The `Ermakov - Lewis' invariants for coupled linear oscillators

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...

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 Approach for Q = 0 Empty Frw Minisuperspace Oscillators

The Wheeler-DeWitt equation for empty FRW minisuperspace universes of Hartle-Hawking factor ordering parameter Q = 0 is mapped onto the dynamics of a unit mass classical oscillator. The latter is studied by the classical Ermakov invariant method. Angle quantities are presented in the same context. The formalism of Ermakov-type invariants [1] can be a useful, alternative method of investigating ...

04 Linear Chain of Coupled Oscillators