title: Geometric nature of the environment-induced Berry phase and geometric dephasing.
abstract: We investigate the geometric phase or Berry phase acquired by a spin half which is both subject to a slowly varying magnetic field and weakly coupled to a dissipative environment (either quantum or classical). We study how this phase is modified by the environment and find that the modification is of a geometric nature. While the original Berry phase (for an isolated system) is the flux of a monopole field through the loop traversed by the magnetic field, the environment-induced modification of the phase is the flux of a quadrupolelike field. We find that the environment-induced phase is complex, and its imaginary part is a geometric contribution to dephasing. Its sign depends on the direction of the loop. Unlike the Berry phase, this geometric dephasing is gauge invariant for open paths of the magnetic field.
authors.affiliation: Departement de Physique Théorique, Universiteé de Genève, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland.
authors.forename: Robert S
authors.initials: RS
authors.lastname: Whitney
authors.forename: Yuriy
authors.initials: Y
authors.lastname: Makhlin
authors.forename: Alexander
authors.initials: A
authors.lastname: Shnirman
authors.forename: Yuval
authors.initials: Y
authors.lastname: Gefen