The Berry phase and the phase of the determinant

Abstract

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.

several references and comments are added. some misprints are corrected

References in corpus (4)

• Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
• The quantum Hall effect in graphene samples and the relativistic Dirac effective action
• Berry phase for ferromagnet with fractional spin
• Topological calculation of the phase of the determinant of a non self-adjoint elliptic operator