Almost-dispersionless pulse transport in long quasiuniform spring-mass chains: A new kind of Newton's cradle

Abstract

Almost-dispersionless pulse transfer between the extremal masses of a uniform harmonic spring-mass chain of arbitrary length can be induced by suitably modifying two masses and their spring's elastic constant at both extrema of the chain. It is shown that a deviation (or a pulse) imposed to the first mass gives rise to a wave packet that, after a time of the order of the chain length, almost perfectly reproduces the same deviation (pulse) at the opposite end, with an amplitude loss that is as small as 1.3 % in the infinite-length limit; such a dynamics can continue back and forth again for several times before dispersion cleared the effect. The underlying coherence mechanism is that the initial condition excites a bunch of normal modes with almost equal frequency spacing. This constitutes a possible mechanism for efficient energy transfer, e.g., in nanofabricated structures.

16 pages, 10 figures, 2 tables

References in corpus (2)

• 99%-fidelity ballistic quantum-state transfer through long uniform channels
• Energy Transport in Trapped Ion Chains

Cited by in corpus (3)

• Analytical solution of open crystalline linear 1D tight-binding models
• Persymmetric Jacobi matrices with square-integer eigenvalues and dispersionless mass-spring chains
• Dispersionless pulse transport in mass-spring chains: All possible perfect Newton's cradles