2014/04/30 by J. Tranchida, Julien Tranchida, Pascal Thibaudeau +6
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum chaos and dynamical systems #cond-mat.mes-hall #math-ph #math.MP #nlin.CD
paper · pdf · doi:10.48550/arxiv.1404.7774
10 pages Revtex, 3 figures
arxiv created 2014/04/30 · openalex publication_date 2014/04/30 · arxiv updated 2014/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A generalization of the Lorenz equations is proposed where the variables take values in a Lie algebra. The finite dimensionality of the representation encodes the quantum fluctuations, while the non-linear nature of the equations can describe chaotic fluctuations. We identify a criterion, for the appearance of such non-linear terms. This depends on whether an invariant, symmetric tensor of the algebra can vanish or not. This proposal is studied in detail for the fundamental representation of \mathfraku(2). We find a knotted structure for the attractor, a bimodal distribution for the largest Lyapunov exponent and that the dynamics takes place within the Cartan subalgebra, that does not contain only the identity matrix, thereby can describe the quantum fluctuations.