Abstract
We develop a formalism to incorporate exchange symmetry considerations into the calculation of collisional frequency shifts for atomic clocks using a density-matrix formalism. The formalism is developed for both fermionic and bosonic atomic clocks. Numerical results for a finite-temperature ${}^{87}$Sr ${}^{1}{S}_{0}$ ($F=9/2$) atomic clock in a magic wavelength optical lattice are presented.
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