Numerical simulation of free dissipative open quantum system and establishment of a formula for π
Agasti, Souvik (2020). Numerical simulation of free dissipative open quantum system and establishment of a formula for π. In Shekhawat, Manoj Singh; Bhardwaj, Sudhir; Suthar, Bhuvneshwer (Eds.) ICC-2019 : 3rd International Conference on Condensed Matter and Applied Physics, AIP Conference Proceedings, 2220. American Institute of Physics, 130010. DOI: 10.1063/5.0001282
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We transform the system/reservoir coupling model into a one-dimensional semi-infinite discrete chain with nearest neighbor interaction through a unitary transformation, and, simulate the dynamics of free dissipative open quantum system. We investigate the consequences of such modeling, which is observed as finite size effect causing the recurrence of particle from the end of the chain. Afterwards, we determine a formula for π in terms of the matrix operational form, which indicates a robustness of the connection between quantum physics and basic mathematics.