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Thermodynamic contacts and breathing mode physics of 1D p-wave Fermi gases in the high temperature limit

An important tool for understanding the effects of interactions in harmonically trapped atomic gases is the examination of their collective modes. One such mode is the breathing or monopole mode, which is special as it is constrained to occur at twice the harmonic trapping frequency when the interactions are scale invariant. When the interactions are not scale invariant, the frequency of the breathing mode will deviate from twice the trap frequency. The deviation itself depends on the thermodynamic contacts, which describe how the energy changes with the interactions. In this work I examine how the thermodynamic contacts and the breathing mode frequency of a spin-polarized one-dimensional (1D) p-wave Fermi gas depend on the 1D scattering volume, $\ell$, and the effective range, $r$, in the high temperature limit. Such dynamics can be studied in experiments and provide a tool for understanding how the dynamics depend on interactions with a finite effective range.