  In 1984 Michael Berry discovered that an isolated eigenstate of an
adiabatically changing periodic Hamiltonian $H(t)$ acquires a phase, called the
Berry phase. We show that under very general assumptions the adiabatic
approximation of the phase of the zeta-regularized determinant of the
imaginary-time Schrodinger operator with periodic Hamiltonian is equal to the
Berry phase.
