Eigenstate thermalization approaching for an atom interacting with fixed scatterers

Eigenstate thermalization is generally studied in many-body systems. It can be approached even if all but one particles have the infinite mass, as demonstrated here. Since n zero-range scatterers along the axis of a circular, transversely harmonic waveguide form a separable potential, millions of eigenstates are calculated using modest computational resources. On increase of n, the common characteristic of quantum chaos — the level spacing statistics — diverges from the Seba one [1] and at n=64 approaches the Wigner-Dyson one for the Gaussian orthogonal ensemble (GOE), expected for complete chaos. When the energy spectrum degeneracy with no scatterers is eliminated by an axial vector potential, at n=16 the level statistics approaches the one for the Gaussian unitary ensemble, expected for complete quantum chaos with no T-invariance. In this case, GOE takes place only for P-invariant distribution of the scatterers, when the Hamiltonian is TP-invariant. Chaotic behavior is revealed also in the inverse participation ratio [1], which drops from 0.4 to 0.028 on increase of n from 4 to 32. Simultaneous 4-time reduction of the eigenstate expectation value dispersion demonstrates the eigenstate thermalization approaching. 1.V. A. Yurovsky and M. Olshanii, PRL 106, 025303 (2011).