» Esercizi svolti di Matematica e Fisica

La particella di Riemann

In fig. 1 the trajectory of a particle of unitary mass moving in a plane seat of an unknown force field. The hourly equations are defined by the real part and the imaginary part of the Riemann zeta function calculated along the critical line.
Qualitatively, the motion is the result of the composition of two one-dimensional motions, both with oscillating potential energy and which therefore give rise to "oscillating" but not periodic forces, with increasing amplitude. The single force seems to be the result of an attractive term (of the type "elastic recall force") and of a repulsive term that tends to move the particle away from the origin, towards infinity. But periodically, the recall force takes over and carries the particle towards the origin. Each passage through the origin corresponds to a non-trivial zero of the Riemann zeta function.
The trajectory is as follows: