메뉴 건너뛰기




Volumn 5, Issue 3, 2008, Pages 569-587

The Vlasov-Poisson equations as the semiclassical limit of the Schrödinger-Poisson equations: A numerical study

Author keywords

Multi valued solution; Schr dinger Poisson system; Semiclassical limit; Vlasov Poisson system

Indexed keywords


EID: 56349132748     PISSN: 02198916     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021989160800160X     Document Type: Article
Times cited : (5)

References (18)
  • 1
    • 1842531889 scopus 로고    scopus 로고
    • Numerical study of time-splitting spectral discretizations of nonlinear Schrodinger equations in the semi-clasical regimes
    • in electronic
    • W. Z. Bao, S. Jin and P. A. Markowich, Numerical study of time-splitting spectral discretizations of nonlinear Schrodinger equations in the semi-clasical regimes, SIAM J. Sci. Comput. 25 (2003) 27-64 (in electronic).
    • (2003) SIAM J. Sci. Comput , vol.25 , pp. 27-64
    • Bao, W.Z.1    Jin, S.2    Markowich, P.A.3
  • 2
    • 0037138007 scopus 로고    scopus 로고
    • On time-spliting spectral approximations for the Schrödinger equation in the semiclassical regime
    • W. Z. Bao, S. Jin and P. A. Markowich, On time-spliting spectral approximations for the Schrödinger equation in the semiclassical regime, J. Comput. Phys. 175 (2002) 487-524.
    • (2002) J. Comput. Phys , vol.175 , pp. 487-524
    • Bao, W.Z.1    Jin, S.2    Markowich, P.A.3
  • 3
    • 0442331533 scopus 로고    scopus 로고
    • Numerical approximations of pressureless and isothermal gas dynamics
    • F. Bouchut, S. Jin and X. T. Li, Numerical approximations of pressureless and isothermal gas dynamics, SIAM J. Num. Anal. 41 (2003) 135-158.
    • (2003) SIAM J. Num. Anal , vol.41 , pp. 135-158
    • Bouchut, F.1    Jin, S.2    Li, X.T.3
  • 4
    • 0021380684 scopus 로고
    • Particle methods for the 1D Vlasov-Poisson equations
    • G. H. Cottet and P. A. Raviart, Particle methods for the 1D Vlasov-Poisson equations, SIAM J. Num. Anal. 21 (1984) 52-76.
    • (1984) SIAM J. Num. Anal , vol.21 , pp. 52-76
    • Cottet, G.H.1    Raviart, P.A.2
  • 5
    • 18344388470 scopus 로고    scopus 로고
    • Discretization of Dirac delta functions in level set methods
    • B. Engquist, A. K. Tornberg and R. Tsai, Discretization of Dirac delta functions in level set methods, J. Comput. Phys. 207(1) (2005) 28-51.
    • (2005) J. Comput. Phys , vol.207 , Issue.1 , pp. 28-51
    • Engquist, B.1    Tornberg, A.K.2    Tsai, R.3
  • 7
    • 0442275913 scopus 로고    scopus 로고
    • On two moment systems for computing multiphase semiclassical limits of the Schrödinger equation
    • L. Gosse, S. Jin and X. T. Li, On two moment systems for computing multiphase semiclassical limits of the Schrödinger equation, Math. Model Meth. Appl. Sci. 13(12) (2003) 1689-1723.
    • (2003) Math. Model Meth. Appl. Sci , vol.13 , Issue.12 , pp. 1689-1723
    • Gosse, L.1    Jin, S.2    Li, X.T.3
  • 8
    • 25444466220 scopus 로고    scopus 로고
    • Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice C IIII. From ab initio models to WKB for Schrödinger-Poisson
    • L. Gosse and N. J. Mauser, Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice C IIII. From ab initio models to WKB for Schrödinger-Poisson, J. Comput. Phys. 211 (2006) 326-346.
    • (2006) J. Comput. Phys , vol.211 , pp. 326-346
    • Gosse, L.1    Mauser, N.J.2
  • 9
    • 0442331531 scopus 로고    scopus 로고
