The present discussion rises a number of the questions. For example, is rotational coherence of large molecules necessarily destroyed in the conventionally statistical limit of structureless non-selective continuum (for fixed total spin and parity va
lues) under the conditions of complete intramolecular energy redistribution and vibrational dephasing in the regime of strong ro-vibrational coupling? For the slow cross-symmetry phase relaxation, quantum coherent superpositions of a large number of complex configurations with, e.g., many different total angular momenta produce image of a rotation of macroscopic object with classically fixed (single) total angular momentum. Suppose that the quantum coherent superpositions involving a very large number of different good quantum numbers play a role, in a hidden form, in a formation of macroscopic world. Then why these quantum superpositions are so stable against quick aging/decay of ordered complex structures preventing or slowing down tendencies towards uniform occupation of the available phase space as prescribed by the random matrix theory? And what kind of complex macroscopic phenomena may reveal traces of partially coherent quantum superpositions involving a huge number of quantum-mechanically different integrals of motion behind of what is referred to as conservation laws in classical physics employed for the description of the macroscopic world?
The idea of a thermalized non-equilibrated state of matter offers a conceptually new understanding of the strong angular asymmetry. In this compact review we present some clarifications, corrections and further developments of the approach, and provi
de a brief account of results previously discussed but not reported in the literature. The cross symmetry compound nucleus $S$-matrix correlations are obtained (i) starting from the unitary $S$-matrix representation, (ii) by explicitly taking into account a process of energy equilibration, and (iii) without taking the thermodynamic limit of an infinite number of particles in the thermalized system. It is conjectured that the long phase memory is due to the exponentially small total spin off-diagonal resonance intensity correlations. This manifestly implies that the strong angular asymmetry intimately relates to extremely small deviations of the eigenfunction distribution from Gaussian law. The spin diagonal resonance intensity correlations determine a new time/energy scale for a validity of random matrix theory. Its definition does not involve overlaps of the many-body interacting configurations with shell model non-interacting states and thus is conceptually different from the physical meaning (inverse energy relaxation time) of the spreading widths introduced by Wigner. Exact Gaussian distribution of the resonance wave functions corresponds to the instantaneous phase relaxation. We invite the nuclear reaction community for the competition to describe, as the first challenge, the strong forward peaking in the typically evaporation part of the proton spectra. This is necessary to initiate revealing long-term misconduct in the heavily cross-disciplinary field, also important for nuclear industry applications.
