Open AccessA general method for rotational averages
Author(s) -
Reed Nessler,
Tuguldur Begzjav
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2090/1/012041
Subject(s) - tensor (intrinsic definition) , nonlinear system , invariant (physics) , rotation (mathematics) , cartesian tensor , mathematics , direction cosine , rank (graph theory) , tensor contraction , expression (computer science) , trigonometric functions , physics , mathematical analysis , classical mechanics , statistical physics , tensor density , geometry , quantum mechanics , tensor field , mathematical physics , exact solutions in general relativity , computer science , combinatorics , programming language
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.