The recent growing interest in nonlinear optical spectroscopy in optically active medium demands the three-dimensional rotational average of high-rank tensors. For example, calculations of the coherent anti-Stokes Raman scattering in optically active medium requires the averaging of the ninth rank tensor. Following the classic work of Andrews et al (1977 J. Chem. Phys. 67 5026) we present a method for finding the rotational average of odd-rank tensors in an overcomplete basis of isotropic tensors. The method is successfully applied to the rotational averages of tensors of rank n = 5, 7, 9, 11. Explicit new results for ninth- and eleventh-rank tensors are given.

Abstract:The OSL, post-IR OSL and pulsed post-IR OSL applied to polymineral grains and calculated by fitting to the data the contributions from fast, medium and slow components revealed that the polymineral samples under study are dominated by the medium component. An increase in D e 's with increasing integration intervals was observed, which is considered as an indication of increasing medium and decayed fast component; and the equivalent doses obtained using different components or minerals reflect also the shape of the dose distributions. The identified fast component in polymineral sample has photoionization cross section of 1.2±0.02 × 10 -17 cm 2 . The present study shows the usefulness of the application of different luminescence techniques combined with fitting procedures as a check which should be adopted in dating protocols. Based on luminescence ages obtained on polymineral grains from prehistoric pottery samples from the Boroo settlement, Mongolia, which are in agreement with independent age control by 14 C on charcoal material, it is argued that the manufacturing of Xiongnu -pottery at this site lasted until ca. 130±75 AD.

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Recently a new class of single-photon timed-Dicke (TD) subradiant states has been introduced with possible applications in single-photon based quantum information storage and on demand ultrafast retrieval [1]. However, the influence of any kind of virtual processes on the decay of these new kind of subradiant states has been left as an open question. In the present paper, we focus on this problem in detail. In particular, we investigate how pure Fano-Agarwal couplings and other virtual processes arising from non-rotating wave approximation impact the decay of otherwise suband superradiant states. In addition to the overall virtual couplings among all TD states, we also focus on the dominant role played by the couplings between specific TD states.

The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for the rotationally invariant tensor of averaged direction cosine products. From it, we obtain some useful new facts about this tensor. Our results serve to speed the inherently lengthy calculations of nonlinear optics.