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Weyl spin-orbit-coupling-induced interactions in uniform and trapped atomic quantum fluids

We establish through analytical and numerical studies of thermodynamic quantities for noninteracting atomic gases that the isotropic three-dimensional spin-orbit coupling, the Weyl coupling, induces interaction which counters "effective" attraction (repulsion) of the exchange symmetry present in zero-coupling Bose (Fermi) gas. The exact analytical expressions for the grand potential and hence for several thermodynamic quantities have been obtained for this purpose in both uniform and trapped cases. It is enunciated that many interesting features of spin-orbit coupled systems revealed theoretically can be understood in terms of coupling-induced modifications in statistical interparticle potential. The temperature-dependence of the chemical potential, specific heat and isothermal compressibility for a uniform Bose gas is found to have signature of the incipient Bose-Einstein condensation in very weak coupling regime although the system does not really go in the Bose-condensed phase. The transition temperature in harmonically trapped case decreases with increase of coupling strength consistent with the weakening of the statistical attractive interaction. Anomalous behavior of some thermodynamic quantities, partly akin to that in dimensions less than two, appears for uniform fermions as soon as the Fermi level goes down the Dirac point on increasing the coupling strength. It is suggested that the fluctuation-dissipation theorem can be utilized to verify anomalous behaviors from studies of long-wavelength fluctuations in bunching and antibunching effects.