The hydrodynamic moment equations for a quantum system described by a two-band Hamiltonian are derived. In the case of pure states, it is proved that the order-0 and order-1 moment equations yield a closed system which is the two band analogue of Madelung's fluid equations.
Vengono dedotte le equazioni per i momenti idrodinamici di un sistema quantistico descritto da un'Hamiltoniana 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.
@article{BUMI_2005_8_8B_1_103_0,
author = {Luigi Barletti},
title = {Quantum moment equations for a two-band $k\cdot p$ Hamiltonian},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {8-A},
year = {2005},
pages = {103-121},
zbl = {1150.81001},
mrnumber = {2122977},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_1_103_0}
}
Barletti, Luigi. Quantum moment equations for a two-band $k\cdot p$ Hamiltonian. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 103-121. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_1_103_0/
[1] , A mathematical introduction to the Wigner formulation of quantum mechanics, B. Unione Mat. Ital. B, 6-B (2003), 693-716. | MR 2014828 | Zbl 1117.81091
[2] , On the thermal equilibrium of a quantum system described by a twoband Kane Hamiltonian, submitted.
[3] , Quantum Mechanics, Springer Verlag, 1979. | MR 580320 | Zbl 0994.81502
[4] - - , 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] - , Quantum moment hydrodynamics and the entropy principle, J. Statist. Phys., 112 (2003), 587-628. | MR 1997263 | Zbl 1035.82028
[6] - - - , Wigner function for multiband transport in semiconductors, Transport Theory Stat. Phys., 32 (2003), 307-325. | MR 2014720 | Zbl 1029.82038
[7] , Statistical Mechanics, W. A. Benjamin Inc., 1972. | Zbl 0997.82500
[8] , Harmonic Analysis in Phase Space, Princeton University Press, 1989. | MR 983366 | Zbl 0682.43001
[9] , The quantum hydrodynamic model for semiconductor devices, SIAM J. Appl. Math., 54 (1994), 409-427. | MR 1265234 | Zbl 0815.35111
[10] - - , Quantum hydrodynamics, in Modeling of Collisions, Gauthier-Villars, 1997.
[11] , Quasi-Hydrodynamic Semiconductor Equations, Birkhäuser, 2001. | MR 1818867 | Zbl 0969.35001
[12] , Zener tunneling in semiconductors, J. Phys. Chem. Solids, 12 (1959), 181-188.
[13] , The method, in Physics of III-V Compounds, Semiconductors and Semimetals, Vol. 1, Academic Press, 1966.
[14] - , Quantum Mechanics: non-relativistic theory, 3rd ed., Pergamon Press, 1977. | MR 400931 | Zbl 0178.57901
[15] , Moment closure hierarchies for kinetic theories, J. Statist. Phys., 83 (1996), 1021-1065. | MR 1392419 | Zbl 1081.82619
[16] - , Sur les mesures de Wigner, Rev. Matematica Iberoamericana, 9 (1993), 553-618. | MR 1251718 | Zbl 0801.35117
[17] - , Motion of electrons and holes in perturbed periodic fields, Phys. Rev., 97 (1955), 869-882. | Zbl 0064.23801
[18] , Quantentheorie in hydrodynamischer Form, Zeitschr. f. Phys., 40 (1926), 322-326.
[19] - - , Semiconductor Equations, Springer Verlag, 1990. | MR 1063852 | Zbl 0765.35001
[20] , Essentials of Semiconductor Physics, Wiley, 1999.
[21] - , Analysis of transmission in polytype interband tunneling heterostructures, J. Appl. Phys., 72 (1992), 4714-4726. | MR 1159619