Energetics of a strongly correlated Fermi gas

By Shina Tan. 2005

513 citations recorded by the source corpus.

Abstract The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution: E internal = ℏ 2 Ω C / 4 π am + ∑ k σ ( ℏ 2 k 2 / 2 m ) ( n k σ - C / k 4 ) where the external potential energy is not included, a is the scattering length, Ω is the volume, n k σ is the average number of fermions with wave vector k and spin σ , and C ≡ lim k → ∞ k 4 n k ↑ = lim k → ∞ k 4 n k ↓ . This result is a universal identity . Its proof is facilitated by a novel mathematical idea, which might be of utility in dealing with ultraviolet divergences in quantum field theories. Other properties of this Fermi system, including pair correlations and the dimer–fermion scattering length, are also studied.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/96a05c342f5db3d58ea01ea04c940110a7f2f706

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Citations in the corpus

Universal few-body physics and cluster formation (2017, methodology): “hat are well described by a separable wavefunction ansatz and its crude improvements at the next level of approximation. One such property identied by Shina Tan in a groundbreaking series of papers (Tan, 2008a,b,c) is the \high energy" limit of the pair correlation function. This Tan contact pa”
Comparing and contrasting nuclei and cold atomic gases (2013, background): “…where the so-called Tan relations can be used to deduce properties of bulk many-body systems from basic knowledge of few-body quantities (Tan 2008a, Tan 2008b, Tan 2008c, Braaten & Platter 2008, Combescot et al. 2009, Barth & Zwerger 2011, Pricoupenko 2011, Valiente et al. 2011, Langmack et al.…”
Fermi gases in one dimension: From Bethe ansatz to experiments (2013, background): “Tan (2008a, 2008b,2008c) has shown that a few universal relations for two-component interacting fermions involve an extensive quantity called the universal contact C.”
Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, background): “Tan defined the contact density C via [79, 80, 81]”
Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond (2012, background): “The possibility of a nontrivial interplay between many-body and few-body physics is a unique feature of ultracold-atom physics, and has attracted significant theoretical [86,87] and experimental [88] interest recently.”
The BCS–BEC crossover: From ultra-cold Fermi gases to nuclear systems (2018, background): “Alternatively, the contact can be defined via the large wave-vector tail of the fermionic distributions nσ(k) with k = |k|, which behaves asymptotically as [359] nσ(k) ≈ C k4 .”