Israel Michael Sigal

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List of Publications

Updated January, 2007

ePrints available
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- on mp_arc (Mathematical Physics Preprint Archive)

  1. On the discrete spectrum of the Schrödinger operators of multiparticle systems, Comm. Math. Phys. 48 (1976) 137-154.
  2. On the point spectrum of the Schrödinger operators of multiparticle systems, Comm. Math. Phys. 48 (1976) 155-164.
  3. Mathematical foundation of quantum scattering theory for multi-particle systems, Memoirs of the Amer. Math. Society, N209 (1978).
  4. On quantum mechanics of many-body systems with dilation-analytic potentials, Bull. of the Amer. Math. Soc. 84 1 (1978).
  5. (with L. P. Horowitz), On a mathematical model for non-stationary physical systems, Helv. Phys. Acta 51 (1978) 685-715.
  6. Number of eigenvalues of many-body Hamiltonians and Effimov's effect, in "Mathematical Problems in Theoretical Physics", Proc. of Int. Conf. on Math. Physics, Lausane, August 1979, Lecture Notes in Physics 116, 56-61.
  7. Mathematical questions of quantum mechanics of many-body systems, Proc. of the Conference on Math. Methods and Applications of Scattering Theory, Washington D. C., May 1979. Lecture Notes Phys. 130 (1980) 149-158.
  8. (with Yu, N. Ovchinnikov), Number of bound state of three-body systems and Effimov effect, Ann. of Phys. 123 (1979) 274-295.
  9. (with P. Perry and B. Simon), Absence of singular continuous spectrum in N-body quantum systems, Bull. AMS 3 (1980) 1019-1023.
  10. Scattering theory in many-body quantum systems, analyticity of the scattering matrix, in Quantum Mechanics in Mathematics, Chemistry and Physics, Plenum Publ. Corp. N.Y. (1981), pp. 307-329.
  11. (with P. Perry and B. Simon), Spectral analysis of N-body Schrödinger operators, Ann. of Math. 114 (1981) 519-567.
  12. Mathematical theory of single-channel systems. Analyticity of scattering matrix, Trans. AMS 270 (1982) 409-437.
  13. Geometric methods in quantum many-body problems, in Mathematical Problems in Theoretical Physics, Proc. of the VI Int. Conf. on Math. Physics, W. Berlin, 1981, R. Schrader et al, eds, Lecture Notes in Physics N153 (1982) 149-156.
  14. Geometric methods in the quantum many-body problem. Non-existence of very negative ions, Comm. Math. Phys. 85 (1982) 309-324.
  15. Mathematical questions of quantum mechanical many-body scattering theory. Springer Lecture Notes in Math. N1011 (1983).
  16. Geometric parametrices and the many-body Birman-Schwinger principle, Duke Math. J. 50 (1983) 517-537.
  17. How many electrons can a nucleus bind? Annals of Phys. 157 (1984).
  18. Asymptotic completeness of many-body short-range systems, Lett. in Math. Phys. 8 (1984) 181-188.
  19. Complex transformation method and resonances in one-body systems, Annal. Inst. H. Poincaré 41 (1984) 103-114, Addendum 41 (1984) 333.
  20. (with E. Lieb, B. Simon and W. Thirring), Asymptotic bulk neutrality of large Z ions, Phys. Rev. Lett. 52 (1984) 994-996.
  21. A generalized Weyl theorem and Lp-spectral of Schrödinger operators, J. Oper. Theory 13 (1985) 119-129.
  22. (with A. Soffer), Asymptotic completeness of short-range many-body systems, Bull AMS 14 (1986) 107-110.
  23. Analytic properties of the scattering matrix of many particle systems, Int. Eq. Oper. Theory 9 (1986) 134-153.
  24. (with A. Soffer), The N-particle scattering problem: asymptotic completeness for short-range systems, Annal. Math. 125 (1987) 35-108.
  25. (with A. Soffer), Asymptotic completeness for N-body quantum mechanics, in VIII Int. Congr. on Math. Phys. (M. Mebkhout and R. Seneor, eds) World Scientific Publ. Co. 1987.
  26. (with P. Hislop), Shape resonances in quantum mechanics, in Diff. Equations and Math. Physics 1986 (Knowles and Saito, eds) Springer Lect. Notes in Math. N1285, 1987.
