  Two zero-range-interacting atoms in a circular, transversely harmonic
waveguide are used as a test-bench for a quantitative description of the
crossover between integrability and chaos in a quantum system with no selection
rules. For such systems we show that the expectation value after relaxation of
a generic observable is given by a linear interpolation between its initial and
thermal expectation values. The variable of this interpolation is universal; it
governs this simple law to cover the whole spectrum of the chaotic behavior
from integrable regime through the well- developed quantum chaos. The
predictions are confirmed for the waveguide system, where the mode occupations
and the trapping energy were used as the observables of interest; a variety of
the initial states and a full range of the interaction strengths have been
tested.
