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Equation of state and contact of a strongly interacting Bose gas in the normal state

We theoretically investigate the equation of state and Tan's contact of a non-degenerate three dimensional Bose gas near a broad Feshbach resonance, within the framework of large-$N$ expansion. Our results agree with the path-integral Monte Carlo simulations in the weak-coupling limit and recover the second-order virial expansion predictions at strong interactions and high temperatures. At resonance, we find that the chemical potential and energy are significantly enhanced by the strong repulsion, while the entropy does not change significantly. With increasing temperature, the two-body contact initially increases and then decreases like $T^{-1}$ at large temperature, and therefore exhibits a peak structure at about $4T_{c0}$, where $T_{c0}$ is the Bose-Einstein condensation temperature of an ideal, non-interacting Bose gas. These results may be experimentally examined with a non-degenerate unitary Bose gas, where the three-body recombination rate is substantially reduced. In particular, the non-monotonic temperature dependence of the two-body contact could be inferred from the momentum distribution measurement.