Contact matrix in dilute quantum systems

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.

arXiv commenttypos corrected, relevant references added

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Cited by in corpus (21)

• Evidence for Bosonization in a three-dimensional gas of SU($N$) fermions
• Normal State Properties of a resonantly interacting p-wave Fermi Gas
• A strongly interacting high partial wave Bose gas
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• $s$-wave Contacts of Quantum Gases in Quasi-one and Quasi-two Dimensions
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• Contact formalism for coupled channels
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• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
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• Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter
• Toward precision Fermi liquid theory in two dimensions
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