Finite temperature current densities and Bose-Einstein condensation in
  topologically nontrivial spaces
  We investigate the finite temperature expectation values of the charge and
current densities for a complex scalar field with nonzero chemical potential in
background of a flat spacetime with spatial topology $R^{p}\times (S^{1})^{q}$.
Along compact dimensions quasiperiodicity conditions with general phases are
imposed on the field. In addition, we assume the presence of a constant gauge
field which, due to the nontrivial topology of background space, leads to
Aharonov-Bohm-like effects on the expectation values. By using the
Abel-Plana-type summation formula and zeta function techniques, two different
representations are provided for both the current and charge densities. The
current density has nonzero components along the compact dimensions only and,
in the absence of a gauge field, it vanishes for special cases of twisted and
untwisted scalar fields. In the high-temperature limit, the current density and
the topological part in the charge density are linear functions of the
temperature. The Bose-Einstein condensation for a fixed value of the charge is
discussed. The expression for the chemical potential is given in terms of the
lengths of compact dimensions, temperature and gauge field. It is shown that
the parameters of the phase transition can be controlled by tuning the gauge
field. The separate contributions to the charge and current densities coming
from the Bose-Einstein condensate and from excited states are also
investigated.
