Une approche alternative de l’évolution adiabatique des résonances de forme 1D .

Francis Nier[1]

  • [1] IRMAR, UMR - CNRS 6625 Université Rennes 1 Campus de Beaulieu 35042 Rennes Cedex, France & CMAP, UMR - CNRS 7641 École Polytechnique 91128 Palaiseau Cedex

Séminaire Équations aux dérivées partielles (2009-2010)

  • page 1-9

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Nier, Francis. "Une approche alternative de l’évolution adiabatique des résonances de forme 1D .." Séminaire Équations aux dérivées partielles (2009-2010): 1-9. <http://eudml.org/doc/251181>.

@article{Nier2009-2010,
affiliation = {IRMAR, UMR - CNRS 6625 Université Rennes 1 Campus de Beaulieu 35042 Rennes Cedex, France & CMAP, UMR - CNRS 7641 École Polytechnique 91128 Palaiseau Cedex},
author = {Nier, Francis},
journal = {Séminaire Équations aux dérivées partielles},
language = {fre},
pages = {1-9},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Une approche alternative de l’évolution adiabatique des résonances de forme 1D .},
url = {http://eudml.org/doc/251181},
year = {2009-2010},
}

TY - JOUR
AU - Nier, Francis
TI - Une approche alternative de l’évolution adiabatique des résonances de forme 1D .
JO - Séminaire Équations aux dérivées partielles
PY - 2009-2010
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 9
LA - fre
UR - http://eudml.org/doc/251181
ER -