    • Multi-phase computations of the semiclassical limit of the Schrödinger equation and related problems: Whitham vs Wigner
    • S. Jin and X. T. Li, Multi-phase computations of the semiclassical limit of the Schrödinger equation and related problems: Whitham vs Wigner, Phys. D 182 (2003) 46-85.
    • (2003) Phys. D , vol.182 , pp. 46-85
    • Jin, S.1    Li, X.T.2
  • 10
    • 37649029921 scopus 로고    scopus 로고
    • An Eulerian method for computing multi-valued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons
    • X. T. Li, J. G. Wohlbier, S. Jin and J. H. Booske, An Eulerian method for computing multi-valued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons, Phys. Rev. E 70 (2004) 016502.
    • (2004) Phys. Rev. E , vol.70 , pp. 016502
    • Li, X.T.1    Wohlbier, J.G.2    Jin, S.3    Booske, J.H.4
  • 12
    • 85066352204 scopus 로고    scopus 로고
    • A field space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations
    • to appear in
    • H. Liu and Z. M. Wang, A field space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations, to appear in J. Comput. Phys.
    • J. Comput. Phys
    • Liu, H.1    Wang, Z.M.2
  • 13
    • 0001599323 scopus 로고
    • Concentrations in the one-dimensional Vlasov-Poisson equations: Temporal development and non-unique weak solutions in the single component case
    • A. J. Majda, G. Majda and Y. X. Zheng, Concentrations in the one-dimensional Vlasov-Poisson equations: Temporal development and non-unique weak solutions in the single component case, Phys. D 74 (1994) 268-300.
    • (1994) Phys. D , vol.74 , pp. 268-300
    • Majda, A.J.1    Majda, G.2    Zheng, Y.X.3
  • 14
    • 0000269855 scopus 로고
    • The classical limit of a self-consistent quantum-Vlasov equation in 3D
    • P. A. Markowich and N. J. Mauser, The classical limit of a self-consistent quantum-Vlasov equation in 3D, Math. Models Meth. Appl. Sci. 3(1) (1993) 109-124.
    • (1993) Math. Models Meth. Appl. Sci , vol.3 , Issue.1 , pp. 109-124
    • Markowich, P.A.1    Mauser, N.J.2
  • 15
    • 84887251437 scopus 로고    scopus 로고
    • Wigner functions vs. WKB methods in multivalued geometrical optics
    • C. Sparber, P. A. Markowich and N. J. Mauser, Wigner functions vs. WKB methods in multivalued geometrical optics, Asympt. Anal. 33 (2003) 153-187.
    • (2003) Asympt. Anal , vol.33 , pp. 153-187
    • Sparber, C.1    Markowich, P.A.2    Mauser, N.J.3
  • 16
    • 33745014742 scopus 로고
    • On the quantum correction for thermodynamic equilibrium
    • E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40 (1932) 742-759.
    • (1932) Phys. Rev , vol.40 , pp. 742-759
    • Wigner, E.1
  • 17
    • 0036100942 scopus 로고    scopus 로고
    • The limit from the Schrödinger-Poisson to the Vlasov-Poisson equations with general data in one dimension
    • P. Zhang, Y. X. Zheng and N. J. Mauser, The limit from the Schrödinger-Poisson to the Vlasov-Poisson equations with general data in one dimension, Commun. Pure Appl. Math. LV (2002) 0582-0632.
    • (2002) Commun. Pure Appl. Math , vol.55 , pp. 0582-0632
    • Zhang, P.1    Zheng, Y.X.2    Mauser, N.J.3
  • 18
    • 84990610649 scopus 로고
    • Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data
    • Y. X. Zheng and A. Majda, Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data, Commun. Pure Appl. Math. XLVII (1994) 1365-1401.
    • (1994) Commun. Pure Appl. Math , vol.47 , pp. 1365-1401
    • Zheng, Y.X.1    Majda, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.