Tilted washboards of potential energy

Abstract Tilted washboard potentials are periodic functions of potential energy whose graphs remind the profile of inclined boards for scrubbing clothes. Practically ignored until the 1970’s, tilted washboard potentials are at present ubiquitous seminal landscapes across diverse physics researches and technologies now receiving attention. Notwithstanding its clear relevance, washboard potentials are still rarely presented to science or to engineering undergraduates. Aiming to promote the presentation of such potentials to physics and engineering undergraduates, we here consider several cases of tilted washboard potentials: two in classical mechanics, and one in quantum physics. Arnold’s phase space formalism of classical mechanics—first presented in a pedagogical journal—is applied to the tilted washboard potential of a particle. The quantum case is the superconducting tunnelling Josephson junction, whose phase point-particle motion is linked to a tilted washboard of potential energy, leading to important applications e.g. the present Volt standard unit based on arrays of Josephson junctions, the phase qubits of quantum computing, and the superconducting quantum interference device among others.