@article{SEDP_2003-2004____A11_0, author = {Dimassi, Mouez and Petkov, Vesselin}, title = {Semiclassical {Resonances} and trace formulae for non-semi-bounded {Hamiltonians}}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:11}, pages = {1--12}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2003-2004}, mrnumber = {2117043}, language = {en}, url = {http://www.numdam.org/item/SEDP_2003-2004____A11_0/} }
TY - JOUR AU - Dimassi, Mouez AU - Petkov, Vesselin TI - Semiclassical Resonances and trace formulae for non-semi-bounded Hamiltonians JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:11 PY - 2003-2004 SP - 1 EP - 12 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2003-2004____A11_0/ LA - en ID - SEDP_2003-2004____A11_0 ER -
%0 Journal Article %A Dimassi, Mouez %A Petkov, Vesselin %T Semiclassical Resonances and trace formulae for non-semi-bounded Hamiltonians %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:11 %D 2003-2004 %P 1-12 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2003-2004____A11_0/ %G en %F SEDP_2003-2004____A11_0
Dimassi, Mouez; Petkov, Vesselin. Semiclassical Resonances and trace formulae for non-semi-bounded Hamiltonians. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2003-2004), Exposé no. 11, 12 p. http://www.numdam.org/item/SEDP_2003-2004____A11_0/
[1] J. Avron, I. Herbst and B. Simon, Schrödinger operators with magnetic fields. I. General interactions, Duke Math. J. 45 (1978), 847-883. | MR | Zbl
[2] J. Avron, I. W. Herbst, Spectral and scattering theory of Schrödinger operators related to the Stark effect, Commun. Math. Phys. 52 (1977), 239-254. | MR | Zbl
[3] E. Bardos, J-C. Guillot and J. Ralston, La relation de Poisson pour l’équation des ondes dans un ouvert non-borné. Commun. PDE. 7, 905–958 (1982). | Zbl
[4] J.-F. Bony, Résonances dans des domaines de taille , Inter. Math. Res. Not. 16 (2001), 817-847. | MR | Zbl
[5] J.-F. Bony, Minoration du nombre de résonances engendrées par une trajectoire fermée, Commun. PDE. 27 (2002), 1021-1078. | MR | Zbl
[6] V. Bruneau, V. Petkov, Meromorphic continuation of the spectral shift function, Duke Math. J. 116 (2003), 389-430. | MR | Zbl
[7] V. Bruneau, V. Petkov, Eigenvalues of the reference operator and semiclassical resonances, J. Funct. Anal. 202 (2003), 571- 590. | MR | Zbl
[8] M. Dimassi, Développements asymptotiques de l’opérateur de Schrödinger avec champ magnétique fort, Commun. PDE. 26 (2001), 596-627. | Zbl
[9] M. Dimassi, Spectral shift function and resonances for perturbations of periodic Schrödinger operators, to appear in J. Funct. Anal. | MR | Zbl
[10] M. Dimassi and J. Sjöstrand, Spectral asymptotics in the semi-classical limit, London Mathematical Society Lecture Note Series, 268, Cambridge University Press, Cambridge, 1999. xii+227. | MR | Zbl
[11] M. Dimassi and V. Petkov, Spectral shift function and resonances for non semi-bounded and Stark Hamiltonians, Journal Math. Pures et Appl. 82 (2003), 1303-1342. | MR | Zbl
[12] M. Dimassi and V. Petkov, Resonances for magnetic Hamiltonians in two dimensional case, Preprint, 2004 (mp-arc 04-137).
[13] C. Ferrari and H. Kovarik, On the Exponential Decay of Magnetic Stark Resonances , Preprint, 2003. | MR | Zbl
[14] C. Ferrari and H. Kovarik, Resonances Width in Crossed Electric and Magnetic Fields, Preprint, 2003. | MR | Zbl
[15] B. Helffer and J. Sjöstrand, Equation de Schrödinger avec champ magnétique et équation de Harper, pp. 118-197 in Lecture Notes in Physics, No. 345, Springer, Berlin, 1989. | MR | Zbl
[16] I. W. Herbst, Unitary equivalence of Stark Hamiltonians, Math. Z. 155 (1977), 55-70. | MR | Zbl
[17] I. W. Herbst, Dilation analytically in constant electric field, Commun. Math. Phys. 64 (1979), 279-298. | MR | Zbl
[18] P. D. Hislop, I. M. Sigal, Introduction to spectral theory with applications to Schrödinger operators, Applied Math. Sciences, 113, Springer Verlag, Berlin, 1996. | MR | Zbl
[19] V. Ivrii, Microlocal analysis and precise spectral asymptotics, Springer, Berlin, 1988. | MR | Zbl
[20] V. Ivrii, Sharp spectral asymptotics for operators with irregular coefficients, III, Schrödinger operators with a strong magnetic field, Preprint, 2003. | MR
[21] A. Jensen, Scattering theory for Stark Hamiltonians. Spectral and inverse spectral theory (Bangalore, 1993). Proc. Indian Acad. Sci. Math. Sci. 104 (1994), no. 4, 599–651. | MR | Zbl
[22] M. Klein, D. Robert, X.-P. Wang, Breit-Wigner formula for the scattering phase in the Stark effect, Commun. Math. Phys. 131 (1990), 109-124. | MR | Zbl
[23] E. Korotyaev and A. Pushinitski, Trace formulae and high energy asymptotics for the perturbed three-dimensional Stark operator, to appear in J. Funct. Anal.
