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Dynamical analysis of mass–spring models using Lie algebraic methods

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  • Urzúa, Alejandro R.
  • Ramos-Prieto, Irán
  • Soto-Eguibar, Francisco
  • Moya-Cessa, Héctor

Abstract

The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants, is presented. Finite circular and linear arrays are studied using classical arguments, and their proper solution is given using methods often found in quantum optical systems. We further study some more complicated arrays where the solutions are given by using Lie algebras.

Suggested Citation

  • Urzúa, Alejandro R. & Ramos-Prieto, Irán & Soto-Eguibar, Francisco & Moya-Cessa, Héctor, 2020. "Dynamical analysis of mass–spring models using Lie algebraic methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317959
    DOI: 10.1016/j.physa.2019.123193
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    1. Steffen Weimann & Armando Perez-Leija & Maxime Lebugle & Robert Keil & Malte Tichy & Markus Gräfe & René Heilmann & Stefan Nolte & Hector Moya-Cessa & Gregor Weihs & Demetrios N. Christodoulides & Ale, 2016. "Implementation of quantum and classical discrete fractional Fourier transforms," Nature Communications, Nature, vol. 7(1), pages 1-8, April.
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