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Volumn 124, Issue 2-4, 2006, Pages 951-996

Some considerations on the derivation of the nonlinear quantum boltzmann equation II: The low density regime

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EID: 33751044122     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-9010-x     Document Type: Article
Times cited : (22)

References (51)
  • 2
    • 2942646600 scopus 로고    scopus 로고
    • Some considerations on the derivation of the nonlinear quantum boltzmann equation
    • D. Benedetto, F. Castella, R. Esposito, and M. Pulvirenti, Some considerations on the derivation of the nonlinear quantum boltzmann equation. J. Stat. Phys. 116(1/4):381-410 (2004).
    • (2004) J. Stat. Phys. , vol.116 , Issue.1-4 , pp. 381-410
    • Benedetto, D.1    Castella, F.2    Esposito, R.3    Pulvirenti, M.4
  • 4
    • 0003930334 scopus 로고
    • Texts and Monographs in Physics, Springer-Verlag
    • A. Bohm, Quantum Mechanics, Texts and Monographs in Physics, Springer-Verlag, 1979).
    • (1979) Quantum Mechanics
    • Bohm, A.1
  • 5
    • 0003342752 scopus 로고
    • On the Boltzmann equation for the Lorentz gas
    • C. Boldrighini, L. A. Bunimovich, and Ya. Sinai, On the Boltzmann equation for the Lorentz gas. J. Stat. Phys. 32(3):477-501 (1983).
    • (1983) J. Stat. Phys. , vol.32 , Issue.3 , pp. 477-501
    • Boldrighini, C.1    Bunimovich, L.A.2    Sinai, Ya.3
  • 6
    • 0035535173 scopus 로고    scopus 로고
    • From the von Neumann equation to the Quantum Boltzmann equation in a deterministic framework
    • F. Castella, From the von Neumann equation to the Quantum Boltzmann equation in a deterministic framework. J. Stat. Phys. 104(1/2):387-447 (2001).
    • (2001) J. Stat. Phys. , vol.104 , Issue.1-2 , pp. 387-447
    • Castella, F.1
  • 7
    • 0036102715 scopus 로고    scopus 로고
    • From the von Neumann equation to the Quantum Boltzmann equation II: Identifying the Born series
    • F. Castella, From the von Neumann equation to the Quantum Boltzmann equation II: identifying the Born series. J. Stat. Phys. 106(5/6):1197-1220 (2002).
    • (2002) J. Stat. Phys. , vol.106 , Issue.5-6 , pp. 1197-1220
    • Castella, F.1
  • 8
    • 84881086254 scopus 로고    scopus 로고
    • Non-derivation of the quantum Boltzmann equation from the periodic Schrödinger equation
    • F. Castella and A. Plagne, Non-derivation of the quantum Boltzmann equation from the periodic Schrödinger equation. Indiana Univ. Math. J. 51(4):963-1016 (2002).
    • (2002) Indiana Univ. Math. J. , vol.51 , Issue.4 , pp. 963-1016
    • Castella, F.1    Plagne, A.2
  • 14
    • 0035839391 scopus 로고    scopus 로고
    • On the generalized golden rule for transition probabilities
    • M. Combescot, On the generalized golden rule for transition probabilities. Phys. A: Math. Gene. 34(31):6087-6104 (2001).
    • (2001) Phys. A: Math. Gene. , vol.34 , Issue.31 , pp. 6087-6104
    • Combescot, M.1
  • 15
    • 0041450241 scopus 로고
    • The low density limit for an N-level system interacting with a free Bose or Fermi gas
    • R. Dümcke, The low density limit for an N-level system interacting with a free Bose or Fermi gas. Comm. Math. Phys. 97(3):331-359 (1985).
    • (1985) Comm. Math. Phys. , vol.97 , Issue.3 , pp. 331-359
    • Dümcke, R.1
  • 16
    • 0000242636 scopus 로고
    • Asymptotic motion of a classical particle in a random potential in two dimensions: The Landau model
    • D. Dürr, S. Goldstein, and J. Lebowitz, Asymptotic motion of a classical particle in a random potential in two dimensions: the Landau model. Comm. Math. Phys. 113:209-230 (1987).
