Contact matrix in dilute quantum systems

TL;DR

This paper introduces the concept of a contact matrix in dilute quantum systems, extending the traditional scalar contact to include off-diagonal coherence terms, which links short-range correlations to macroscopic quantum phenomena like superfluidity.

Contribution

It proposes defining contact as a matrix to fully describe pairwise correlations, including off-diagonal coherence terms, advancing the understanding of thermodynamic properties in quantum systems.

Findings

Contact matrix includes all partial wave contacts and off-diagonal coherence terms.

Off-diagonal terms determine momentum distribution and coherence.

Connection established between contact matrix and superfluid order parameters.

Abstract

Contact has been well established as an important quantity to govern dilute quantum systems, in which the pairwise correlation at short distance traces a broad range of thermodynamic properties. So far, studies have been focusing on contact in individual angular momentum channels. Here, we point out that, to have a complete description of the pairwise correlation in a general dilute quantum systems, contact should be defined as a matrix. Whereas the diagonal terms of such matrix include contact of all partial wave scatterings, the off-diagonal terms, which elude previous studies in the literature, characterise the coherence of the asymptotic pairwise wavefunction in the angular momentum space and determine important thermodynamic quantities including the momentum distribution. Contact matrix allows physicists to access unexplored connections between short-range correlations and macroscopic quantum phenomena. As an example, we show the direct connection between contact matrix and order parameters of a superfluid with mixed partial waves.