Generalized “phase diagram” and critical behavior for quantum systems

Abstract

Quantum systems that obey Fermi-Dirac and Bose-Einstein statistics and that interact via “noble-gas-like” potentials are studied within the context of the quantum theorem of corresponding states. The phase diagrams for the crystalline, liquid, and gaseous phases are constructed inP*-T*-η space, whereP* is the reduced pressure,T* is the reduced temperature, and η=ħ/mεσ ₂ is the quantum parameter. Both theoretical and experimental results are used in constructing the phase diagrams. In both the Bose and Fermi cases there is a line of critical points which terminates in a critical end point at zero temperature. In the Bose caseP ^* _c =0 atT ^* _c =0, whereas in the Fermi caseP ^* _c ≠ 0 atT ^* _c =0. It is shown that, in the critical region forT<0, the singular behavior of the thermodynamic quantities as a function of η is the same as that of a function ofT with the well-known critical parameters for the liquid-to-gas transition. AtT=0, it has been found previously that the transition is molecular-field-like. Thus, it is conjectured that there is a “crossover” scaling region. Finally, spin-aligned deuterium is considered. It may be that this system, if it can be prepared, is a gas atT=0 and can be liquefied under pressure. Thus, it may have a very low critical temperature and may be a system in which it might be possible to observe quantum effects on the scaling parameters.