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Heating map in classical and quantum mechanics
Authors:Olga V. Man’ko
Affiliation:(1) P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Pr. 53, Moscow, 119991, Russia
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 Planckrsquos constant scaling transform is discussed.
Keywords:scaling transform  positive map  tomogram  Wigner function  quadratic form  quasidistribution
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