Formulation of general dynamical invariants and their unitary relations
for time-dependent coupled quantum oscillators
- URL: http://arxiv.org/abs/2210.07551v1
- Date: Fri, 14 Oct 2022 06:10:42 GMT
- Title: Formulation of general dynamical invariants and their unitary relations
for time-dependent coupled quantum oscillators
- Authors: Jeong Ryeol Choi
- Abstract summary: An exact invariant operator of time-dependent coupled oscillators is derived using the Liouville-von Neumann equation.
The unitary relation between this invariant and the invariant of two uncoupled simple harmonic oscillators is represented.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: An exact invariant operator of time-dependent coupled oscillators is derived
using the Liouville-von Neumann equation. The unitary relation between this
invariant and the invariant of two uncoupled simple harmonic oscillators is
represented. If we consider the fact that quantum solutions of the simple
harmonic oscillator is well-known, this unitary relation is very useful in
clarifying quantum characteristics of the original systems, such as
entanglement, probability densities, fluctuations of the canonical variables,
and decoherence. We can identify such quantum characteristics by inversely
transforming the mathematical representations of quantum quantities belonging
to the simple harmonic oscillators. As a case in point, the eigenfunctions of
the invariant operator in the original systems are found through inverse
transformation of the well-known eigenfunctions associated with the simple
harmonic oscillators.
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