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1 Analyse et synthèse sonores Paris STMS - Sciences et Technologies de la Musique et du Son

Abstract : We consider variational problems where the velocity depends on a scale. After recalling the fundamental principles that lead to classical and quantum mechanics, we study the dynamics obtained by replacing the velocity by some physical observable at a given scale into the expression of the Lagrangian function. Then, discrete Euler-Lagrange and Hamilton-Jacobi equations are derived for a continuous model that incorporates a real-valued discrete velocity. We also examine the paradigm for complex-valued discrete velocity, inspired by the scale relativity of Nottale. We present also rigorous definitions and preliminary results in this direction.

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Keywords : scale relativity quantum operators

Mots-clés : Informatique musicale

Author: François Dubois - Isabelle Greff - Thomas Hélie -

Source: https://hal.archives-ouvertes.fr/


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