Abstract
Heating map of the classical probability-distribution function (in the phase space) and of density matrix (in the position representation) in quantum mechanics is introduced and its positivity is proved. The relation of the heating map to scaling transform and unitary squeezing transform of the momentum variable in the Wigner function is used to prove that noncanonical scaling transform of the position and momentum provides positive (but not completely positive!) map of density operator. The connection of momentum scaling transform with time scaling transform and Planck’s constant scaling transform is discussed.
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Man’ko, O.V. Heating map in classical and quantum mechanics. J Russ Laser Res 26, 109–115 (2005). https://doi.org/10.1007/s10946-005-0010-8
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DOI: https://doi.org/10.1007/s10946-005-0010-8