Virial Expansion of Quantum Particles

Hui Hu

Hai-cang Ren

Alexandre M. Gavrilik, A. P. Rebesh

In the study of many-particle systems both the interaction of particles can be essential and such feature as their internal (composite) structure. To describe these aspects, the theory of deformed oscillators is very efficient. Viewing the particles as p,q-deformed bosons, in the corresponding p,q-Bose gas model we obtain in explicit form virial expansion along with the 2nd to 5th virial coefficients. The obtained virial coefficients depend on the deformation parameters p,q in the form symmetric under p<->q, and at p->1, q->1 turn into those known for usual bosons. Besides real parameters, we analyze the case of complex mutually conjugate p and q and find interesting implications. Also, the critical temperature is derived (for the p,q-Bose gas) and compared with the T_c of standard case of Bose condensation. Similar results are presented for the deformed Bose gas model of the Tamm-Dancoff type.

T. A. Osborn, T.Y. Tsang

Hiroshi Ichimura

As an application of the general expansion formula of the grand partition function for the system of interacting particles, we derive the virial expansion formula for quantum gases under the assumption that the degeneracy parameter λ is very small. We get a formula for the second virial coefficient which is effective at extremely low temperatures.

Herbert Leinfelder