Higher order terms for the quantum evolution of a Wick observable within the Hepp method

• Sébastien Breteaux ^[1]
  1. [1] Universite de Rennes campus de Beaulieu
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 14, Nº. 2, 2012, págs. 91-109
• Idioma: inglés
• DOI: 10.4067/S0719-06462012000200006
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• Referencias bibliográficas
  • Ammari, Z,Nier, F. (2008). Mean field limit for bosons and infinite dimensional phase-space analysis. Ann. Henri Poincare. 9. 1503-1574
  • Baez, J. C,Segal, I. E,Zhou, Z.-F. (1992). Introduction to algebraic and constructive quantum feld theory. Princeton University Press. Princeton,...
  • Berezin, F. A. (1966). The method of second quantization. Academic Press. New York.
  • Berezin, F. A,Shubin, M. A. (1991). The Schrodinger equation. Kluwer Academic Publishers Group. Dordrecht.
  • Bruneau, L,Dereziński, J. (2007). Bogoliubov Hamiltonians and one-parameter groups of Bogoli-ubov transformations. J. Math. Phys. 48. 02210124
  • Combescure, M,Ralston, J,Robert, D. (1999). A proof of the Gutzwiller semiclassical trace formula using coherent states decomposition. Comm....
  • Combescure, M,Robert, D. (1997). Semiclassical spreading of quantum wave packets and applications near unstable fixed points of the classical...
  • Combescure, M,Robert, D. (2006). Quadratic quantum Hamiltonians revisited. Cubo. 8. 61-86
  • Cycon, H. L,Froese, R. G,Kirsch, W,Simon, B. (1987). Schrodinger operators: with application to quantum mechanics and global geometry. Springer-Verlag....
  • Faris, W. G,Lavine, R. B. Commutators and self-adjointness of Hamiltonian operators.
  • Fröhlich, J,Graffi, S,Schwarz, S. (2007). Mean-field- and classical limit of many-body Schrodinger dynamics for bosons. Comm. Math. Phys....
  • Ginibre, J,Velo, G. (1979). The classical field limit of scattering theory for nonrelativistic many-boson systems. I. Comm. Math. Phys. 66....
  • Ginibre, J,Velo, G. (1979). The classical field limit of scattering theory for nonrelativistic many-boson systems. II. Comm. Math. Phys. 68....
  • Ginibre, J,Velo, G. (1980). The classical field limit of nonrelativistic bosons: I. Borel summability for bounded potentials. Ann. Physics....
  • Ginibre, J,Velo, G. (1980). The classical field limit of nonrelativistic bosons. 334. II. Asymptotic expansions for general potentials.
  • Grillakis, M. G,Machedon, M,Margetis, D. (2010). Second-order corrections to mean field evolution of weakly interacting bosons. I. Comm. Math....
  • Hagedorn, G. A. (1998). Raising and lowering operators for semiclassical wave packets. Ann. Physics. 269. 77-104
  • Hagedorn, G. A,Joye, A. (1999). Semiclassical dynamics with exponentially small error estimates. Comm. Math. Phys. 207. 439-465
  • Hagedorn, G. A,Joye, A. (2000). Exponentially accurate semiclassical dynamics: propagation, localization, Ehrenfest times, scattering, and...
  • Hepp, K. (1974). Phys: The classical limit for quantum mechanical correlation functions. Comm.Math. 35. 265-277
  • Hille, E. (1969). Lectures on ordinary differential equations. Addison-Wesley Publ. Co. London.
  • Hörmander, L. (1995). Symplectic classifcation of quadratic forms, and general Mehler formulas. Math.Z. 219. 413-449
  • Kato, T. (1970). Linear evolution equations of "hyperbolic". J. Fac. Sci. Univ. Tokyo Sect. I.
  • Kisyński, J. (1964). Sur les opńerateurs de Green des problmes de Cauchy abstraits. Studia Math. 23. 285-328
  • Paul, T,Uribe, A. (1993). A construction of quasi-modes using coherent states. Ann. Inst. H. Poincare Phys. Theor. 59. 357-381
  • Polley, L,Reents, G,Streater, R. F. (1981). Some covariant representations of massless boson fields. J. Phys. A. 14. 2479-2488
  • Reed, M,Simon, B. (1975). Methods of modern mathematical physics. II. Fourier analysis: self-adjointness. Academic Press [ Harcourt Brace...
  • Rodnianski, I,Schlein, B. (2009). Quantum fuctuations and rate of convergence towards mean field dynamics. Comm. Math. Phys. 291. 31-61
  • Shale, D. (1962). Linear symmetries of free boson fields. Trans. Amer. Math. Soc. 103. 149-167