Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators
Ander Tobalina, E. Torrontegui, I. Lizuain, M. Palmero, J. G. Muga
Abstract
Two-dimensional (2D) systems with time-dependent controls admit a quadratic Hamiltonian modeling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some systems are not separable into independent modes by a point transformation. For these ``coupled systems'' 2D invariants may still guide the Hamiltonian design. The theory to perform the inversion and two application examples are provided: (i) We control the deflection of wave packets in transversally harmonic wave guides and (ii) we design the state transfer from one coupled oscillator to another.
Topics & Concepts
Harmonic oscillatorInverseHamiltonian (control theory)Maxima and minimaQuadratic equationHamiltonian systemInvariant (physics)Wave packetPhysicsControl theory (sociology)MathematicsClassical mechanicsMathematical analysisComputer scienceQuantum mechanicsGeometryMathematical optimizationControl (management)Artificial intelligenceMechanical and Optical ResonatorsNeural Networks and Reservoir ComputingNonlinear Dynamics and Pattern Formation