Adding Decoherence to the Wigner Equation

Abstract

Starting from the detailed description of the single-collision decoherence mechanism proposed by Adami, Hauray and Negulescu (2016), we derive a Wigner equation endowed with a decoherence term of a fairly general form. This equation is shown to contain well known decoherence models, such as the Wigner–Fokker–Planck equation, as particular cases. The effect of the decoherence mechanism on the dynamics of the macroscopic moments (density, current, energy) is illustrated by deriving the corresponding set of balance laws. The issue of large-time asymptotics of our model is addressed in the particular, although physically relevant, case of Gaussian solutions. It is shown that the addition of a Caldeira–Legget friction term provides the asymptotic behavior that one expects on the basis of physical considerations.

Keywords:

• Decoherence
• Wigner equation
• quantum open systems

Acknowledgments

The authors wish to express their gratitude to Prof. Claudia Negulescu for her valuable support and for many stimulating discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

L. B. acknowledges support from the Italian-French project PICS (Projet International de Coopération Scientifique) “MANUS - Modelling and Numerics for Spintronics and Graphene” (Ref. PICS07373).

E. G. acknowledges support from INdAM-GNFM (Italian National Group for Mathematical Physics).

Part of this work was accomplished during E. G. staying at Paul Sabatier University in Toulouse with a grant MAE-2018 from the French Ministère de l'Europe et des Affaires étrangères.