Weak limits of the quantum hydrodynamic model

VLSI Design

Volumn 9, Issue 4, 1999, Pages 427-434

  Pietra, Paola ^a,c,d,e,f   Pohl, Carsten ^b,g  

^a CNR   (Italy)

^b JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^c UNIVERSITY OF PAVIA   (Italy)

^d Istituto di Analisi Numerica   (Italy)

^e UNIVERSITY OF CHICAGO   (United States)

^f PURDUE UNIVERSITY   (United States)

^g TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

HYDRODYNAMICS; MATHEMATICAL MODELS; OSCILLATIONS; PROBLEM SOLVING;

QUANTUM HYDRODYNAMIC MODELS; SCALED PLANCK CONSTANT;

QUANTUM THEORY;

EID: 0033348545     PISSN: 1065514X     EISSN: None     Source Type: None    
DOI: 10.1155/1999/46852     Document Type: Article

References (19)

1. Ascher, U., Markowich, P. A., Pietra, P. and Schmeiser, C. (1991). A Phase Plane Analysis of Transonic Solutions for the Hydrodynamic Semiconductor Model. Math. Mod. and Meth. in the Appl. Sci., 1, 347-376.
2. Ancona, M. G. and Iafrate, G. J. (1989). Quantum correction to the equation of state of an electron gas in a semiconductor. Phys. Rev., B39, 9536-9540.
3. Forest, M. G. and McLaughlin, D. W. (1984). Modulations of perturbed KdV wavetrains. SIAM J. Appl. Math., 44, 287-300.
4. Fornberg, B. and Whitham, G. B. (1978). A numerical and theoretical study of certain non-linear wave phenomena. Proc. Roy. Soc. London, 289, 373-404.
5. Gardner, C. L. (1994). The quantum hydrodynamic model for semiconductor devices. SIAM J. Appl. Math., 54, 409-427.
6. Gasser, I. and Markowich, P. A. (1997). Quantum hydrodynamics, Wigner transforms and the classical limit. Asymptotic Analysis, 14, 97-116.
7. Gérard, P., Markowich, P. A., Mauser, N. J. and Poupaud, F. (1997). Homogenization Limits and Wigner Transforms. Comm. Pure and Appl. Math., 50, 321-377.
8. Gasser, I., Markowich, P. A., Schmidt, D. and Unterreiter, A. (1995). Macroscopic Theory of Charged Quantum Fluids, In: Mathematical Problems in Semiconductor Physics, Marcati, P., Markowich, P. A. and Natalini, R. (Eds.), Pitman Research Notes in Mathematics Series 340, Longman, pp. 42-75.
9. Grenier, E. (1995). Limite semi-classique de l'équation de Schrödinger non linaire en temps petit. C.R. Acad. Sci. Paris Sr. I Math., 320(6), 691 -694.
10. Gardner, C. L. and Ringhofer, C. (1998). Smooth Quantum Hydrodynamic Model Simulation of the Resonant Tunneling Diode. To appear in VLSI Design.
11. Gardner, C. L. and Ringhofer, C. (1996). Smooth Quantum Potential for the Hydrodynamic Model. Physical Review E, 53, 157-167.
12. Lax, P. D. and Levermore, C. D. (1983). The small dispersion limit of the KdV equation. Comm. Pure Appl. Math., 36, I 253-290; II 571-593; III 809-830.
13. Landau, L. D. and Lifschitz, E. M. (1985). Lehrbuch der Theoretischen Physik III-Quantenmechanik. Akademie-Verlag.
14. Lions, P. L. and Paul, T. (1993). Sur les Mesures de Wigner. Revista Mat. Iberoamericana, 9, 553-618.
15. Markowich, P. A. and Mauser, N. J. (1993). The Classical Limit of a Self-consistent Quantum-Vlasov Equation in 3-D. Math. Mod. and Meth. in Appl. Sciences, 9, 109-124.
16. Pietra, P. and Pohl, C., A numerical Study of the isentropic Quantum Hydrodynamic Equation for Semiconductors, in preparation
17. Schonbek, M. E. (1982). Convergence of solutions to nonlinear dispersive equations. Comm. Partial Differ. Eq., 7, 959-1000.
18. Schmeiser, C., in preparation
19. Venakides, S. (1987). The zero dispersion limit of the periodic KdV equations. AMS Transaction, 301, 189-226.