    • (1987) Comm. Math. Phys. , vol.113 , pp. 209-230
    • Dürr, D.1    Goldstein, S.2    Lebowitz, J.3
  • 20
    • 0004265556 scopus 로고    scopus 로고
    • Amer. Math. Soc., Providence, RI
    • Contemp. Math., 211, Amer. Math. Soc., Providence, RI (1998).
    • (1998) Contemp. Math. , vol.211
  • 21
    • 0034418177 scopus 로고    scopus 로고
    • Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
    • L. Erdös and H. T. Yau, Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation, Comm. Pure Appl. Math. 53(6):667-735 (2000).
    • (2000) Comm. Pure Appl. Math. , vol.53 , Issue.6 , pp. 667-735
    • Erdös, L.1    Yau, H.T.2
  • 22
    • 0033451117 scopus 로고    scopus 로고
    • The Boltzmann equation for a one-dimensional quantum lorentz gas
    • and Erratum: "The Boltzmann equation for a one-dimensional quantum Lorentz gas," Comm. Math. Phys. 214(2):493-494 (2000)
    • R. Esposito, M. Pulvirenti, and A. Teta, The Boltzmann Equation for a One-Dimensional Quantum Lorentz gas, Comm. Math. Phys. 204(3):619-649 (1999), and Erratum: "The Boltzmann equation for a one-dimensional quantum Lorentz gas," Comm. Math. Phys. 214(2):493-494 (2000).
    • (1999) Comm. Math. Phys. , vol.204 , Issue.3 , pp. 619-649
    • Esposito, R.1    Pulvirenti, M.2    Teta, A.3
  • 23
    • 0031693941 scopus 로고    scopus 로고
    • Theory of electron transport in small semiconductor devices using the Pauli master equations
    • M. V. Fischetti, Theory of electron transport in small semiconductor devices using the Pauli master equations. J. Appl. Phys. 83(1):270-291 (1998).
    • (1998) J. Appl. Phys. , vol.83 , Issue.1 , pp. 270-291
    • Fischetti, M.V.1
  • 25
    • 0000249735 scopus 로고
    • Divergences and approach to equilibrium in the Lorenz and the wind-tree models
    • Divergences and approach to equilibrium in the Lorenz and the wind-tree models. Phys. Rev. 185:308-322 (1969).
    • (1969) Phys. Rev. , vol.185 , pp. 308-322
  • 26
    • 0003580191 scopus 로고    scopus 로고
    • See also the book, Appendix A2 to Ch. 1, Springer-Verlag
    • See also the book Statistical Mechanics, Appendix A2 to Ch. 1, Springer-Verlag (1999).
    • (1999) Statistical Mechanics
  • 27
    • 0031138950 scopus 로고    scopus 로고
    • Fermi gas on a lattice in the van Hove limit
    • T. G. Ho and L. J. Landau, Fermi gas on a lattice in the van Hove limit. J. Stat. Phys. 87(3-4):821-845 (1997).
    • (1997) J. Stat. Phys. , vol.87 , Issue.3-4 , pp. 821-845
    • Ho, T.G.1    Landau, L.J.2
  • 28
    • 0000111115 scopus 로고
    • On the weak coupling limit for a Fermi gas in a random potential
    • T. G. Ho, L. J. Landau, and A. J. Wilkins, On the weak coupling limit for a Fermi gas in a random potential. Rev. Math. Phys. 5(2):209-298 (1993).
    • (1993) Rev. Math. Phys. , vol.5 , Issue.2 , pp. 209-298
    • Ho, T.G.1    Landau, L.J.2    Wilkins, A.J.3
  • 29
    • 0040399380 scopus 로고
    • Derivation of the Boltzmann equation for a Fermi gas
    • N. M. Hugenholtz, Derivation of the Boltzmann equation for a Fermi gas. J. Stat. Phys. 32(2):231-254 (1983).
    • (1983) J. Stat. Phys. , vol.32 , Issue.2 , pp. 231-254
    • Hugenholtz, N.M.1
  • 30
    • 0001467016 scopus 로고
    • Global validity of the Boltzmann equation for a two dimensional rare gas in vacuum
    • Erratum and improved result. Comm. Math. Phys. 121:143-146 (1989)
    • R. Illner and M. Pulvirenti, Global Validity of the Boltzmann equation for a two dimensional rare gas in vacuum. Comm. Math. Phys. 105:189-203 (1986). Erratum and improved result. Comm. Math. Phys. 121:143-146 (1989).
