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arXiv:1512.03265

Geometric phase and its applications to fundamental physics

Antonio Capolupo, Giuseppe Vitiello

Published Dec 9, 2015• 1 citation
arXivHTMLPDF

Abstract

We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects and thermal states. We show that the geometric phases appearing in the time evolution of mixed meson systems like $B_{s}^{0}-\bar{B}_{s}^{0}$ and the $K^{0}-\bar{K}^{0}$ are linked to the parameter $z$ describing the $CPT$ violation. A non zero phase difference between particle and antiparticle arises only in the presence of $CPT$ symmetry breaking. Then the geometric phase can represent a completely new test for the $CPT$ invariance. Moreover, we study the geometric phase of systems represented by mixed state and undergoing a nonunitary evolution and propose the realization of interferometers which can prove the existence of the Unruh effect and can allow very precise measurements of temperature. We are glad to dedicate this paper to Professor Gaetano Vilasi in the occasion of his 70th birthday.

DOI
10.48550/arxiv.1512.03265

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We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects and thermal states. We show that the geometric phases appearing in the time evolution of mixed meson systems like Bs0−Bˉs0B_{s}^{0}-\bar{B}_{s}^{0}Bs0​−Bˉs0​ and the K0−Kˉ0K^{0}-\bar{K}^{0}K0−Kˉ0 are linked to the parameter zzz describing the CPTCPTCPT violation. A non zero phase difference between particle and antiparticle arises only in the presence of CPTCPTCPT symmetry breaking. Then the geometric phase can represent a completely new test for the CPTCPTCPT invariance. Moreover, we study the geometric phase of systems represented by mixed state and undergoing a nonunitary evolution and propose the realization of interferometers which can prove the existence of the Unruh effect and can allow very precise measurements of temperature. We are glad to dedicate this paper to Professor Gaetano Vilasi in the occasion of his 70th birthday.
We report on the recent results revealing the presence of the geometric phase in all the systems characterized by particle creation from vacuum and vacuum condensates. This fact makes the geometric phase a useful tool in the study and the understanding of disparate phenomena. Its possible application ranges from the dynamical Casimir effect to the Hawking effect, from quantum field theory in curved space to the study of CP and CPT symmetries, from the graphen physics to superconductivity and to the Bose Einstein condensate. Here, we consider the possibility of the detection of the Unruh effect and of the fabrication of a very precise quantum thermometer. We analyze the Mukunda-Simon phase for a two level atom system and consider two case: 1) atoms accelerated in electromagnetic field, and 2) atoms interacting with thermal states. The Mukunda-Simon phase generalizes the Berry phase to the case of non-cyclic and non-adiabatic evolutions; therefore it represents a more useful instrument in experimental implementations with respect to the Berry phase.
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