Naslov
Derivation of new quantum hydrodynamic equations using entropy minimization

Autori
Jüngel, Ansgar ; Matthes, Daniel ; Milišić, Josipa Pina

Izvornik
SIAM journal on applied mathematics (0036-1399) 67 (2006); 46-68

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
quantum moment hydrodynamics; entropy minimization; quantum Maxwellian; moemnt method; finite-difference discretization; numerical simulations; resonant tunneling diode; current-voltage characteristics

Sažetak
New quantum hydrodynamic equations are derived from a Wigner-Boltzmann model, using the quantum entropy minimization method recently developed by Degond and Ringhofer. The model consists of conservation equations for the carrier, momentum, and energy densities. The derivation is based on a careful expansion of the quantum Maxwellian in powers of the Planck constant. In difference to the standard quantum hydrodynamic equations derived by Gardner, the new model includes vorticity terms and a dispersive term for the velocity. Numerical current-voltage characteristics of a one-dimensional resonant tunneling diode for both the new quantum hydrodynamic equations and Gardner's model are presented. The numerical results indicate that the dispersive velocity term regularizes the solution of the system.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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