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Gauge theory and two level systems

By A. Bruno, A. Capolupo, S. Kak, G. Raimondo and G. Vitiello

Abstract

We consider the time evolution of a two level system (a two level atom or a qubit) and show that it is characterized by a local (in time) gauge invariant evolution equation. The covariant derivative operator is constructed and related to the free energy. We show that the gauge invariant characterization of the time evolution of the two level system is analogous to the birefringence phenomenon in optics. The relation with Berry-like and Anandan--Aharonov phase is pointed out. Finally, we discuss entropy, environment effects and the distance in projective Hilbert space between two level states in their evolution.Comment: 7 page

Topics: Quantum Physics, Condensed Matter - Other Condensed Matter
Year: 2011
DOI identifier: 10.1142/S021798491102698X
OAI identifier: oai:arXiv.org:1104.3743
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