Approach to Equilibrium of a Restricted Class of Isolated Quantum Systems After a Quench

This paper was received with skepticism by several reviewers (and hence never published in mainstream journals) due to its hypothetical character. Nevertheless, it gives an exact mathematical proof for the density matrix of some quenched quantum systems to evolve unitarily towards a generalized Gibbs ensemble (signaling equilibrium), provided some sufficient conditions apply:

• The system is infinite and one-dimensional.
• The perturbing potential is local (and necessarily symmetry-breaking).
• The integrals of motion of the unperturbed system form a Lie algebra.

These conditions imply equilibration without invoking any dissipation mechanism during the evolution. Do such a restricted class of systems actually exist?