메뉴 건너뛰기




Volumn 6, Issue 1, 2007, Pages 246-272

Isothermal quantum hydrodynamics: Derivation, asymptotic analysis, and simulation

Author keywords

Asymptotic analysis; Density matrix; Entropic quantum drift diffusion; Entropy minimization; Local equilibria; Madelung equations; Numerical simulations; Quantum Euler; Quantum Liouville equation; Quantum moment hydrodymics

Indexed keywords

ASYMPTOTIC ANALYSIS; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; DIFFUSION; ENTROPY; EULER EQUATIONS; FREE ENERGY; HYDRODYNAMICS;

EID: 39049102079     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/06067153X     Document Type: Article
Times cited : (26)

References (24)
  • 1
    • 7544228429 scopus 로고    scopus 로고
    • An analysis of quantum Fokker-Planck models: A Wigner function approach
    • A. ARNOLD, J. L, LOPEZ, P. A. MARKOWICH, AND J. SOLER, An analysis of quantum Fokker-Planck models: A Wigner function approach, Rev. Mat. Iberoamericana, 20 (2004), pp. 771-814.
    • (2004) Rev. Mat. Iberoamericana , vol.20 , pp. 771-814
    • ARNOLD, A.1    LOPEZ, J.L.2    MARKOWICH, P.A.3    SOLER, J.4
  • 3
    • 19844379054 scopus 로고    scopus 로고
    • Quantum hydrodynamics: Mixed states, dissipation, and a new hybrid quantum-classical approach
    • I. BURGHARDT, K. B. MOLLER, L. S. CEDERBAUM, AND E. R. BITTNER, Quantum hydrodynamics: Mixed states, dissipation, and a new hybrid quantum-classical approach, Int. J. Quant. Chem., 100 (2004), pp. 1153-1162.
    • (2004) Int. J. Quant. Chem , vol.100 , pp. 1153-1162
    • BURGHARDT, I.1    MOLLER, K.B.2    CEDERBAUM, L.S.3    BITTNER, E.R.4
  • 4
    • 0016072199 scopus 로고
    • Resonant tunneling in semiconductor double barriers
    • L. L. CHANG, L. ESAKI, AND R. TSU, Resonant tunneling in semiconductor double barriers, Appl. Phys. Lett., 24 (1974), pp. 593-595.
    • (1974) Appl. Phys. Lett , vol.24 , pp. 593-595
    • CHANG, L.L.1    ESAKI, L.2    TSU, R.3
  • 5
    • 0000449846 scopus 로고
    • Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode
    • Z. CHEN, B. COCKBURN, C. GARDNER, AND J. JEROME, Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode, J. Comput. Phys., 117 (1995), pp. 274-280.
    • (1995) J. Comput. Phys , vol.117 , pp. 274-280
    • CHEN, Z.1    COCKBURN, B.2    GARDNER, C.3    JEROME, J.4
  • 6
    • 0034291813 scopus 로고    scopus 로고
    • Nanoscale device modeling: The Green's function method
    • S. DATTA, Nanoscale device modeling: The Green's function method, Superlattices and Microstructures, 28 (2000), pp. 253-278.
    • (2000) Superlattices and Microstructures , vol.28 , pp. 253-278
    • DATTA, S.1
  • 7
    • 33846177213 scopus 로고    scopus 로고
    • An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes
    • P. DEGOND, S. GALLEGO, AND F. MÉHATS, An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes, J. Comput. Phys., 221 (2007), pp. 226-249.
    • (2007) J. Comput. Phys , vol.221 , pp. 226-249
    • DEGOND, P.1    GALLEGO, S.2    MÉHATS, F.3
  • 9
    • 15244345981 scopus 로고    scopus 로고
    • Quantum energy-transport and drift-diffusion models
    • P. DEGOND, F. MÉHATS, AND C. RINGHOFER, Quantum energy-transport and drift-diffusion models, J. Stat. Phys., 118 (2005), pp. 625-665.
    • (2005) J. Stat. Phys , vol.118 , pp. 625-665
    • DEGOND, P.1    MÉHATS, F.2    RINGHOFER, C.3
  • 10
    • 0037837827 scopus 로고    scopus 로고
    • Quantum moment hydrodynamics and the entropy principle
    • P. DEGOND AND C. RINGHOFER, Quantum moment hydrodynamics and the entropy principle, J. Statist. Phys., 112 (2003), pp. 587-628.
    • (2003) J. Statist. Phys , vol.112 , pp. 587-628
    • DEGOND, P.1    RINGHOFER, C.2
  • 11
    • 33646388746 scopus 로고    scopus 로고
    • Entropic discretization of a quantum drift-diffusion model
    • S. GALLEGO AND F. MÉHATS, Entropic discretization of a quantum drift-diffusion model, SIAM J. Numer. Anal., 43 (2005), pp. 1828-1849.
    • (2005) SIAM J. Numer. Anal , vol.43 , pp. 1828-1849
    • GALLEGO, S.1    MÉHATS, F.2
  • 12
    • 0028413338 scopus 로고
