Vengono dedotte le equazioni per i momenti idrodinamici di un sistema quantistico descritto da un'Hamiltoniana $k \cdot p$ a due bande. Nel caso di stati puri si dimostra che le equazioni dei momenti di ordine 0 e di ordine 1 forniscono un sistema chiuso che costituisce l'analogo a due bande delle equazioni del fluido di Madelung.
Referenze Bibliografiche
[2] L. BARLETTI, On the thermal equilibrium of a quantum system described by a twoband Kane Hamiltonian, submitted.
[4]
G. BORGIOLI -
G. FROSALI -
P. F. ZWEIFEL,
Wigner approach to the two-band Kane model for a tunneling diode,
Transport Theory Stat. Phys.,
32 (
2003), 347- 366. |
MR 2014722 |
Zbl 1035.81028[5]
P. DEGOND -
C. RINGHOFER,
Quantum moment hydrodynamics and the entropy principle,
J. Statist. Phys.,
112 (
2003), 587-628. |
MR 1997263 |
Zbl 1035.82028[6]
L. DEMEIO -
L. BARLETTI -
P. BORDONE -
C. JACOBONI,
Wigner function for multiband transport in semiconductors,
Transport Theory Stat. Phys.,
32 (
2003), 307-325. |
MR 2014720 |
Zbl 1029.82038[7]
R. P. FEYNMAN,
Statistical Mechanics,
W. A. Benjamin Inc.,
1972. |
Zbl 0997.82500[8]
G. B. FOLLAND,
Harmonic Analysis in Phase Space,
Princeton University Press,
1989. |
MR 983366 |
Zbl 0682.43001[9]
C. L. GARDNER,
The quantum hydrodynamic model for semiconductor devices,
SIAM J. Appl. Math.,
54 (
1994), 409-427. |
MR 1265234 |
Zbl 0815.35111[10] I. GASSER - P. A. MARKOWICH - A. UNTERREITER, Quantum hydrodynamics, in Modeling of Collisions, Gauthier-Villars, 1997.
[12] E. O. KANE, Zener tunneling in semiconductors, J. Phys. Chem. Solids, 12 (1959), 181-188.
[13] E. O. KANE, The $k \cdot p$ method, in Physics of III-V Compounds, Semiconductors and Semimetals, Vol. 1, Academic Press, 1966.
[14]
L. D. LANDAU -
E. M. LIFSHITZ,
Quantum Mechanics: non-relativistic theory, 3rd ed.,
Pergamon Press,
1977. |
MR 400931 |
Zbl 0178.57901[15]
C. D. LEVERMORE,
Moment closure hierarchies for kinetic theories,
J. Statist. Phys.,
83 (
1996), 1021-1065. |
MR 1392419 |
Zbl 1081.82619[16]
P. L. LIONS -
T. PAUL,
Sur les mesures de Wigner,
Rev. Matematica Iberoamericana,
9 (
1993), 553-618. |
MR 1251718 |
Zbl 0801.35117[17]
J. M. LUTTINGER -
W. KOHN,
Motion of electrons and holes in perturbed periodic fields,
Phys. Rev.,
97 (
1955), 869-882. |
Zbl 0064.23801[18] E. MADELUNG, Quantentheorie in hydrodynamischer Form, Zeitschr. f. Phys., 40 (1926), 322-326.
[19]
P. A. MARKOWICH -
C. A. RINGHOFER -
C. SCHMEISER,
Semiconductor Equations,
Springer Verlag,
1990. |
MR 1063852 |
Zbl 0765.35001[20] T. WENCKEBACH, Essentials of Semiconductor Physics, Wiley, 1999.
[21]
R. Q. YANG -
J. M. XU,
Analysis of transmission in polytype interband tunneling heterostructures,
J. Appl. Phys.,
72 (
1992), 4714-4726. |
MR 1159619
Con il contributo del Ministero per i Beni e le Attività Culturali