Correlations within Eigenvectors and Transition Amplitudes in the Two-Body Random Interaction Model

TL;DR

This paper reveals that the two-body nature of interactions in many-body systems induces specific correlations in compound states, affecting transition amplitudes and leading to a phenomenon called 'correlation resonance' within the Two-Body Random Interaction Model.

Contribution

It develops a statistical theory incorporating these correlations and demonstrates their impact on transition amplitude distributions in many-body quantum systems.

Findings

Correlations increase with more active particles.

Transition amplitudes show a 'correlation resonance' effect.

Correlations reduce tail amplitudes and enhance near-maximum amplitudes.

Abstract

It is shown that the two-body character of the interaction in a many-body system gives rise to specific correlations between the components of compound states, even if this interaction is completely random. Surprisingly, these correlations increase with the increase of the number of active (valence) particles. Statistical theory of transition amplitudes between compound states, which takes into account these correlation is developed and tested within the framework of the Two-Body Random Interaction Model. It is demonstrated that a feature, which can be called ``correlation resonance'', appears in the distribution of the transition matrix amplitudes, since the correlations strongly reduce the transition amplitudes at the tails and increase them near the maximum of the distribution.