Relating interfacial Rossby wave interaction in shear flows with Feynman's two-state coupled quantum system model for the Josephson junction

Abstract

Here we show how Feynman's simplified model for the Josephson junction, as a macroscopic two-state coupled quantum system, has a one-to-one correspondence with the stable dynamics of two interfacial Rossby waves in piecewise linear shear flows. The conservation of electric charge and energy of the superconducting electron gas layers become, respectively, equivalent to the conservation of wave action and pseudoenergy of the Rossby waves. Quantumlike tunneling is enabled via action at a distance between the two Rossby waves. Furthermore, the quantumlike phenomena of avoided crossing between eigenstates, described by the Klein-Gordon equation, is obtained as well in the classical shear flow system. In the latter, it results from the inherent difference in pseudoenergy between the in-phase and antiphased normal modes of the interfacial waves. This provides an intuitive physical meaning to the role of the wave function's phase in the quantum system. A partial analog to the quantum collapse of the wave function is also obtained due to the existence of a separatrix between normal mode regions of influence on the phase plane, describing the system's dynamics. As for two-state quantum bits (qubits), the two-Rossby wave system solutions can be represented on a Bloch sphere, where the Hadamard gate transforms the two normal modes and eigenstates into an intuitive computational basis in which only one interface is occupied by a Rossby wave. Yet, it is a classical system which lacks exact analogs to collapse and entanglement, and thus cannot be used for quantum computation, even in principle.