Entropic Leggett\u2013Garg inequality in neutrinos and B(K) meson systems

Javid Naikoo,Subhashish Banerjee

doi:10.1140/epjc/s10052-018-6084-6

Javid Naikoo, Subhashish Banerjee

Open Access

https://doi.org/10.1140/epjc/s10052-018-6084-6

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Abstract

Entropic Leggett–Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral B_d, B_s and K mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering B / K meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-s systems. The effect of decoherence is found to bring the deficit parameter mathscr {D}^{[n]} closer to its classical value zero, as expected. The violation of entropic Leggett–Garg inequality lasts for a much longer time in K meson system than in B_d and B_s systems.

Highlights

There is no sharp boundary between the classical and the quantum worlds
We provide a brief review of some rudiments of information theory used in the development of the entropic Leggett–Garg inequality
A clear violation of the ELGI is seen in all the cases

Summary

Introduction

There is no sharp boundary between the classical and the quantum worlds. physicists have developed some important notions which can shed light on the distinction of the two domains. Leggett–Garg inequalities (LGIs), considered to be the temporal analogue of Bell inequalities, were constructed to understand the extrapolation of quantum theory to macroscopic systems, by assuming macro-realism and noninvasive measurability [34]. The entropic version of Bell inequality was formulated in [55]. C (2018) 78:602 terpart of Bell inequality was developed in [58] This was followed by an application of the entropic version of Leggett– Garg inequality to a spin-s system in [59]. We will analyze the entropic Leggett–Garg inequality for the neutrino system in the context of neutrino oscillations and for the decohering K and B mesons by using the formalism of open quantum systems. 4 wherein we discuss the construction of entropic Leggett– Garg inequality for the meson system.

Entropic Leggett–Garg inequality

Neutrino oscillation

Time evolution of B and K meson systems

Results and discussion

Conclusion