    • (1986) Comm. Math. Phys. , vol.105 , pp. 189-203
    • Illner, R.1    Pulvirenti, M.2
  • 31
    • 0030388835 scopus 로고    scopus 로고
    • Transport equations for elastic and other waves in random media
    • J. B. Keller, G. Papanicolaou, and L. Ryzhik, Transport equations for elastic and other waves in random media. Wave Motion 24(4):327-370 (1996).
    • (1996) Wave Motion , vol.24 , Issue.4 , pp. 327-370
    • Keller, J.B.1    Papanicolaou, G.2    Ryzhik, L.3
  • 35
    • 0001518823 scopus 로고
    • Time evolution of large classical systems
    • E. J. Moser ed., Springer-Verlag
    • O. Lanford III, Time evolution of large classical systems. Lecture Notes in Physics 38:1-111, E. J. Moser ed., Springer-Verlag (1975).
    • (1975) Lecture Notes in Physics , vol.38 , pp. 1-111
    • Lanford III, O.1
  • 36
    • 21844517262 scopus 로고
    • Observation of quantum particles on a large space-time scale
    • L. J. Landau, Observation of Quantum Particles on a Large Space-Time Scale. J. Stat. Phys. 77(1-2):259-309 (1994).
    • (1994) J. Stat. Phys. , vol.77 , Issue.1-2 , pp. 259-309
    • Landau, L.J.1
  • 38
    • 21844502570 scopus 로고
    • Asymptotic analysis of a scaled Wigner equation and Quantum scattering
    • F. Nier, Asymptotic Analysis of a scaled Wigner equation and Quantum Scattering. Transp. Theor. Stat. Phys. 24(4 et 5):591-629 (1995).
    • (1995) Transp. Theor. Stat. Phys. , vol.24 , Issue.4-5 , pp. 591-629
    • Nier, F.1
  • 39
    • 0001485147 scopus 로고    scopus 로고
    • A semi-classical picture of quantum scattering
    • Sér., t. 29
    • F. Nier, A semi-classical picture of quantum scattering.Ann. Sci. Ec. Norm. Sup. 4(Sér., t. 29):149-183 (1996).
    • (1996) Ann. Sci. Ec. Norm. Sup. , vol.4 , pp. 149-183
    • Nier, F.1
  • 44
    • 0001200202 scopus 로고
    • Derivation of the transport equation for electrons moving through random impurities
    • H. Spohn, Derivation of the transport equation for electrons moving through random impurities. J. Stat. Phys. 17(6):385-412 (1977).
    • (1977) J. Stat. Phys. , vol.17 , Issue.6 , pp. 385-412
    • Spohn, H.1
  • 46
    • 35949020007 scopus 로고
    • Kinetic equations from Hamiltonian dynamics: Markovian limits
    • H. Spohn, Kinetic equations from Hamiltonian dynamics: Markovian limits, Rev. Modern Phys. 52(3):569-615 (1980).
    • (1980) Rev. Modern Phys. , vol.52 , Issue.3 , pp. 569-615
    • Spohn, H.1
  • 47
    • 4344683720 scopus 로고
    • Quantum kinetic equations
    • On Three Levels: Micro-Meso and Macro Approaches in Physics, M. Fannes, C. Maes, A. Verbeure eds, Nato ASI Series B
    • H. Spohn, Quantum Kinetic Equations, in On Three Levels: Micro-Meso and Macro Approaches in Physics, M. Fannes, C. Maes, A. Verbeure eds, Nato ASI Series B: Physics, V.324:1-10 (1994).
    • (1994) Physics, V , vol.324 , pp. 1-10
    • Spohn, H.1
  • 51
    • 0004098699 scopus 로고
    • P.H.E. Meijer ed., (Gordon and Breach, New-York)
    • R. Zwanzig, Quantum Statistical Mechanics, P.H.E. Meijer ed., (Gordon and Breach, New-York, 1966).
    • (1966) Quantum Statistical Mechanics
    • Zwanzig, R.1


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