메뉴 건너뛰기




Volumn 43, Issue 5, 2011, Pages 2116-2149

Strong phase-space semiclassical asymptotics

Author keywords

(Smoothed) Wigner transform; Regularity of Wigner equation; Semiclassical limit in strong topology

Indexed keywords

TOPOLOGY;

EID: 81255169997     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/10078712X     Document Type: Article
Times cited : (11)

References (26)
  • 2
    • 41349085351 scopus 로고    scopus 로고
    • Exact equations for smoothed Wigner transforms and homogenization of wave propagation
    • A. Athanassoulis, Exact equations for smoothed Wigner transforms and homogenization of wave propagation, Appl. Comput. Harmon. Anal., 24 (2008), pp. 378-392.
    • (2008) Appl. Comput. Harmon. Anal. , vol.24 , pp. 378-392
    • Athanassoulis, A.1
  • 3
    • 81255186862 scopus 로고    scopus 로고
    • Smoothed Wigner transforms in the numerical simulation of semiclassical (high-frequency) wave propagation
    • A. Athanassoulis, Smoothed Wigner transforms in the numerical simulation of semiclassical (high-frequency) wave propagation, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 14 (2007), suppl. S2, pp. 247-252.
    • (2007) Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. , vol.14 , Issue.SUPPL. S2 , pp. 247-252
    • Athanassoulis, A.1
  • 4
    • 62249148742 scopus 로고    scopus 로고
    • Coarse-scale representations and smoothed Wigner transforms
    • A. Athanassoulis, N. J. Mauser, and T. Paul, Coarse-scale representations and smoothed Wigner transforms, J. Math. Pures Appl. (9), 91 (2008), pp. 296-338.
    • (2008) J. Math. Pures Appl. , vol.9 , Issue.91 , pp. 296-338
    • Athanassoulis, A.1    Mauser, N.J.2    Paul, T.3
  • 6
    • 0000980347 scopus 로고    scopus 로고
    • Long time semiclassical approximation of quantum flows: A proof of the ehrenfest time
    • D. Bambusi, S. Graffi, and T. Paul, Long time semiclassical approximation of quantum flows: A proof of the Ehrenfest time, Asymptot. Anal., 21 (1999), pp. 149-160. (Pubitemid 129565609)
    • (1999) Asymptotic Analysis , vol.21 , Issue.2 , pp. 149-160
    • Bambusi, D.1    Graffi, S.2    Paul, T.3
  • 7
    • 0036487116 scopus 로고    scopus 로고
    • Uniform semiclassical estimates for the propagation of quantum observables
    • A. Bouzouina and D. Robert, Uniform semiclassical estimates for the propagation of quantum observables, Duke Math. J., 111 (2002), pp. 223-252.
    • (2002) Duke Math.J. , vol.111 , pp. 223-252
    • Bouzouina, A.1    Robert, D.2
  • 9
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • R. DiPerna and P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98 (1989), pp. 511-547.
    • (1989) Invent. Math. , vol.98 , pp. 511-547
    • DiPerna, R.1    Lions, P.L.2
  • 10
    • 4644278519 scopus 로고    scopus 로고
    • Nonlinear Hartree equation as the mean field limit of weakly coupled fermions
    • DOI 10.1016/j.matpur.2004.03.006, PII S0021782404000492
    • A. Elgart, L. Erdós, B. Schlein, and H.-T. Yau, Nonlinear Hartree equation as the mean field limit of weakly coupled fermions, J. Math. Pures Appl. (9), 83 (2004), pp. 1241-1273. (Pubitemid 39274818)
    • (2004) Journal des Mathematiques Pures et Appliquees , vol.83 , Issue.10 , pp. 1241-1273
    • Elgart, A.1    Erdos, L.2    Schlein, B.3    Yau, H.-T.4
  • 11
    • 0034418177 scopus 로고    scopus 로고
    • Linear Boltzmann equation as the weak coupling limit of a random Schródinger equation
    • L. Erdós and H.-T. Yau, Linear Boltzmann equation as the weak coupling limit of a random Schródinger equation, Comm. Pure Appl. Math., 53 (2000), pp. 667-735.
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 667-735
    • Erdós, L.1    Yau, H.-T.2
  • 12
    • 33646865343 scopus 로고    scopus 로고
    • Semiclassical Wigner function and geometrical optics
    • S. Filippas and G. N. Makrakis, Semiclassical Wigner function and geometrical optics, Multiscale Model. Simul., 1 (2003), pp. 674-710.
    • (2003) Multiscale Model. Simul. , vol.1 , pp. 674-710
