We show that in a quantum system with no selection rules, the expectation value of a generic observable after relaxation is given by a linear interpolation between its initial and thermal expectation values. The variable of this interpolation is universal, and this simple law covers the whole spectrum of the chaotic behavior, from the integrable regime through the well-developed quantum chaos [1]. These predictions are confirmed for two zero-range-interacting atoms in a circular, transversely harmonic, multimode waveguide. Relaxation of this system demonstrates non-exponential behavior and fluctuations [2]. The relaxation time scales inversely-proportionally to the density of states. The fluctuation amplitude scales inversely-proportionally to the square root of the number of eigenstates in the initial state.

1\t V. A. Yurovsky and M. Olshanii, Phys. Rev. Lett. 106, 025303 (2011).
2\t V. A. Yurovsky, A. Ben-Reuven, and M. Olshanii, J. Phys. Chem. B 115, 5340 (2011).