Numerically absorbing boundary conditions for quantum evolution equations

VLSI Design

Volumn 6, Issue 1-4, 1998, Pages 313-319

  Arnold, Anton ^a,b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Absorbing boundary conditions; Discrete transparent boundary conditions; Finite differences; Quantum device contacts; Schr dinger equation; Transparent boundary conditions

Indexed keywords

BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; NUMERICAL ANALYSIS; QUANTUM THEORY; SEMICONDUCTOR QUANTUM WELLS;

SCHROEDINGER EQUATION;

SEMICONDUCTOR DEVICES;

EID: 0031632570     PISSN: 1065514X     EISSN: None     Source Type: Journal    
DOI: 10.1155/1998/38298     Document Type: Article

References (20)

1. A. Arnold, Math. Meth. Num. Anal. 7 (1994) 853-872.
2. A. Arnold, M. Peszyńska, Absorbing boundary conditions for the Schrödinger equation : an unconditionally stable discretizition, in preparation (1995).
3. A. Arnold, N. Ben Abdallah, On a transient Schrödinger-Poisson model with absorbing boundaries, in preparation (1995).
4. V.A. Baskakov, A.V. Popov, Wave Motion 14 (1991) 123-128.
5. N. Ben Abdallah, P. Degond, P.A. Markowich, On a one-dimensional Schrödinger-Poisson scattering model, submitted (1995).
6. J. Douglas Jr., J.E. Santos, D. Sheen, L.S. Bennethum, Math. Mod. and Meth. in Appl. Sc. (1993) 171-194.
7. B. Engquist, A. Majda, Math. Comp. 31 (1977) 629-651.
8. G.R. Hadley, IEEE J. Quantum Electron. 28 (1992) 363-370.
9. J.R. Hellums, W.R. Frensley, Phys. Rev. B 49 (1994) 2904-2906.
10. N. Kluksdahl, A.M. Kriman, D.K. Ferry, C. Ringhofer, Self-consistent study of the resonant tunneling diode, Phys. Rev. B 39 (1989) 7720-7735.
11. R. Kosloff, D. Kosloff, J. Comput. Phys. 63 (1986) 363-376.
12. C.S. Lent, D.J. Kirkner, J. Appl. Phys. 67 (1990) 6353-6359.
13. B. Mayfield, Non-local boundary conditions for the Schrödinger equation, Ph.D. thesis, University of Rhode Island, Providence, RI (1989).
14. J.S. Papadakis, Impedance formulation of the bottom boundary condition for the parabolic equation model in underwater acoustics. NORDA Parabolic Equation Workshop, NORDA Tech. Note 143 (1982).
15. J.S. Papadakis, M.I. Taroudakis, P.J. Papadakis, B. Mayfield, J. Acoust. Soc. Am. 92 (1992) 2030-2038.
16. C. Ringhofer, D. Ferry, N. Kluksdahl, Transp. Theory and Stat. Phys. 18 (1989) 331-346.
17. F. Schmidt, P. Deuflhard, Computers Math. Applic. 29 (1995) 53-76.
18. D.J. Thomson, M.E. Mayfield, J. Comput. Acoust. 2 (1994) 113-132.
19. D. Yevick, B. Hermansson, IEEE J. Quantum Electron. 25 (1989) 221-229.
20. D. Yevick, J. Yu, Y. Yayon, J. Opt. Soc. Am. A 12 (1995) 107-110.