Search results for "Quantum hydrodynamics"

showing 3 items of 3 documents

A derivation of the isothermal quantum hydrodynamic equations using entropy minimization

2005

Isothermal quantum hydrodynamic equations of order O(h 2 ) using the quantum entropy minimization method recently developed by Degond and Ringhofer are derived. The equations have the form of the usual quantum hydrodynamic model including a correction term of order O(h 2 ) which involves the vorticity. If the initial vorticity is of order 0(h), the standard model is obtained up to order O(h 4 ). The derivation is based on a careful expansion of the quantum equilibrium obtained from the entropy minimization in powers of h 2 .

Minimisation (psychology)Standard Model (mathematical formulation)Classical mechanicsQuantum hydrodynamicsApplied MathematicsComputational MechanicsOrder (ring theory)Von Neumann entropyVorticityQuantumIsothermal processMathematical physicsMathematicsZAMM
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Numerical approximation of the viscous quantum hydrodynamic model for semiconductors

2006

The viscous quantum hydrodynamic equations for semiconductors with constant temperature are numerically studied. The model consists of the one-dimensional Euler equations for the electron density and current density, including a quantum correction and viscous terms, coupled to the Poisson equation for the electrostatic potential. The equations can be derived formally from a Wigner-Fokker-Planck model by a moment method. Two different numerical techniques are used: a hyperbolic relaxation scheme and a central finite-difference method. By simulating a ballistic diode and a resonant tunneling diode, it is shown that numerical or physical viscosity changes significantly the behavior of the solu…

Numerical AnalysisApplied MathematicsNumerical analysisFinite difference methodResonant-tunneling diodeFinite differenceRelaxation (iterative method)Euler equationsComputational Mathematicssymbols.namesakeClassical mechanicsQuantum hydrodynamicssymbolsPoisson's equationMathematicsApplied Numerical Mathematics
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Analysis of the viscous quantum hydrodynamic equations for semiconductors

2004

The steady-state viscous quantum hydrodynamic model in one space dimension is studied. The model consists of the continuity equations for the particle and current densities, coupled to the Poisson equation for the electrostatic potential. The equations are derived from a Wigner–Fokker–Planck model and they contain a third-order quantum correction term and second-order viscous terms. The existence of classical solutions is proved for “weakly supersonic” quantum flows. This means that a smallness condition on the particle velocity is still needed but the bound is allowed to be larger than for classical subsonic flows. Furthermore, the uniqueness of solutions and various asymptotic limits (sem…

PhysicsElliptic curveClassical mechanicsInviscid flowQuantum hydrodynamicsApplied MathematicsSemiclassical physicsUniquenessPoisson's equationQuantumExponential functionEuropean Journal of Applied Mathematics
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