Quantum hydrodynamic models derived from the entropy principle

2005 ◽  
pp. 107-131 ◽  
Author(s):  
Pierre Degond ◽  
Florian Méhats ◽  
Christian Ringhofer
Keyword(s):  
Hydrodynamic Models ◽  
Entropy Principle ◽  
Quantum Hydrodynamic

Recent Progress on Quantum Hydrodynamic Models for Semiconductors

2003 ◽  
pp. 217-226 ◽  
Author(s):  
Ansgar Jüngel ◽  
Hailiang Li ◽  
Peter A. Markowich ◽  
Shu Wang
Keyword(s):  
Recent Progress ◽  
Hydrodynamic Models ◽  
Quantum Hydrodynamic

ON QUANTUM HYDRODYNAMIC MODELS FOR ELECTRONIC TRANSPORT IN NANOSCALE SEMICONDUCTOR DEVICES

2010 ◽  
Vol 24 (04n05) ◽  
pp. 401-409
Author(s):  
EUGENIA TULCAN-PAULESCU ◽  
DAN COMǍNESCU ◽  
MARIUS PAULESCU
Keyword(s):  
Numerical Simulation ◽  
Electronic Transport ◽  
Resonant Tunneling ◽  
Semiconductor Devices ◽  
Resonant Tunneling Diode ◽  
Hydrodynamic Models ◽  
Tunneling Diode ◽  
Quantum Hydrodynamic ◽  
Ballistic Diode

This article deals with quantum hydrodynamic models (QHD) for electronic transport in semiconductor devices. Numerical simulation of ballistic diode and resonant tunneling diode is discussed. Based on overall results, it can be concluded that the considered QHD models have remarkable abilities to express the refinements of electronic transport in nanodevices.

A PROPER NONLOCAL FORMULATION OF QUANTUM MAXIMUM ENTROPY PRINCIPLE IN STATISTICAL MECHANICS

2012 ◽  
Vol 26 (12) ◽  
pp. 1241007 ◽  
Author(s):  
M. TROVATO ◽  
L. REGGIANI
Keyword(s):  
Statistical Mechanics ◽  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Quantum Statistical Mechanics ◽  
Fundamental Principle ◽  
Quantum Entropy ◽  
Closure Condition ◽  
Entropy Principle ◽  
Quantum Hydrodynamic ◽  
Reduced Density

By considering Wigner formalism, the quantum maximum entropy principle (QMEP) is here asserted as the fundamental principle of quantum statistical mechanics when it becomes necessary to treat systems in partially specified quantum states. From one hand, the main difficulty in QMEP is to define an appropriate quantum entropy that explicitly incorporates quantum statistics. From another hand, the availability of rigorous quantum hydrodynamic (QHD) models is a demanding issue for a variety of quantum systems. Relevant results of the present approach are: (i) The development of a generalized three-dimensional Wigner equation. (ii) The construction of extended quantum hydrodynamic models evaluated exactly to all orders of the reduced Planck constant ℏ. (iii) The definition of a generalized quantum entropy as global functional of the reduced density matrix. (iv) The formulation of a proper nonlocal QMEP obtained by determining an explicit functional form of the reduced density operator, which requires the consistent introduction of nonlocal quantum Lagrange multipliers. (v) The development of a quantum-closure procedure that includes nonlocal statistical effects in the corresponding quantum hydrodynamic system. (vi) The development of a closure condition for a set of relevant quantum regimes of Fermi and Bose gases both in thermodynamic equilibrium and nonequilibrium conditions.

scholarly journals EFFECTIVE POTENTIALS AND QUANTUM FLUID MODELS: A THERMODYNAMIC APPROACH

2003 ◽  
Vol 13 (03) ◽  
pp. 771-801 ◽  
Author(s):  
CHRISTIAN RINGHOFER ◽  
CARL GARDNER ◽  
DRAGICA VASILESKA
Keyword(s):  
Semiconductor Device ◽  
Thermodynamic Approach ◽  
Hydrodynamic Models ◽  
Hydrodynamic Simulations ◽  
Quantum Fluid ◽  
Effective Potentials ◽  
Tunneling Diode ◽  
Oxide Barrier ◽  
Quantum Hydrodynamic ◽  
Classical Transport

We present a thermodynamic approach to introducing quantum corrections to the classical transport picture in semiconductor device simulation. This approach leads to a modified Boltzmann equation with a quantum corrected force term and to quantum corrected fluid, or quantum hydrodynamic models. We present the quantum interaction of electrons with a gate oxide barrier potential and quantum hydrodynamic simulations of a resonant tunneling diode as application examples.

Nonlocal Hydrodynamic Models for the Optical Response of Plasmonic Nanostructures

2021 ◽  
Vol 35 (11) ◽  
pp. 1388-1389
Author(s):  
Mario Kupresak ◽  
Xuezhi Zheng ◽  
Guy Vandenbosch ◽  
Victor Moshchalkov
Keyword(s):  
Hydrodynamic Model ◽  
Hydrodynamic Equation ◽  
Nanometer Scale ◽  
Plasmonic Nanostructures ◽  
Hydrodynamic Models ◽  
Quantum Hydrodynamic Model ◽  
Coupled Equations ◽  
Hydrodynamic Approach ◽  
Plasmonic Structures ◽  
Quantum Hydrodynamic

In order to model the interaction between light and plasmonic structures at deep-nanometer scale, which is governed by non-classical effects, a nonlocal hydrodynamic approach has been extensively studied. Several hydrodynamic models have been proposed, solving the coupled equations: the linearized hydrodynamic equation of motion and the electrodynamic Maxwell’s equations, by employing additional boundary conditions. This work compares four hydrodynamic models: the hard wall hydrodynamic model (HW-HDM), the curl-free hydrodynamic model (CF-HDM), the shear forces hydrodynamic model (SF-HDM), and the quantum hydrodynamic model (Q-HDM). The analysis is conducted for a metallic spherical nanoparticle, as an example. The above hydrodynamic models are also compared with experiments available in literature. It is demonstrated that HW-HDM and QHDM outperform the other two hydrodynamic models.

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