Free Fermions with a Localized Source

P. L. Krapivsky (1) , Kirone Mallick (2) , Dries Sels (3, 4)

1 Department of Physics [Boston]
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 Department of Physics [Harvard University]
4 TQC - Theory of Quantum systems and Complex systems

We study an open quantum system of free fermions on an infinite lattice coupled to a localized particle source. In the long time limit, the total number of fermions in the system increases linearly with growth rate dependent on the lattice geometry and dimensionality. We express the growth rate in terms of lattice Green functions and derive explicit formulae in one dimension and for the square lattice. The interplay between the dynamics and the coupling to the environment leads, in contrast to classical systems, to a non-monotonic dependence of the particle growth rate on the input rate. We show that for all lattices the particle growth rate is inversely proportional to the input rate when the latter becomes large. This is a manifestation of the quantum Zeno effect.

Domaines: Mécanique statistique [cond-mat.stat-mech]

P. L. Krapivsky, Kirone Mallick, Dries Sels. Free Fermions with a Localized Source. Journal of Statistical Mechanics: Theory and Experiment, 2019, 2019 (11), pp.113108. ⟨10.1088/1742-5468/ab4e8e⟩. ⟨cea-02923417⟩