Thermodynamics and phase transitions in a fluid confined by a harmonic trap.

We study a fluid of interacting atoms confined by a three-dimensional anisotropic harmonic potential, similar to those produced by the magnetic traps used to confine cold atoms. We show that instead of the usual thermodynamic variables pressure and volume, no longer existing in this case, there appear "new" variables: the volume is replaced by (the inverse cube of) the geometric average of the oscillator frequencies of the trap, and the hydrostatic pressure is replaced by an intensive variable, conjugate to the previous one, and responsible for the mechanical equilibrium of the fluid in the trap. We discuss the origin and physical meaning of these new variables. With the aid of molecular dynamics simulations we show the emergence of novel liquid, vapor and solid-like phases in a classical fluid. In particular, we calculate the liquid-vapor-like coexistence curve and show evidence for the appearance of a critical point. These phase transitions should be observable in fluids of not-so-cold alkaline atoms.