotopologue H2DO+ and respective sensitivity to mu-variation is close to 200. This is about two orders of magnitude larger than the sensitivity of the inversion transition in ammonia, which is currently used for the search of mu-variation in astrophysics.Comment: 6 pages; v2: references correcte

On the dichotomy of a system of linear differential equations with conditionally periodic coefficients

We show that a system of linear differential equations with conditionally periodic coefficients is exponentially dichotomous if and only if the spectrum of the monodromy operator does not meet the unit circle. © 2013 Pleiades Publishing, Ltd

Electric dipole moment enhancement factor of thallium

The goal of this work is to resolve the present controversy in the value of the EDM enhancement factor of Tl. We have carried out several calculations by different high-precision methods, studied previously omitted corrections, as well as tested our methodology on other parity conserving quantities. We find the EDM enhancement factor of Tl to be equal to -573(20). This value is 20% larger than the recently published result of Nataraj et al. [Phys. Rev. Lett. 106, 200403 (2011)], but agrees very well with several earlier results.Comment: 5 pages; v2: link to supplemental material adde

On the efficiency of computational imaging with structured illumination

A generic computational imaging setup is considered which assumes sequential illumination of a semi-transparent object by an arbitrary set of structured illumination patterns. For each incident illumination pattern, all transmitted light is collected by a photon-counting bucket (single-pixel) detector. The transmission coefficients measured in this way are then used to reconstruct the spatial distribution of the object's projected transmission. It is demonstrated that the squared spatial resolution of such a setup is usually equal to the ratio of the image area to the number of linearly independent illumination patterns. If the noise in the measured transmission coefficients is dominated by photon shot noise, then the ratio of the spatially-averaged squared mean signal to the spatially-averaged noise variance in the "flat" distribution reconstructed in the absence of the object, is equal to the average number of registered photons when the illumination patterns are orthogonal. The signal-to-noise ratio in a reconstructed transmission distribution is always lower in the case of non-orthogonal illumination patterns due to spatial correlations in the measured data. Examples of imaging methods relevant to the presented analysis include conventional imaging with a pixelated detector, computational ghost imaging, compressive sensing, super-resolution imaging and computed tomography.Comment: Minor corrections and clarifications compared to the original versio

Enhancement of the electric dipole moment of the electron in PbO

The a(1) state of PbO can be used to measure the electric dipole moment of the electron d_e. We discuss a semiempirical model for this state, which yields an estimate of the effective electric field on the valence electrons in PbO. Our final result is an upper limit on the measurable energy shift, which is significantly larger than was anticipated earlier: $2|W_d|d_e \ge 2.4\times 10^{25} \textrm{Hz} [ \frac{d_e}{e \textrm{cm}} ]$.Comment: 4 pages, revtex4, no figures, submitted to PR