[24] P. Lax, R. Phillips, The scatering of sound waves by an obstacle, Comm. Pures Appl. Math. 30 (1977), 195-233. | MR | Zbl
[25] M. Melgaard, G. Rosenblum, Eigenvalues asymptotics for weakly perturbed Dirac and Schrödinger operators with constant magnetic field of full rank, Commun. PDE. 28 (2003), 1-52. | MR | Zbl
[26] R. Melrose, Scattering theory and the trace of wave group. J. Funct. Anal. 45 (1982), 429-440. | MR | Zbl
[27] R. Melrose, Weyl asymptotics for the phase in obstacle scattering, Commun. PDE., 13 (1988), 1431-1439. | MR | Zbl
[28] V. Petkov, M. Zworski, Breit-Wigner approximation and the distribution of resonances, Commun. Math. Phys. 204 (1999), 329-351, Erratum, Commun. Math. Phys. 214 (2000), 733-735. | MR | Zbl
[29] V. Petkov, M. Zworski, Semi-classical estimates on the scattering determinant, Annales H. Poincaré, 2 (2001), 675-711. | MR | Zbl
[30] G. Raikov, Eigenvalue asymptotics for teh Schrödinger operator with homogeneous magnetic potential and decreasing electiric potential. I. Behavior near the essential spectrum tips, Commun. PDE, 15 (1990), 407-434. | MR | Zbl
[31] G. Raikov, S. Warzel, Quasi-classical versus non-classical spectral asymptotics for magnetic Schrödinger operators with decreasing electric potentials, Rev. Math. Phys. 14 (2002), 1051-1072. | MR | Zbl
[32] D. Robert, Autour de l’approximation semi-classique, PM, 68, Basel, Birkhäuser 1987. | Zbl
[33] D. Robert, X. P. Wang, Existence of time-delay operators for Stark Hamiltonians, Commun. PDE. 14 (1989), 63-98. | MR | Zbl
[34] D. Robert, X. P. Wang, Time-delay and spectral density for Stark Hamiltonians, (II), Asymptotics of trace formulae, Chin. Ann. Math. Ser. B 12 (1991), 358-384. | MR | Zbl
[35] I. M. Sigal, Geometric theory of Stark resonances in multi-elecrin systems, Commun. Math. Phys. 19 (1988), 287-314. | MR | Zbl
[36] J. Sjöstrand, A trace formula and review of some estimates for resonances, in Microlocal analysis and spectral theory (Lucca, 1996), 377–437, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.,490, Dordrecht, Kluwer Acad. Publ.1997. | MR | Zbl
[37] J. Sjöstrand, Resonances for bottles and trace formulae, Math. Nachrichten, 221 (2001), 95-149. | MR | Zbl
[38] J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc. 4 (1991),729-769. | MR | Zbl
[39] J. Sjöstrand and M. Zworski, Lower bound on the number of scattering poles, II, J. Funct. Anal. 123 (1994), 336-367. | MR | Zbl
[40] X. P. Wang, Bounds on widths of resonances for Stark Hamiltonians, Acta Math. Sinica, Ser. B, 6 (1990), 100-119. | MR | Zbl
[41] X. P. Wang, On the Magnetic Stark Resonances in Two Dimensional Case, Lecture Notes in Physics, 403, Springer, Berlin, 1992, pp. 211-233. | MR | Zbl
[42] X. P. Wang, Barrier resonances in strong magnetic fields, Commun. PDE. 17 (1992), 1539-1566. | MR | Zbl
[43] D. Yafaev, Mathematical Scattering Theory, Amer. Math. Society, Providence, RI, 1992. | MR | Zbl
[44] K. Yajima, Spectral and scattering theory for Schrödinger operators with Stark effect, J. Fac. Sc. Univ. Tokyo, Sect. I, 26 (1979), 377-390. | MR | Zbl
[45] M. Zworski, Poisson formulae for resonances, Séminaire E.D.P., Ecole Polytechnique, Exposé XIII, 1966-1997. | Numdam | MR | Zbl