  27. (with A. Soffer), Asymptotic completeness of multiparticle scattering, in Differential Equations and Mathematical Physics (I. W. Knowles and Saito, eds) Springer Lect. Notes in Math. N1285, 1987.
  28. (with A. Soffer), Local decay and velocity bounds for time-independent and time-dependent Hamiltonians, Preprint, Princeton,1987.
  29. Mathematical questions of Quantum many-body theory, Seminaire Eq. Deriv. Part., 1986-1987, Ecole Polytechnique.
  30. Lectures on scattering theory, preprint, Toronto 1988.
  31. Sharp exponential bounds on resonance states and width of resonances, Adv. in Appl. Math. 9 (1988) 127-166.
  32. Life-time of Stark resonances, in Proceedings of Conf. on Field Theory and Related Topics, CMS Conf. Proceedings 9 (1988) 233-246.
  33. Geometrical theory of Stark resonances in multielectron systems, Comm. Math. Phys. 119 (1988) 287-314.
  34. (with E. Lieb, S. Simon and W. Thirring), Approximate neutrality of large-Z ions, Comm. Math. Phys. 116 (1988) 635-649.
  35. Stark effect in multielectron systems: non-existence of bound states, Comm. Math. Phys. 122 (1989) 1-22.
  36. (with Hislop), Shape resonances, A Memoir AMS, 78, N399, 1989.
  37. Geometrical theory of resonances in multi-particle systems, Proceedings of the IX Congress on Mathematical Physics, B. Simon, A. Truman and I. Davies, eds. U.K., Adam Hilger 1989.
  38. On long-range scattering, Duke Math. J. 60 N2, (1990), 473-496.
  39. (with A. Soffer), Long-range many-body scattering, asymptotic clustering for Coulomb-type potentials, Invent. Math. 99 (1990) 115-143.
  40. Many-body scattering problem, in Proceedings of the Nordic Summer School (H. Holden and A. Jensen, eds), Lecture Notes in Physics, Sringer-Verlag, 1990.
  41. (with L.A. Seco and J.P. Solovej), Bound on the ionization energy  . . . , Comm. Math. Phys. 131 (1990), 307-315.
  42. (with J.-M. Combes), Dynamical behaviour of multiple well Schrödinger operators, Proceedings in Quantum Mechanics, Poiana Brasov, Romania, Springer-Verlag, 1991.
  43. (with Yu. Ovchinnikov), The decay rate of metastable state, J. of Low Temp. Phys. 85 (1991), 125-135.
  44. Mathematical questions of quantum mechanics of many-particle systems, in Proceedings of the ICM, Kyoto, 1990, Springer-Verlag 1991.
  45. (with S. DeBievre and P. Hislop), Scattering theory for wave equation on non-compact manifolds, Reviews in Mathematical Physics Vol. 4, No. 4 (1992), 575-618.
  46. (with C.L. Fefferman, V. Ivrii, L.A. Seco), The energy asymptotics of large coulomb systems, in Proceedings of Danish Summer School on Mathematical Physics, Springer-Verlag 1992.
  47. (with C. Gérard), Time-space picture of resonance, Comm. Math. Phys. 145 (1992), 281-328.
  48. (with A. Soffer), Asymptotic completeness for N=4 particle systems with the Coulomb-type interactions, Duke Math. J. 70 (1993), 243-298.
  49. (with V. Ivrii), Asymptotics of the ground state energies of large Coulomb systems, Annals of Mathematics 138 (1993), 243-335.
  50. Non-Linear wave and Schrödinger equations I, instability of periodic and quasiperiodic solutions, Comm. Math. Phys. 153 (1993) 297-320.
  51. (with Yu. N. Ovchinnikov), Decay of vortex states in superconductors, Phys. Rev. B. 48 (1993), 1085-1096.
  52. General characteristics of non-linear dynamics, in "Spectral and Scattering Theory" (M. Ikawa, ed.), Marcel Dekker, Inc. 1994.
  53. (with A. Soffer) Asymptotic completeness of N particle long range scattering, Journal of AMS 7 (1994), 307-334.
  54. Lectures on large Coulomb systems, in the Proceedings of the Vancouver Mathematical Physics Summer School (J.  Feldman, R. Froese and L. Rosen, eds.), CRM Proceedings and Lecture Notes, v. 7, AMS, 1995, 73-107.