    • Filippas, S.1    Makrakis, G.N.2
  • 15
    • 0004615396 scopus 로고    scopus 로고
    • The interference structure of the Wigner distribution and related time-frequency signal representations
    • Elsevier, Amsterdam
    • F. Hlawatsch and P. Flandrin, The interference structure of the Wigner distribution and related time-frequency signal representations, in The Wigner Distribution, Elsevier, Amsterdam, 1997, pp. 59-133.
    • (1997) The Wigner Distribution , pp. 59-133
    • Hlawatsch, F.1    Flandrin, P.2
  • 16
    • 59149086364 scopus 로고    scopus 로고
    • Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics
    • S. Kube, C. Lasser, and M. Weber, Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics, J. Comput. Phys., 228 (2009), pp. 1947-1962.
    • (2009) J. Comput. Phys. , vol.228 , pp. 1947-1962
    • Kube, S.1    Lasser, C.2    Weber, M.3
  • 17
    • 77953817594 scopus 로고    scopus 로고
    • Computing expectation values for molecular quantum dynamics
    • C. Lasser and S. Róblitz, Computing expectation values for molecular quantum dynamics, SIAM J. Sci. Comput., 32 (2010), pp. 1465-1483.
    • (2010) SIAM J. J. Sci. Comput. , vol.32 , pp. 1465-1483
    • Lasser, C.1    Róblitz, S.2
  • 19
    • 84988209878 scopus 로고
    • On the equivalence of the Schródinger and quantum Liouville equations
    • P. A. Markowich, On the equivalence of the Schródinger and quantum Liouville equations, Math. Methods Appl. Sci., 11 (1989), pp. 459-469.
    • (1989) Math. Methods Appl. Sci. , vol.11 , pp. 459-469
    • Markowich, P.A.1
  • 20
    • 0000269855 scopus 로고
    • The classical limit of a self-consistent quantum Vlasov equation
    • P. A. Markowich and N. J. Mauser, The classical limit of a self-consistent quantum Vlasov equation, Math. Models Methods Appl. Sci., 3 (1993), pp. 109-124.
    • (1993) Math. Models Methods Appl. Sci. , vol.3 , pp. 109-124
    • Markowich, P.A.1    Mauser, N.J.2
  • 21
    • 36449006348 scopus 로고
    • A Wigner function approach to (semi)classical limits: Electrons in a periodic potential
    • P. A. Markowich, N. J. Mauser, and F. Poupaud, A Wigner function approach to (semi)classical limits: Electrons in a periodic potential, J. Math. Phys., 35 (1994), pp. 1066-1094.
    • (1994) J. Math. Phys. , vol.35 , pp. 1066-1094
    • Markowich, P.A.1    Mauser, N.J.2    F. Poupaud, N.J.3
  • 22
    • 0034148496 scopus 로고    scopus 로고
    • Refraction of high-frequency waves density by sharp interfaces and semiclassical measures at the boundary
    • L. Miller, Refraction of high-frequency waves density by sharp interfaces and semiclassical measures at the boundary, J. Math. Pures Appl. (9), 79 (2000), pp. 227-269.
    • (2000) J. Math. Pures Appl. , vol.9 , Issue.79 , pp. 227-269
    • Miller, L.1
  • 24
    • 81255183461 scopus 로고    scopus 로고
    • Échelles de temps pour l' Évolution quantique à petite constante de Planck S Éminaire X-EDP 2007-2008
    • T. Paul, Échelles de temps pour l' Évolution quantique à petite constante de Planck, S Éminaire X-EDP 2007-2008, Publications de l' École Polytechnique, 2008.
    • (2008) Publications de l' École Polytechnique
    • Paul, T.1
  • 25
    • 33744762804 scopus 로고    scopus 로고
    • Semiclassical expansion of Wigner functions
    • M. Pulvirenti, Semiclassical expansion of Wigner functions, J. Math. Phys., 47 (2006), 052103.
    • (2006) J. Math. Phys. , vol.47 , pp. 052103
    • Pulvirenti, M.1
  • 26
    • 0030388835 scopus 로고    scopus 로고
    • Transport equations for elastic and other waves in random media
    • DOI 10.1016/S0165-2125(96)00021-2, PII S0165212596000212
    • L. Ryzhik, G. Papanicolaou, and J. B. Keller, Transport equations for elastic and other waves in random media, Wave Motion, 24 (1996), pp. 327-370. (Pubitemid 126324199)
    • (1996) Wave Motion , vol.24 , Issue.4 , pp. 327-370
    • Ryzhik, L.1    Papanicolaou, G.2    Keller, J.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.