Thermalized Non-Equilibrated Matter against Random Matrix Theory, Quantum Chaos and Direct Interaction: Warming up

TL;DR

This paper discusses a new understanding of thermalized non-equilibrated matter, emphasizing long phase memory, angular asymmetry, and deviations from random matrix theory, with implications for nuclear reactions and quantum chaos.

Contribution

It introduces a novel approach to cross symmetry S-matrix correlations considering energy equilibration without the thermodynamic limit, and links angular asymmetry to eigenfunction distribution deviations.

Findings

Long phase memory due to small off-diagonal resonance correlations.

Strong angular asymmetry related to deviations from Gaussian eigenfunction distribution.

A new time/energy scale for random matrix theory validity, distinct from traditional physical interpretations.

Abstract

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 provide 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.