Quantum-Classical Correspondence for Two Interacting Particles in a One-Dimensional Box

Abstract

We study the model of two interacting particles moving in a 1D box, paying main attention to the quantum‐classical correspondence for the average shape of quantum eigenstates and for the local density of states (LDOS). We show that if the classical motion is chaotic, in a deep semi‐classical region of a quantum system, both the shape of eigenstates and of the LDOS coincide with their classical analogs, on average. However, individual eigenstates exhibit quite large fluctuations which may not be treated as statistical ones. Thus, comparison of quantum quantities to the classical ones allows one to detect quantum effects of localization which for conservative systems emerge in the energy space.

Quantum chaos and thermalization in isolated systems of interacting particles

“…The quantum-classical correspondence for the strength functions, as well as for the envelopes of eigenstates, has been thoroughly studied in Refs. [64,65,66,67,68,69,70,71,72,73,73] for various models of interacting particles.…”

“…The results presented in Refs. [64,65,66,67,68,70,69,72,71,73] give evidence for a quantum-classical correspondence of the strength function. In the classical limit, the meaning of the strength function is just a projection of the energy surface of H 0 onto that of H, the fact that simplifies the analysis of quantum systems having a well defined classical limit.…”