Time Evolution of the Wigner Operator as a Quasi-density Operator in Amplitude Dessipative Channel

For developing quantum mechanics theory in phase space, we explore how the Wigner operator Δ ( α , α ∗ ) ≡ 1 π : e − 2 ( α ∗ − α ‡ ) ( α − α ) :, when viewed as a quasi-density operator correponding to the Wigner quasiprobability distribution, evolves in a damping channel. with the damping constant...

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Bibliographic Details
Published in:International journal of theoretical physics 2018-06, Vol.57 (6), p.1888-1893
Main Authors: Yu, Zhisong, Ren, Guihua, Yu, Ziyang, Wei, Chenhuinan, Fan, Hongyi
Format: Article
Language:English
Subjects:
Damping
Elementary Particles
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum mechanics
Quantum Physics
Theoretical
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Summary:For developing quantum mechanics theory in phase space, we explore how the Wigner operator Δ ( α , α ∗ ) ≡ 1 π : e − 2 ( α ∗ − α ‡ ) ( α − α ) :, when viewed as a quasi-density operator correponding to the Wigner quasiprobability distribution, evolves in a damping channel. with the damping constant κ . We derive that it evolves into 1 T + 1 : exp 2 T + 1 [ − ( α ∗ e − κ t − a ‡ ) ( α e − κ t − a ) ] : where T ≡ 1 − e − 2 κ t . This in turn helps to directly obtain the final state ρ ( t ) out of the dessipative channel from the initial classical function corresponding to initial ρ (0). Throught the work, the method of integration within ordered product (IWOP) of operators is employed.
ISSN:0020-7748
1572-9575
DOI:10.1007/s10773-018-3714-6