Geometrical Phase Effects and Bohm's Quantum Potential

Ruth E. Kastner

R.S. Vinke

R. Y. Chiao, Nader A. Inan, Michael Scheibner +3 more

Recently we showed that quantum systems in orbit around a massive body may be compared to ground clocks to test the gravitational Aharonov-Bohm effect. To be sensitive, orbits must have non-zero eccentricity, so geometric phase effects related to the time varying gravitation potential will be present. Since the quantum system will be in free-fall, by the equivalence principle, the quantum system is locally screened from the gravitational field. However, the time varying gravitational potential will change the energy levels of the quantum system and develop side bands, which are harmonics of the orbit frequency and is the signature of the scalar Aharonov-Bohm effect. Experiments that have the potential to measure such geometric phases include atomic clocks in space, such as the ACES mission, as well as other missions that propose optical clocks in space. Also, worth investigating is the possible use of data from Galileo clocks with non-zero eccentricity.

Cássio Cecato Favarato

In this work, we make a review of the literature that the so-called Berry’s geometric phase. A recent issue, which has been employed in various areas of physics. For this, we use, in a number of references, in which many were critical to the theoretical foundation of this work. At first, we focus on the study of the time evolution of quantum systems governed by Hamiltonians operators whose time dependence is manifested by a set of parameters called classical fields. The adiabatic approximation, is justified mathematically when demonstrated the adiabatic theorem. Under these conditions, we obtain geometric phases - Berry’s phase - associated with these systems in different representations, each displaying its particularity. Finally, as a particular case of geometric phase, we studi from the viewpoint of duality transformations of Maxwell’s equations, the dual Aharonov-Bohm effect, extracting the geometric Berry’s phase associated with the dynamics of the magnetic monopole in the presence of the electric vector potential

Jean-Marc Lévy-Leblond