We study the level statistics of the quantum spectrum of a harmonic oscillator with biquadratic corrections. The distribution of interlevel spacings along the lines of constant scaled energy, whose values determine the classical dynamics, is obtained numerically. A transition from the Poisson to the Wigner character of the distribution is observed with the increase of the scaled energy. Using a quasi- classical approximation and assuming ergodic chaos we derive the level correlation function along the lines of constant scaled energy by employing the trace formula and keeping only the diagonal term. Our calculation yields a smoothed out tail of a Gaussian ensemble and is based on the exact cancellation of two ratios: the ratio of the mean level density along the line of constant scaled energy to that at a fixed bi- quadratic coupling and the ratio of the action to the period of a long periodic orbit. We further argue that the Wigner distribution will be found along any smooth line crossing the spectrum in the region of classical chaos. Applicability of our findings to quantum-dot structures at semiconductor interfaces is discussed.

• Received 10 February 1994

DOI:https://doi.org/10.1103/PhysRevB.50.2492