Theory of boson mixtures

Abstract

We investigate the thermodynamic ground state of binary boson mixtures using a variational ansatz. With a pair-independent trial function we map the isotopic boson mixture onto a quantum theorem of corresponding-states picture which enables us to conclude that all such isotopic boson mixtures completely phase-separate at zero temperature. We also investigate mixtures of spin-aligned hydrogen (H\ensuremath{\uparrow}) and spin-aligned tritium (T\ensuremath{\uparrow}) with $^{4}\mathrm{He}$. We find that these systems also prefer to completely phase-separate. However, due to important differences in the sizes of "cores" of the interaction, allowance must be made for different correlations between different types of pairs. We then find that at zero pressure the zero-concentration chemical potential for H\ensuremath{\uparrow} in $^{4}\mathrm{He}$ is 40 K and for T\ensuremath{\uparrow} in $^{4}\mathrm{He}$ it is 0.5 K.