Ermakov-Lewis angles for one-parameter supersymmetric families of Newtonian free damping modes

Supersymmetric partner chirping of Newtonian free damping

We connect the classical free damping cases by means of Ros-ner's construction in supersymmetric quantum mechanics. Starting with the critical damping, one can obtain in the underdamping case a chirping of instantaneous physical frequency ω 2 (t) ∝ ω 2 u sech 2 (ω u t), whereas in the overdamped case the " chirping " is of the (unphysical) type ω 2 (t) ∝ ω 2 o sec 2 (ω o t), where ω u and ω o a...

Supersymmetric Partner Damping of Free Damping

We determine the class of damped modes ỹ which are related to the common free damping modes y by supersymmetry. They are obtained by employing the factorization of Newton’s differential equation of motion for the free damped oscillator by means of the general solution of the corresponding Riccati equation together with Witten’s method of constructing the supersymmetric partner operator. This pr...

Ermakov-Lewis symmetry in photonic lattices.

We present a class of waveguide arrays that is the classical analog of a quantum harmonic oscillator, where the mass and frequency depend on the propagation distance. In these photonic lattices, refractive indices and second-neighbor couplings define the mass and frequency of the analog quantum oscillator, while first-neighbor couplings are a free parameter to adjust the model. The quantum mode...

Ermakov-lewis Dynamic Invariants with Some Applications

Generalised Symmetries and the Ermakov-Lewis Invariant

Generalised symmetries and point symmetries coincide for systems of first-order ordinary differential equations and are infinite in number. Systems of linear first-order ordinary differential equations possess a generalised rescaling symmetry. For the system of first-order ordinary differential equations corresponding to the time-dependent linear oscillator the invariant of this symmetry has th...