Authors: Schulz, Lukas
Inci, B.
Pech, M.
Schulz, Dirk
Title: Subdomain-based exponential integrators for quantum Liouville-type equations
Language (ISO): en
Abstract: In order to describe quantum mechanical effects, the use of the von-Neumann equation is apparent. In this work, we present a unified numerical framework so that the von-Neumann equation in center-of-mass coordinates leads to a Quantum Liouville-type equation when choosing a suitable basis. In particular, the proposed approach can be related to the conventional Wigner equation when a plane wave basis is used. The drawback of the numerical methods is the high computational cost. Our presented approach is extended to allow reducing the dimension of the basis, which leads to a computationally efficient and accurate subdomain approach. Not only the steady-state behavior is of interest, but also the dynamic behavior. In order to solve the time-dependent case, suitable approximation methods for the time-dependent exponential integrator are necessary. For this purpose, we also investigate approximations of the exponential integrator based on Faber polynomials and Krylov methods. In order to evaluate and justify our approach, various test cases, including a resonant tunnel diode as well as a double-gate field-effect transistor, are investigated and validated for the stationary and the dynamic device behavior.
Subject Headings: Computational nanotechnology
Transient quantum transport
Wigner transport equation
Numerical methods
Time integration techniques
Exponential integrators
Subject Headings (RSWK): Computational nanotechnology
Numerisches Verfahren
Issue Date: 2021-10-15
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Appears in Collections:Lehrstuhl für Hochfrequenztechnik

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