Importance Sampling for Multiscale Diffusions

We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale processes there are additional complications, and indeed the straightforward adaptation of methods for standard small noise diffusions will not produce efficient schemes. Using the subsolution approach we construct schemes and identify conditions under which the schemes will be asymptotically optimal. Examples and simulation results are provided

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

Sensitivity of the H3O+ inversion-rotational spectrum to changes in m_e/m_p

Quantum mechanical tunneling inversion transition in ammonia NH3 is actively used as a sensitive tool to study possible variations of the electron-to-proton mass ratio, mu = m_e/m_p. The molecule H3O+ has the inversion barrier significantly lower than that of NH3. Consequently, its tunneling transition occurs in the far-infrared (FIR) region and mixes with rotational transitions. Several such FIR and submillimiter transitions are observed from the interstellar medium in the Milky Way and in nearby galaxies. We show that the rest-frame frequencies of these transitions are very sensitive to the variation of mu, and that their sensitivity coefficients have different signs. Thus, H3O+ can be used as an independent target to test hypothetical changes in mu measured at different ambient conditions of high (terrestrial) and low (interstellar medium) matter densities. The environmental dependence of mu and coupling constants is suggested in a class of chameleon-type scalar field models - candidates to dark energy carrier.Comment: 8 pages, 2 figures, accepted to ApJ; v2: reformatted for ApJ and discussion of systematics significantly extende

Study of quadrupole polarizabilities with combined configuration interaction and coupled-cluster method

The recently developed method combining the configuration interaction and the coupled-cluster method was demonstrated to provide accurate treatment of correlation corrections in divalent atomic systems [M.S.Safronova, M.G.Kozlov, and C.W.Clark, Phys. Rev. Lett. 107, 143006 (2011)]. We have extended this approach to the calculation of quadrupole polarizabilities alpha_2 and applied it to evaluate alpha_2 for the ground state of Mg and Mg-like Si^{2+}. Performing the calculations in three different approximations of increasing accuracy allowed us to place the upper bounds on the uncertainty of the final results. The recommended values alpha_2(3s^2 1S0)= 35.86(13) a.u. for Si^{2+} and alpha_2(3s^2 1S0)= 814(3) a.u. for Mg are estimated to be accurate to 0.37%. Differences in quadrupole polarizability contributions in neutral Mg and Si^{2+} ion are discussed.Comment: 6 pages, submitted to Phys. Rev.

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

Polarizabilities of Si^{2+}: a benchmark test of theory and experiment

We have calculated electric-dipole polarizabilities of the 3s^2 ^1S_0, 3s3p ^3P_0, and 3s3p ^1P_1 states of the Si^{2+} ion using recently developed configuration interaction + all-order method. Detailed evaluation of the uncertainties of the final results is carried out. Our value for the ground state electric-dipole polarizability 11.670(13) a.u. is in excellent agreement with the resonant excitation Stark ionization spectroscopy value 11.669(9) a.u. [Komara et al., J. Phys. B 38, 87 (2005); Mitroy, Phys. Rev. A 78, 052515 (2008)]. This work represents the most precise benchmark test to date of theory and experiment in divalent atoms. The near cancellation of the ns^2 ^1S_0 ground state and the lowest nsnp ^3P_0 polarizabilities previously observed in B+, Al+, In+, Tl+, and Pb^{2+} is also found in Si^{2+} ion.Comment: 6 page