On the approximation of the von-Neumann equation in the semi-classical limit. Part I: Numerical algorithm
Copyright policy )On the approximation of the von-Neumann equation in the semi-classical limit. Part I: Numerical algorithm
We propose a new approach to discretize the von Neumann equation, which is efficient in the semi-classical limit. This method is first based on the so called Weyl's variables to address the stiffness associated with the equation. Then, by applying a truncated Hermite expansion of the density operator, we successfully handle this stiffness. Additionally, we develop a finite volume approximation for practical implementation and conduct numerical simulations to illustrate the efficiency of our approach. This asymptotic preserving numerical approximation, combined with the use of Hermite polynomials, provides an efficient tool for solving the von Neumann equation in all regimes, near classical or not.
Hermite polynomial expansion. Contents, Finite volume methods for boundary value problems involving PDEs, quantum mechanics, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], von Neumann equation, Quantum mechanics, Hermite polynomial expansion, 510, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Quantum mechanics von Neumann equation Hermite polynomial expansion. Contents, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], PDEs in connection with quantum mechanics, Analysis of PDEs (math.AP)
Hermite polynomial expansion. Contents, Finite volume methods for boundary value problems involving PDEs, quantum mechanics, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], von Neumann equation, Quantum mechanics, Hermite polynomial expansion, 510, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Quantum mechanics von Neumann equation Hermite polynomial expansion. Contents, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], PDEs in connection with quantum mechanics, Analysis of PDEs (math.AP)
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