  55. (with W. Hunziker), On general theory of N-body quantum systems, CRM Proceedings and Lecture Notes, v. 7, AMS, 1995, 35-72.
  56. (with P. Hislop), Introduction to Spectral Theory with Applications to Schrödinger Operators, Springer-Verlag series of monographs on Applied Mathematical Sciences, 1996.
  57. (with V. Bach and J. Fröhlich), Mathematical theory of non-relativistic matter and radiation, Letters in Math. Phys. 34 (1995), 183-201.
  58. Asymptotic completeness, AMS Transl. 175 (1996), 199-206.
  59. (with Yu. N. Ovchinnikov), Ginzburg-Landau equation I. Static vortices. Part. Diff. Eqn and their Appl. CRM Proceedings 12 (1997), 199-220.
  60. (with R. Pyke), Nonlinear wave equations: Constraints on periods and exponential bounds for periodic solutions, Duke Math. J. 88 (1997), 133-180.
  61. (with V. Bach and J. Fröhlich), Mathematical Theory of Radiation, Foundations of Physics 178 (1997), 227-237.
  62. (with R. Pyke), Positive commutator methods for nonlinear wave equations, in Partial Differential Equations and their Applications, CRM Proceedings 12 (1997), 239-249.
  63. (with V. Bach and J. Fröhlich), Quantum electrodynamics of confined non-relativistic particles, Adv. Math. 137 (1998), 205-298.
  64. (with V. Bach and J. Fröhlich), The renormalization group approach to spectral problems in QFT, Adv. in Math. 137 (1998), 299-395.
  65. (with Yu. N. Ovchinnikov), The Landau-Ginzburg equation III. Vortex dynamics, Nonlinearity 11 No.5 (1998), 1277-1294.
  66. (with Yu. N. Ovchinnikov), Dynamics of localized structures, Physica A 261 (1998) 143-158.
  67. (with Yu. N. Ovchinnikov), On the Ginzburg-Landau and related equations, Ecole Polytechnique, Exposé nº XX1 (1998), 1-13.
  68. (with Yu. N. Ovchinnikov), Long-time behaviour of Ginzburg-Landau vortices, Nonlinearity 11 No.5 (1998), 1295-1309.
  69. (with M. Merkli), A time dependent theory of quantum resonance, Comm. Math. Phys. 201 No.3 (1999), 549-576.
  70. (with V. Bach, J. Fröhlich and A. Soffer), Positive commutators and spectrum of the radiation Hamiltonian, Comm. Math. Phys. 207 (1999), 557-587.
  71. (with W. Hunziker and A. Soffer), Minimal escape velocities revisited, Comm. in PDE 24 (1999), 2279-2295.
  72. (with V. Bach and J. Fröhlich), Mathematical theory of non-relativistic matter and radiation, Comm. Math. Phys. 207 No.2 (1999), 249-290.
  73. (with Yu. N. Ovchinnikov), Collapse in the nonlinear Schrödinger equation, J. Exp. Theor. Phys. 89 (1999), 35-40.
  74. (with S. Gustafson), The stability of magnetic vortices, Comm. Math. Phys. 210 No.2 (2000), 257-276.
  75. (with A. Laptev), Global Fourier integral operators and semiclassical asymptotics, Reviews in Math. Phys. 12 (2000), 749-766.
  76. (with V. Bach and J. Fröhlich), Return to equilibrium, J. Math. Phys.  41 (2000) 3985-4060.
  77. (with W. Hunziker), Quantum many-body problem, J. Math. Phys. 41 (2000), 3448-3510.
  78. (with Yu. N. Ovchinnikov), Asymptotic behaviour of solutions of Ginzburg-Landau and related equations, Rev. Math. Phys. 12 (2000), 287-299.
  79. (with W. Hunziker), Time-dependent scattering theory of N-body systems, Rev. Math. Phys. 12 No. 8 (2000), 1033-1084.
  80. Perron-Frobenius theory and symmetry of solutions to nonlinear PDE's, Letters Math Phys., 53 No.4 (2000), 313-320.
  81. (with Yu. N. Ovchinnikov), Optical bistability, Journal of Experimental and Theorretical Physics 93 (2001), 1004-1016
  82. Renormalization group approach in spectral analysis and problem of radiation, CMS Notes 33 (3) (2001), 3-9
  83. (with Yu. N. Ovchinnikov), The energy of Ginzburg-Landau vortex, European Journal of Applied Mathematics 13 (2002), 153-178.
