The one-loop quark contribution to the QCD effective potential for the
homogeneous Abelian gluon field in the presence of external strong
electromagnetic field is evaluated. The structure of extrema of the potential
as a function of the angles between chromoelectric, chromomagnetic and
electromagnetic fields is analyzed. In this setup, the electromagnetic field is
considered as an external one while the gluon field represents domain
structured nonperturbative gluon configurations related to the QCD vacuum in
the confinement phase. Two particularly interesting gluon configurations,
(anti-)self-dual and crossed orthogonal chromomagnetic and chromoelectric
fields, are discussed specifically. Within this simplified framework it is
shown that the strong electromagnetic fields can play a catalysing role for a
deconfinement transition. At the qualitative level, the present consideration
can be seen as a highly simplified study of an impact of the electromagnetic
fields generated in relativistic heavy ion collisions on the strongly
interacting hadronic matter.Comment: 9 pages, 4 figure