    • The quantum hydrodynamic model for semiconductor devices
    • C. L. GARDNER, The quantum hydrodynamic model for semiconductor devices, SIAM J. Appl. Math., 54 (1994), pp. 409-427.
    • (1994) SIAM J. Appl. Math , vol.54 , pp. 409-427
    • GARDNER, C.L.1
  • 13
    • 0001719509 scopus 로고    scopus 로고
    • The smooth quantum potential for the hydrodynamic model
    • C. GARDNER AND C. RINGHOFER, The smooth quantum potential for the hydrodynamic model, Phys. Rev. E (3), 53 (1996), pp, 157-167.
    • (1996) Phys. Rev. E , vol.53 , Issue.3 , pp. 157-167
    • GARDNER, C.1    RINGHOFER, C.2
  • 14
    • 0033672512 scopus 로고    scopus 로고
    • The Chapman-Enskog expansion and the quantum hydrodynamic model for semiconductor devices
    • C. GARDNER AND C. RINGHOFER, The Chapman-Enskog expansion and the quantum hydrodynamic model for semiconductor devices, VLSI Des., 10 (2000), pp. 415-435.
    • (2000) VLSI Des , vol.10 , pp. 415-435
    • GARDNER, C.1    RINGHOFER, C.2
  • 15
    • 0039768709 scopus 로고    scopus 로고
    • The quantum hydrodynamic model for semiconductors in thermal equilibrium
    • I. GASSER AND A. JÜNGEL, The quantum hydrodynamic model for semiconductors in thermal equilibrium, Z. Angew. Math. Phys., 48 (1997), pp. 45-59.
    • (1997) Z. Angew. Math. Phys , vol.48 , pp. 45-59
    • GASSER, I.1    JÜNGEL, A.2
  • 16
    • 0002375163 scopus 로고    scopus 로고
    • Quantum hydrodynamics, Wigner transforms and the classical limit
    • I. GASSER AND P. A. MARKOWICH, Quantum hydrodynamics, Wigner transforms and the classical limit, Asymptot. Anal., 14 (1997), pp. 97-116.
    • (1997) Asymptot. Anal , vol.14 , pp. 97-116
    • GASSER, I.1    MARKOWICH, P.A.2
  • 17
    • 0024930617 scopus 로고
    • Quantum moment balance equations and resonant tunneling structures
    • H. GRUBIN AND J. KRESKOVSKY, Quantum moment balance equations and resonant tunneling structures, Solid-State Electron, 32 (1989), pp. 1071-1075.
    • (1989) Solid-State Electron , vol.32 , pp. 1071-1075
    • GRUBIN, H.1    KRESKOVSKY, J.2
  • 18
    • 0007341961 scopus 로고    scopus 로고
    • Quasi-hydrodynamic Semiconductor Equations, Progr
    • Birkhäuser, Basel
    • A. JÜNGEL, Quasi-hydrodynamic Semiconductor Equations, Progr. Nonlinear Differential Equations Appl., Birkhäuser, Basel, 2001.
    • (2001) Nonlinear Differential Equations Appl
    • JÜNGEL, A.1
  • 19
    • 27744473992 scopus 로고    scopus 로고
    • A derivation of the isothermal quantum hydrodynamic equations using entropy minimization
    • A. JÜNGEL AND D. MATTHES, A derivation of the isothermal quantum hydrodynamic equations using entropy minimization, ZAMM Z. Angew. Math. Mech., 85 (2005), pp. 806-814.
    • (2005) ZAMM Z. Angew. Math. Mech , vol.85 , pp. 806-814
    • JÜNGEL, A.1    MATTHES, D.2
  • 20
    • 0030534703 scopus 로고    scopus 로고
    • Moment closure hierarchies for kinetic theories
    • C. D. LEVERMORE, Moment closure hierarchies for kinetic theories, J. Statist. Phys., 83 (1996), pp. 1021-1065.
    • (1996) J. Statist. Phys , vol.83 , pp. 1021-1065
    • LEVERMORE, C.D.1
  • 21
    • 34250913931 scopus 로고
    • Quantentheorie in hydrodynamischer Form
    • E. MADELUNG, Quantentheorie in hydrodynamischer Form, Z. Phys., 40 (1926), pp. 322-326.
    • (1926) Z. Phys , vol.40 , pp. 322-326
    • MADELUNG, E.1
  • 22
    • 0001300815 scopus 로고
    • A stationary Schrödinger-Poisson system arising from the modeling of electronic devices
    • F. NIER, A stationary Schrödinger-Poisson system arising from the modeling of electronic devices, Forum Math., 2 (1990), pp. 489-510.
    • (1990) Forum Math , vol.2 , pp. 489-510
    • NIER, F.1
  • 24
    • 0037116027 scopus 로고    scopus 로고
    • E. POLIZZI AND N. BEN ABDALLAH, Self-consistent three dimensional models for quantum ballistic transport in open systems, Phys. Rev. B, 66 (2002), pp. 245-301.
    • E. POLIZZI AND N. BEN ABDALLAH, Self-consistent three dimensional models for quantum ballistic transport in open systems, Phys. Rev. B, 66 (2002), pp. 245-301.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.