An exact solution to the Bertsch problem and the non-universality of the Unitary Fermi Gas

E. Ruiz Arriola; S. Szpigel; V. S. Timoteo

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arXiv · 1712.05931

An exact solution to the Bertsch problem and the non-universality of the Unitary Fermi Gas

E. Ruiz Arriola·S. Szpigel·V. S. Timoteo

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Abstract

We analyze the universality of the Unitary Fermi Gas in its ground state from a Wilsonian renormalization point of view and compute the effective range dependence of the Bertsch parameter $\xi$ exactly. To this end we construct an effective block-diagonal two-body separable interaction with the Fermi momentum as a cut-off which reduces the calculation to the mean field level. The interaction is separable in momentum space and is determined by Tabakin's inverse scattering formula. For a vanishing effective range we get $\xi = \frac{176}{9 \pi }-\frac{17}{3} = 0.56$. By using phase-equivalent similarity transformations we can show that there is a class of exact solutions with any value in the range $ 0.56 \ge \xi \ge -1/3$.

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E. Ruiz Arriola, S. Szpigel, V. S. Timoteo. 2017-12-16. An exact solution to the Bertsch problem and the non-universality of the Unitary Fermi Gas. https://arxiv.org/abs/1712.05931

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