We consider Kane's quantum model for two-band charged particles, composed of two Schroedinger-like equations coupled by a kp term which describes interband tunneling. Using the WKB method we derive the hydrodynamic equations both for a zero-temperature and for a nonzero-temperature two-band quantum fluid. In the latter case, we introduce a family of closure relations and write in full details the simplest two-band, isentropic, fluiddynamical model. Finally, introducing appropriate relaxation terms and performing drift-diffusive limits, we obtain the corresponding quantum drift-diffusion models for zero and nonzero-temperature quantum fluids, while the general closure problem and numerical implementation are left to future work. Key words: Kane model.Quantum hydrodynamic model. WKB method AMS Subject Classification: 82C40, 47D06, 35Q35.

Quantum hydrodynamic models for the two-band Kane system / G. ALI'; G. FROSALI. - In: IL NUOVO CIMENTO DELLA SOCIETÀ ITALIANA DI FISICA. B, GENERAL PHYSICS, RELATIVITY, ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS. - ISSN 1594-9982. - STAMPA. - 120 B (12):(2005), pp. 1279-1298. [10.1393/ncb/i2005-10096-1]

Quantum hydrodynamic models for the two-band Kane system

FROSALI, GIOVANNI
2005

Abstract

We consider Kane's quantum model for two-band charged particles, composed of two Schroedinger-like equations coupled by a kp term which describes interband tunneling. Using the WKB method we derive the hydrodynamic equations both for a zero-temperature and for a nonzero-temperature two-band quantum fluid. In the latter case, we introduce a family of closure relations and write in full details the simplest two-band, isentropic, fluiddynamical model. Finally, introducing appropriate relaxation terms and performing drift-diffusive limits, we obtain the corresponding quantum drift-diffusion models for zero and nonzero-temperature quantum fluids, while the general closure problem and numerical implementation are left to future work. Key words: Kane model.Quantum hydrodynamic model. WKB method AMS Subject Classification: 82C40, 47D06, 35Q35.
2005
120 B (12)
1279
1298
G. ALI'; G. FROSALI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/209393
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