References

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  1. S. Albeverio et K. Pankrashkin. A remark on Krein’s resolvent formula and boundary conditions. J. Phys. A, 38(22) :4859–4864, 2005. Zbl1071.47003MR2148628
  2. W.K. Abou Salem et J. Fröhlich. Adiabatic theorems for quantum resonances. Comm. Math. Phys., 273(3) :651–675, 2007. Zbl1153.81010MR2318861
  3. J. Aguilar et J. M. Combes. A class of analytic perturbations for one-body Schrödinger Hamiltonians. Comm. Math. Phys., 22 :269–279, 1971. Zbl0219.47011MR345551
  4. J. E. Avron, R. Seiler et L. G. Yaffe. Adiabatic theorems and applications to the quantum Hall effect. Comm. Math. Phys., 110(1) :33–49, 1987. Zbl0626.58033MR885569
  5. E. Balslev et J. M. Combes. Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions. Comm. Math. Phys., 22 :280–294, 1971. Zbl0219.47005MR345552
  6. N. Ben Abdallah, P. Degond, and P.A. Markowich. On a one-dimensional Schrödinger-Poisson scattering model. Z. Angew. Math. Phys. Zbl0885.34067
  7. N. Ben Abdallah. On a multidimensional Schrödinger-Poisson scattering model for semiconductors. J. Math. Phys., 41(7) :4241–4261, 2000. Zbl0977.82052MR1765586
  8. V. Bonnaillie-Noël, A. Faraj et F. Nier. Simulation of resonant tunneling heterostructures : numerical comparison of a complete Schrödinger-Poisson system and a reduced nonlinear model. J. Comput. Elec., 8(1) :11–18, 2009. 
  9. V. Bonnaillie-Noël, F. Nier et Y. Patel. Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures. J. Comput. Phys., 219(2) :644–670, 2006. Zbl1189.82129MR2274952
  10. V. Bonnaillie-Noël, F. Nier et Y. Patel. Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells. I. Ann. Inst. H. Poincaré Anal. Non Linéaire, 25(5) :937–968, 2008. Zbl1149.82349MR2457818
  11. V. Bonnaillie-Noël, F. Nier et Y. Patel. Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells. II. J. Math. Soc. Japan, 61(1) :65–106, 2009. Zbl1157.82046MR2272872
  12. M. Büttiker, Y. Imry, R. Landauer et S. Pinhas. Generalized manychannel conductance formula with application to small rings. Phys. Rev. B31 (1985) pp. 6207–6215. 
  13. H. L. Cycon, R. G. Froese, W. Kirsch et B. Simon. Schrödinger operators with application to quantum mechanics and global geometry. Texts and Monographs in Physics. Springer-Verlag, Berlin, study edition, 1987. Zbl0619.47005MR883643
  14. A. Faraj, A. Mantile et F. Nier. Adiabatic evolution of 1D shape resonances : an artificial interface conditions approach. Prépublication de l’IRMAR janvier 2010, hal-00448868. Zbl1223.35125MR2782724
  15. B. Helffer et J. Sjöstrand. Résonances en limite semi-classique. Number 24-25 in Mém. Soc. Math. France (N.S.). 1986. Zbl0631.35075MR871788
  16. P. D. Hislop et I. M. Sigal. Semiclassical theory of shape resonances in quantum mechanics, volume 78(399) of Mem. Amer. Math. Soc. 1989. Zbl0704.35115MR989524
  17. G. Jona-Lasinio, C. Presilla et J. Sjöstrand. On Schrödinger equations with concentrated nonlinearities. Ann. Physics, 240(1) :1–21, 1995. Zbl0820.34050MR1329589
  18. A. Joye et C.E. Pfister. Exponential estimates in adiabatic quantum evolution. In XIIth International Congress of Mathematical Physics (ICMP ’97) (Brisbane), pages 309–315. Int. Press, Cambridge, MA, 1999. Zbl1253.81060MR1697294
  19. A. Joye. General adiabatic evolution with a gap condition. Comm. Math. Phys., 275(1) :139–162, 2007. Zbl1176.47032MR2335771
  20. T. Kato. Perturbation theory for linear operators. Second edition. Grundlehren der Mathematischen Wissenschaften, Band 132. Springer-Verlag (1976). Zbl0342.47009MR407617
  21. M. Klein et J. Rama. Almost exponential decay of quantum resonance states and Paley-Wiener type estimates in Gevrey spaces. preprint, mp-arc 09-64, 2009. Zbl1208.81092MR2671569
  22. M. Klein, J. Rama et R. Wüst. Time evolution of quantum resonance states. Asymptot. Anal., 51(1) :1–16, 2007. Zbl1216.81065MR2294102
  23. R. Landauer. Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J. Res. Develop.1 (1957) pp. 223–231. MR90369
  24. G. Nenciu. Linear adiabatic theory. Exponential estimates. Comm. Math. Phys., 152(3) :479–496, 1993. Zbl0768.34038MR1213299
  25. G. Nenciu et G. Rasche. On the adiabatic theorem for nonselfadjoint Hamiltonians. J. Phys. A, 25(21) :5741–5751, 1992. MR1192026
  26. F. Nier. The dynamics of some quantum open systems with short-range nonlinearities. Nonlinearity, 11(4) :1127–1172, 1998. Zbl0909.34052MR1632618
  27. F. Nier. Accurate WKB approximation for a 1D problem with low regularity. Serdica Math. J., 34(1) :113–126, 2008. Zbl1199.81023MR2414416
  28. K. Pankrashkin. Resolvents of self-adjoint extensions with mixed boundary conditions. Rep. Math. Phys., 58(2) :207–221, 2006. Zbl1143.47017MR2281536
  29. G. Perelman. Evolution of adiabatically perturbed resonant states. Asymptot. Anal., 22(3-4) :177–203, 2000. Zbl1075.81521MR1753764
  30. C. Presilla et J. Sjöstrand. Transport properties in resonant tunneling heterostructures. J. Math. Phys., 37(10) :4816–4844, 1996. Zbl0868.35112MR1411610
  31. B. Simon. Resonances and complex scaling : a rigorous overview. Int.J. Quantum Chem., 14(4) :529–542, 1978. 
  32. B. Simon. The definition of molecular resonance curves by the method of exterior complex scaling. Phys. Lett., 71A(2,3) :211–214, 1979. 
  33. J. Sjöstrand. Projecteurs adiabatiques du point de vue pseudodifférentiel. C. R. Acad. Sci. Paris Sér. I Math., 317(2) :217–220, 1993. Zbl0783.35087MR1231425
  34. J. Sjöstrand et M. Zworski. Complex scaling and the distribution of scattering poles. J. Amer. Math. Soc., 4(4) :729–769, 1991. Zbl0752.35046MR1115789
  35. E. Skibsted. Truncated Gamow functions, α -decay and the exponential law. Comm. Math. Phys., 104(4) :591–604, 1986. Zbl0594.58062MR841672
  36. E. Skibsted. Truncated Gamow functions and the exponential decay law. Ann. Inst. H. Poincaré Phys. Théor., 46(2) :131–153, 1987. Zbl0618.58029MR887144
  37. E. Skibsted. On the evolution of resonance states. J. Math. Anal. Appl., 141(1) :27–48, 1989. Zbl0688.47006MR1004582
  38. A. Soffer et M. I. Weinstein. Time dependent resonance theory. Geom. Funct. Anal., 8(6) :1086–1128, 1998. Zbl0917.35023MR1664792

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