Scientific seminar “Evolution equation for the Wigner function for arbitrary linear quantization”

12:00, 28 September, 2021

We consider a class of linear Hermitian quantizations defined by an integral transformation connecting the matrix of a quantum operator with its classical symbol. For arbitrary linear quantization, the equations of the evolution of the density matrix and the Wigner function are constructed. It is shown that only for the Weyl quantization, the Wigner function evolution equation does not contain a source of quasi-probability, which distinguishes this quantization as the only physically adequate one in the class under consideration. An example of an exact stationary solution for the Wigner function of a harmonic oscillator with arbitrary linear quantization is given, and a sequence of quantizations approximating the Weyl quantization and converging to it in a weak sense is constructed so that the Wigner function remains positive definite.

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