KvN mechanics approach to the time-dependent frequency harmonic oscillator

Abstract

Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville operator associated with the time-dependent frequency harmonic oscillator can be transformed using an Ermakov-Lewis invariant, which is also time dependent and commutes with itself at any time. Finally, because the solution of the Ermakov equation is involved in the evolution of the classical state vector, we explore some analytical and numerical solutions.

17 pages, 2 figures

References in corpus (4)

• Topics in Koopman-von Neumann Theory
• The time-dependent quantum harmonic oscillator revisited: Applications to Quantum Field Theory
• Three Approaches to Classical Thermal Field Theory
• No thermalization without correlations

Cited by in corpus (11)

• Koopman wavefunctions and classical-quantum correlation dynamics
• On deformations of classical mechanics due to Planck-scale physics
• Ermakov-Lewis invariant in Koopman-von Neumann mechanics
• Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems
• The Schwinger action principle for classical systems
• Classical dynamics from a unitary representation of the Galilei group
• Operational classical mechanics: Holonomic Systems
• Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics
• Unitary representation of the Poincaré group for classical relativistic dynamics
• Adiabatic amplification of the harmonic oscillator energy when the frequency passes through zero
• Separability and entanglement in classical eigenfunctions as a criterion for Hamiltonian chaos