Subdomain-based exponential integrators for quantum Liouville-type equations

Abstract In order to describe quantum mechanical effects, the use of von-Neumann equation is apparent. this work, we present a unified numerical framework so that in center-of-mass coordinates leads Quantum Liouville-type when choosing suitable basis. particular, proposed approach can be related conventional Wigner plane wave basis used. The drawback methods high computational cost. Our presented extended allow reducing dimension basis, which computationally efficient and accurate subdomain approach. Not only steady-state behavior interest, but also dynamic behavior. solve time-dependent case, approximation for exponential integrator are necessary. For purpose, investigate approximations based on Faber polynomials Krylov methods. evaluate justify our approach, various test cases, including resonant tunnel diode as well double-gate field-effect transistor, investigated validated stationary device