  84. (with A. Soffer and L. Zielinski), On the spectral properties of Hamiltonians without conservation of the particle number, J. Math. Phys. 43 (2002), 1844-1855.
  85. (with B. Vasilijevic), Mathematical theory of tunneling at positive temperatures, Annales de l'Institut Henri Poincaré, 3 (2002), 1-41.
  86. (with Yu. Ovchinnikov), Collapse in the nonlinear Schrödinger equation, JETP, 89 (2002), 35-40.
  87. (with Yu. Ovchinnikov), Collape in critical nonlinear Schrödinger equation, JETP Letters, 75 (2002), 357-361.
  88. (with V. Bach, T. Chen and J. Fröhlich), Smooth Feshbach map, J. Funct. Anal., 203 (2003), 44-92.
  89. (with Yu. Ovchinnikov), Multiparameter family of collapsing solutions of the critical nonlinear Schrödingers equation, JETP. 97 (2003) 194-203.
  90. (with S. Gustafson), Mathematical Concepts of Quantum Mechanics, Springer, Universitext Series (2003).
  91. (with J. Fröhlich and M. Merkli), Ionization of Atoms in a Thermal Field, J. of Statistical Mechanics 116 (2004) 311-359.
  92. (with P. Bizon and Yu. Ovchinnikov), Collapse of an instanton Nonlinearity 17 (2004) 1179-1191
  93. (with F. Ting) Pinning of magnetic vortices, Algebra and Analysis 16 (2004) 239-268.
  94. (with Yu. Ovchinnikov), Symmetry Breaking Solutions to the Ginzburg-Landau Equations, JETP (2004), 1090-1108.
  95. (with J. Fröhlich, S. Gustafon and L. Jonsson) Dynamics of solitary waves external potentials, Commun Math Phys 250 (2004) 613-642.
  96. (with Zhou Gang), Asymptotic stability of nonlinear Schrödinger equations with potential, Reviews in Mathematical Physics, 17 (2005), 1193-1207.
  97. (with S. Gustafson), Dynamics of Magnetic Vortices, Advances in Mathematics, 199 (2006) 448-498
  98. (with S. Dejak), Long time dynamics of KdV solitary waves over variable bottom, Commun in Pure Applied Mathematics, LIX (2006), 869-905.
  99. (with Y. Strauss), Effective Dynamics of a Magnetic Vortex in a Local potential, Journal of Nonlinear Science, 16 (2006) 123-157.
  100. (with J. Fröhlich, S. Gustafon and L. Jonsson) Long time motion of NLS solitary waves in a confining potential, Annals Henri Poincare 7 (2006), 621-660.
  101. (with S. Gustafson), Mathematical Concepts of Quantum Mechanics, 2nd enlarged edition, Springer, Universitext Series (2006).
  102. (with M. Merkli and M. Mück), Instability of equilibrium states for systems coupled to reservoirs at different temperatures, 40 pages, J. Functional Analysis, 2007, to appear.
  103. (with V. Bach, T. Chen, J. Fröhlich) Determination of the renormalized mass for the Pauli-Fierz model, 94 pages, J. Functional Analysis, 2007, to appear.
  104. (with Gang Zhou) On Soliton Dynamics in Nonlinear Schrödinger Equations, 14 pages, GAFA, 2007, to appear.
  105. (with M. Merkli and M. Mück) Theory of non-equilibrium stationary states as a theory of resonances. Existence and Properties of NESS, 2006, ePrint, arXiv.org.
  106. (with J. Fröhlich, and S. Griesemer) Mourre Estimate and Spectral Theory for the Standard Model of Non-Relativistic QED, 2006, ePrint, arXiv.org.
  107. (with S. Dejak, Zhou Gang, and S. Wang) Blow-up in Nonlinear Heat Equations, 2006, ePrint, arXiv.org.
  108. (with G.D. Berman and M. Merkli) Decoherence and Thermalization, 2006, ePrint, arXiv.org.
  109. (with Gang Zhou) Relaxation of Solitons in Nonlinear Schrodinger Equations with Potential, 2006, ePrint, arXiv.org.

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