For a homogeneous massive scalar field on a prescribed FLRW background, the Bateman and doubled Caldirola-Kanai systems are canonically equivalent via an explicit time-dependent point transformation, with a conserved Hamiltonian for the p=2/3 background.
Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics
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A Time-Dependent Canonical Transformation between Bateman and Doubled Caldirola--Kanai Systems for a Homogeneous Massive Scalar Field on a Prescribed FLRW Background
For a homogeneous massive scalar field on a prescribed FLRW background, the Bateman and doubled Caldirola-Kanai systems are canonically equivalent via an explicit time-dependent point transformation, with a conserved Hamiltonian for the p=2/3 background.