The Study of Lindblad Equation, Entangled K-meson System, and Its Decoherence
A Syahbana (a*), F P Zen (a,b), D Dwiputra (a)

a) Theoretical Physics Laboratory, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung, 40132, West Java, Indonesia
*ahmadbaskarasyahbana[at]gmail.com
b) Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Jl. Ganesha 10 Bandung, 40132, West Java, Indonesia

Abstract

In this paper, Lindblad equation, entangled K-meson model according to Lindblad equation, and decoherence phenomenon in the system is studied. Lindblad equation is derived from microscopic dynamics and as a completely positive and trace-preserving (CPT) generator. Using Lindblad equation, dynamical equation of entangled K-meson system that interacts with the environment is obtained. We find that non-Hermitian Hamiltonian of the system makes the evolution of density matrix does not satisfy completely positive and trace preserving properties. We also find that purity of density matrix could be less than \(1/d\) which does not satisfy the property of purity. From the dynamical equation, parameters related to the decoherence of the system, decoherence parameter (\(\lambda\)) and effective decoherence parameter (\(\zeta\)), are determined. Using Standard Least-Squares method, we obtained \(\zeta=0,13\pm 0,865\). This result corresponds with reference result that uses effective variance method, \(\zeta=0,13\pm_{-0,15}^{+0,16}\), which corresponds with \(\lambda=(1,84\pm_{-2,17}^{+2,50})\times 10^{-12}\) MeV. The value of these parameters from the reference are relatively small which means the information from the system is relatively maintained. On the other hand, we find that the value of \(\lambda\) does not exactly correspond with the value of \(\zeta\). This could mean the experimental data used are not sufficient enough to measure \(\zeta\).

Keywords: decoherence, K-meson, Lindblad equation, open quantum system

Topic: Theoretical High Energy Physics