an:01262511
Zbl 0940.82026
Maslov, V. P.
Phase transition for classical bosons, fermions, and ordinary classical particles
EN
Math. Notes 63, No. 5, 695-699 (1998); translation from Mat. Zametki 63, No. 5, 792-795 (1998).
00053452
1998
j
82B26 82D50 81V25 81Q20
phase transition; classical particle; boson; fermion; Hartree equation; Vlasov-Poisson-Boltzmann equation; Bogolyubov's formula
The self-consistent field equation for classical bosons, fermions, particles obeying other parastatistics, as well as for classical particles under zero external field is studied. More realistic pair potentials attaining their minimum at some non-zero distance between two particles are considered. Different types of phase transitions derived from the equation and their physical meaning are discussed briefly.
`Metastable' equilibrium states can take place in the systems with a large number of particles. This corresponds to a temperature equilibrium with some series of eigenvalues [see \textit{V. P. Maslov}, Quasi-particles associated with isoenergetic manifolds corresponding to classical self-consistent fields. I-XII, Russ. J. Math. 2-5 (1994-1997)] for which the probabilities of transitions to the other energy levels are small.
Semiclassical corrections for the case of low temperature are also studied and dispersion relations for quasi-particles are derived. The one-dimensional result provides a reasonable numerical estimate of the critical velocity for helium and differs from the analogous Bogolyubov's formula [\textit{N. N. Bogolyubov}, Izv. Akad. Nauk SSSR, Ser. Fiz. 11, No. 1, 77-90 (1947)].
P.Dyshlovenko (Ul'yanovsk)
Zbl 0904.58053; Zbl 0909.58043; Zbl 0909.58040; Zbl 0909.58041; Zbl 0909.58042; Zbl 0920.58072; Zbl 0911.58048; Zbl 0911.58049; Zbl 0911.58050