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Universal Relations for Fermions with Large Scattering Length

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The BCS-BEC Crossover and the Unitary Fermi Gas

Part of the book series: Lecture Notes in Physics ((LNP,volume 836))

Abstract

Particles with short-range interactions that produce a large scattering length have universal properties that depend only on the scattering length [1]. A system consisting of such particles is strongly interacting in the sense that there are effects of the interactions that must be treated nonperturbatively. These strong interactions give rise to strong correlations among the particless. Many theoretical methods, even if they are nonperturbative, are inadequate for dealing with such strong correlations. However, such a system is also governed by universal relations that follow from the short-distance and short-time dynamics associated with the large scattering length. These universal relations provide powerful constraints on the behavior of the system. They hold for any state of the system: few-body or many-body, ground state or nonzero temperature, homogeneous or in a trapping potential, normal state or superfluid, balanced in the two spin states or imbalanced. They connect various properties of the system, ranging from thermodynamic variables to large-momentum and high-frequency tails of correlation functions.

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Notes

  1. 1.

    In Ref. [13], the contact density was denoted by \(16 \pi^2 \hbar^2 C\) and the total number density was denoted by \(2n\) instead of \(n.\)

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Acknowledgments

This research was supported in part by a joint grant from the Army Research Office and the Air Force Office of Scientific Research. I would like to acknowledge useful comments by Lucas Platter, Shina Tan, Edward Taylor, Felix Werner, and Shizhong Zhang.

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  1. Department of Physics, The Ohio State University, Columbus, OH, 43210, USA

    Eric Braaten

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  1. Eric Braaten
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Correspondence to Eric Braaten .

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  1. Fakultät für Physik, Physik-Department, Technische Universität München, James-Franck-Straße, Garching, 85747, Germany

    Wilhelm Zwerger

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Braaten, E. (2012). Universal Relations for Fermions with Large Scattering Length. In: Zwerger, W. (eds) The BCS-BEC Crossover and the Unitary Fermi Gas. Lecture Notes in Physics, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21978-8_6

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  • DOI: https://doi.org/10.1007/978-3-642-21978-8_6

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