The non-stationary quadratic quantum system which can be considered as a quantum model of a damped oscillator is investigated in the framework of the Wigner representation. The explicit expressions of the ordinary and smoothed Wigner functions for this system are obtained.

Journal of Physics A Mathematical and GeneralSep 21, 199512 citations

Physica A Statistical Mechanics and its Applications

On one controversy about the smoothed Wigner function

Dragomir M Davidović, D. Lalović

Published Apr 1, 1992• 7 citations

Publisher

DOI: 10.1016/0378-4371(92)90028-o

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Smoothed Wigner function of a quantum damped oscillator

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Journal of Physics A Mathematical and GeneralSep 21, 199512 citations

In this paper, we correct a mistake we made in [Phys. Rev. Lett.

\textbf{122}

, 190402 (2019)] and [Phys. Rev. A

\textbf{103}

, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here smoothing refers to estimation of properties at time

t

using information obtained in measurements both before and after

t

. The SWV state is a pseudo-state (Hermitian but not necessarily positive) that gives, by the usual trace formula, the correct value for a weak measurement preformed at time

t

\textit{i.e.}

, its weak value. The Wigner function is a pseudo-probability-distribution (real but not necessarily positive) over phase-space. A smoothed (in this estimation sense) Wigner distribution at time

t

can also be defined by applying classical smoothing for probability-distributions to the Wigner functions. The smoothed Wigner distribution (SWD) gives identical means for the canonical phase-space variables as does the SWV state. However, contrary to the assumption in the above references, the Wigner function of the SWV state is not the smoothed Wigner distribution.