Integrability and Coherence of Hopping between 1D Correlated Electron Systems

We present numerical evidence that the hopping of electrons between chains described by the $t-J$ model is much more coherent in the integrable cases ( $J=0\mathrm{}$ and $J=2\mathrm{}$) than in the nonintegrable ones. This effect is not related to the value of the exponent $\alpha$ which is restricted to the interval $[0,1/8]$ when $0\le J\le 2$. We propose that enhanced coherence is characteristic of integrable systems and argue that it might be related to the level statistics.