Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics
arXiv:2207.09515 · doi:10.1088/1751-8121/ac97cf
Abstract
It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time coordinate transformation. We demonstrate that an equivalent transformation can be performed for classical systems in the context of Koopman von-Neumann (KvN) dynamics. We further extend this mapping to dissipative evolutions in both the quantum and classical cases, and show that this mapping imparts an identical time-dependent scaling on the dissipation parameters for both types of dynamics. The derived classical procedure presents a number of opportunities to import squeezing dependent quantum procedures (such as Hamiltonian amplification) into the classical regime.
arXiv comment5 pages, no figures
References in corpus (18)
- Decoherence, einselection, and the quantum origins of the classical
- Operational Dynamic Modeling Transcending Quantum and Classical Mechanics
- Wigner flow reveals topological order in quantum phase space dynamics
- Inverted Oscillator
- Koopman wavefunctions and classical-quantum correlation dynamics
- Wigner phase space distribution as a wave function
- Efficient method to generate time evolution of the Wigner function for open quantum systems
- Equivalence between focussed paraxial beams and the quantum harmonic oscillator
- Special-case closed form of the Baker-Campbell-Hausdorff formula
- Minimal Coupling in Koopman-von Neumann Theory
- KvN mechanics approach to the time-dependent frequency harmonic oscillator
- Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes
- Amplification of quadratic Hamiltonians
- Beating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation
- Ermakov-Lewis invariant in Koopman-von Neumann mechanics
- Decoherence-Free Entropic Gravity: Model and Experimental Tests
- Free Particle Wave Function and Niederer's Transformation
- Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems