The Lindblad equation is commonly used for studying quantum dynamics in open systems that cannot be completely isolated from an environment, relevant to a broad variety of research fields, such as atomic physics, materials science, quantum biology and quantum information and computing. For electrons in condensed matter systems, the Lindblad dynamics is intractable even if their mutual Coulomb repulsion could somehow be switched off. This is because they would still be able to affect each other by interacting with the bath. Here, we develop an approximate approach, based on the Hubbard–Stratonovich transformation, which allows to evolve non-interacting Fermions in open quantum systems. We discuss several applications for systems of trapped 1D Fermions showing promising results.
Bibliographical noteFunding Information:
Israel Science Foundation [grant number 189/14]. This article is submitted to the Festschrift in honor of the pioneer of nonadiabatic dynamics Prof. Michael Baer. The second author, Roi Baer, hereby extends to his father a happy 80th birthday with deep love, appreciation and gratitude! Both authors gratefully thank the Israel Science Foundation Grant No. 189-14 for kindly funding this research.
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- Lindblad equations
- density matrix
- open fermion system
- open quantum systems