Abstract
By mapping the system of prime numbers to a physical problem, it is possible to characterise the hidden nonlinear dynamics associated with it. In order to study the properties of primes, first the single particle Schr\({\ddot{o}}\)dinger equation is solved. The wave function used in this case is constructed from the prime counting function and their interaction potential is obtained. In the corresponding classical nonlinear system, the phase trajectories and the associated fixed points which happens to be half stable and half unstable are also studied. It is interesting to note that the Lambert W function appears in connection to solutions for the fixed points as a function of energy.
Subodha Mishra deceased on 8th January 2022.
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Pal, C.C., Mishra, S. (2022). Classical Nonlinear Dynamics Associated with Prime Numbers: Non-relativistic and Relativistic Study. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_104
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DOI: https://doi.org/10.1007/978-3-030-99792-2_104
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