Thermodynamic contacts and breathing mode physics of 1D odd-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 talk I study the thermodynamic contacts and the breathing mode of a spin-olarized one-dimensional Fermi gas with odd wave interactions in the high-temperature limit. In this case, the energy dependence of the interactions, characterized by the effective range, can not be neglected.  I explicitly show how the breathing mode changes with interaction strength from weak to strong interactions for a finite effective range. Such dynamics can be studied in experiments and provide a tool for understanding how the dynamics depend on interactions with a finite effective range.