![]() ![]() The Lax flow is given by where brackets indicate the usual matrix commutator, : = A B − B A, A † is the conjugate transpose of A and the matrix d u is the matrix equal to along diagonal and upper triangular entries and zero below diagonal. ![]() We study an isospectral flow (Lax flow) that provides an explicit deformation from upper Hessenberg complex matrices to normal matrices, extending to the complex case and to the case of normal matrices the results of. This is a technologically relevant situation for today's semiconductor devices for which quantum mechanical effects are prominent. The numerical experiment chosen for the comparisons consists of a Gaussian wave packet tunneling through a realistic source-to-drain potential profile. We show that excellent agreement is reached with our Monte Carlo technique which is also computationally efficient. Both approaches are compared to the direct solution of the Schrödinger equation. Then we adapt the concept of potential decomposition, widely utilized to simplify the numerical treatment of the Wigner equation, to our method. In this paper we focus on the Wigner equation, a convenient reformulation of the Schrödinger equation in terms of a phase-space, and present a Monte Carlo technique to solve it, based on signed particles. ![]() As nowadays semiconductor devices are characterized by active lengths on the nanometer scale, it is important to use models including fully the quantum mechanical effects. ![]()
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