Experimental observation of exceptional points in coupled pendulums
arXiv:2308.01089 · doi:10.1016/j.jsv.2024.118239
Abstract
The concept of exceptional point (EP) is demonstrated experimentally in the case of a simple mechanical system consisting of two linearized coupled pendulums. Exceptional points correspond to specific values of the system parameters that yield defective eigenvalues. These spectral singularities which are typical of non-Hermitian system means that both the eigenvalues and their associated eigenvectors coalesce. The existence of an EP requires an adequate parameterization of the dynamical system. For this aim, the experimental device has been designed with two controllable parameters which are the length of one pendulum and a viscous-like damping which is produced via electromagnetic induction. Thanks to the observation of the free response of the coupled pendulums, most EP properties are experimentally investigated, showing good agreements with theoretical considerations. In contrast with many studies on EPs, mainly in the field of physics, the novelty of the present work is that controllable parameters are restricted to be real-valued, and this requires the use of adequate search algorithms. Furthermore, it offers the possibility of exploiting the existence of EPs in time-domain dynamic problems.
References in corpus (17)
- The physics of exceptional points
- Loss-induced suppression and revival of lasing
- Topological energy transfer in an optomechanical system with exceptional points
- Observation of the exceptional point in cavity magnon-polaritons
- Observation of an exceptional point in a chaotic optical microcavity
- Encircling an Exceptional Point
- Dynamically encircling an exceptional point in anti-PT-symmetric systems: asymmetric mode switching for symmetry-broken states
- Experimental observation of exceptional surface in synthetic dimensions with magnon polaritons
- Coupling of eigenvalues of complex matrices at diabolic and exceptional points
- Non-Hermitian engineering of terahertz light using exceptional points in electrically tuneable collective light-matter interactions
- Stabilization of acoustic modes using Helmholtz and Quarter-Wave resonators tuned at exceptional points
- Exceptional points in coupled dissipative dynamical systems
- Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters
- Degenerate perturbation theory in thermoacoustics: high-order sensitivities and exceptional points
- A high order continuation method to locate exceptional points and to compute Puiseux series with applications to acoustic waveguides
- Non-hermitian time evolution: from static to parametric instability
- New insights into mode behaviours in waveguides with impedance boundary conditions