Gardner, Carl L.; Ringhofer, Christian Approximation of thermal equilibrium for quantum gases with discontinuous potentials and application to semiconductor devices. (English) Zbl 0957.76099 SIAM J. Appl. Math. 58, No. 3, 780-805 (1998). The authors derive Wigner’s approximate solution to the Bloch equation for quantum mechanical thermal equilibrium distribution function for high temperatures and small external potential. The validity of the approximate solution is demonstrated numerically and analytically, by proving the convergence of the approximate Wigner functions and the corresponding particle densities. The results are applied to the technologically important case of piecewise continuous potential in quantum semiconductor devices. Reviewer: Oleg Titow (Berlin) Cited in 10 Documents MSC: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 82D05 Statistical mechanics of gases 81V55 Molecular physics 82D37 Statistical mechanics of semiconductors Keywords:quantum gases; quantum hydrodynamics; conservation laws; Wigner’s approximate solution; Bloch equation; quantum mechanical thermal equilibrium distribution function; convergence; piecewise continuous potential; quantum semiconductor devices PDFBibTeX XMLCite \textit{C. L. Gardner} and \textit{C. Ringhofer}, SIAM J. Appl. Math. 58, No. 3, 780--805 (1998; Zbl 0957.76099) Full Text: DOI