DOI 10.1393/ncb/i2005-10096-1 IL NUOVO CIMENTO Online First Dicembre 2005 Quantum hydrodynamic models for the two-band Kane system

pubblicato online l’1 Febbraio 2006) Summary. — We consider Kane’s quantum model for two-band charged particles, composed of two Schrödinger-like equations coupled by a k · p term which describes interband tunneling. Using the WKB method we derive the hydrodynamic equa-tions 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, fluid-dynamical model. Finally, introduc-ing appropriate relaxation terms and performing drift-diffusive limits, we obtain the corresponding quantum drift-diffusion models for zero and nonzero-temperature quantum fluids. PACS 72.10.Bg – General formulation of transport theory. PACS 85.30.De – Semiconductor-device characterization, design, and modeling. 1