  We analyze the many-particle Schrodinger equation for fermions in a thermal
ensemble by introducing an exponential operator expansion, defined in the
context of thermofield dynamics. The expansion is optimized variationally at
each time step through changes in the basis of excitations, which leads to a
method of generating approximate differential equations to solve the time
dependent problem, and can also be used to cool the system in imaginary time.
The method is applied for a specific set of basis transformations and
truncation scheme, leading to an explicit set of differential equations that
reduce to the Hartree Fock solution in the low temperature limit. This
procedure can also be generalized to include quantum correlation, which will be
pursued in a future publication.
