Sudden excitations of harmonic normal modes

Abstract

AbstractThe N-harmonium boson system, i.e., a completely integrable model of N particles where both the external confinement and the two-particle interaction are harmonic, is investigated under the action of sudden time-dependent perturbation. This quench-like external perturbation of confinement has a quadrupolar space-character. The time-independent transition probabilities, which characterize the impact of quench as average occupation numbers, form a complete distribution in the sense of probability theory. The quench-generated energy shift $$\Delta E$$ Δ E in the correlated many-body system, and a purity-type Rényi entropy $$S_{\alpha =2}$$ S α = 2 are calculated. Challenging reinterpretations of such an energy change in terms of variables of a classical thermodynamical system of $$N(N-1)/2$$ N ( N - 1 ) / 2 pairs are given as well. As in the case of the ground-state correlated system, an entropy could characterize a global link to energetically optimized independent-particle models.