2016/02/17 by N. E. Martínez-Pérez, Martínez-Pérez, N. E., C. Ramírez +1
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Nonlinear Photonic Systems #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1602.05255
12 pages. arXiv admin note: substantial text overlap with arXiv:1501.05018
arxiv created 2016/02/17 · openalex publication_date 2016/02/17 · arxiv updated 2016/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply Noether's theorem to show how the invariances of conservative systems are broken for nonconservative systems, in the variational formulation of Galley. This formulation considers a conservative action, extended by the inclusion of a time reversed sector and a nonconservative generalized potential. We assume that this potential is invariant under the symmetries of the initial conservative system. The breaking occurs because the time reversed sector requires inverse symmetry transformations, under which the nonconservative potential is not invariant. The resulting violation of the conservation laws is consistent with the equations of motion. We generalize this formulation for fermionic and sypersymmetric systems. In the case of a supersymmetric oscillator, the effect of damping is that the bosonic and fermionic components become different frequencies. Considering that initially the nonconservative action is invariant under supersymmetry, and that the breaking is associated to an instability, this result is reminiscent of spontaneous symmetry breaking.