Bloch-Redfield-Wangsness relaxation theory engine implementation using symbolic processing software

bilinear Orderly description of nested rotations using irreducible spherical tensor operators and Wigner functions (reasonably neat and compact): quadratic Transforming the eigenframe expressions to the irreducible spherical tensor notation (equally applicable to linear, bilinear and quadratic spin interactions). Setting up internal rotations (to position interactions in a given molecule) and an overall molecular rotation. The angles corresponding to internal rotations may optionally be treated as fixed. The so-called 'upvalues ' are used, which are instructions to the symbolic processing kernel to do the following throughout thecalculations: to keep an eye on the occurrence of Wigner function products that match the left hand side, and on encountering a match to replace it with the right hand side. The variables with trailing underscores may stand for anything and are simply carried over to the right hand side. Due to lack of knowledge of the functional form of the correlation functions, a brute-force symbolic integration would fail. A much improved solution at this stage is not to rely on explicit integration, but rather to create a dedicated integrator which is only aware of a specific set of properties and is therefore very fast. Stage 1: preprocessing the Hamiltonian to expose rotation group properties (each with its own orientation and inter-dependent motional modulation) linear trigonometric description of rotations group-theoretical description of rotations relaxation theory treatmentAlgebrai