Israel Michael Sigal

List of Publications

Updated July, 2019

ePrints available
- on (Los Alamos Archive)
- on mp_arc (Mathematical Physics Preprint Archive)

  1. 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.
  2. (with P. Perry and B. Simon), Spectral analysis of N-body Schrödinger operators, Ann. of Math. 114 (1981) 519-567.
  3. Mathematical theory of single-channel systems. Analyticity of scattering matrix, Trans. AMS 270 (1982) 409-437.
  4. 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.
  5. Geometric methods in the quantum many-body problem. Non-existence of very negative ions, Comm. Math. Phys. 85 (1982) 309-324.
  6. Mathematical questions of quantum mechanical many-body scattering theory. Springer Lecture Notes in Math. N1011 (1983).
  7. Geometric parametrices and the many-body Birman-Schwinger principle, Duke Math. J. 50 (1983) 517-537.
  8. How many electrons can a nucleus bind? Annals of Phys. 157 (1984).
  9. Asymptotic completeness of many-body short-range systems, Lett. in Math. Phys. 8 (1984) 181-188.
  10. Complex transformation method and resonances in one-body systems, Annal. Inst. H. Poincaré 41 (1984) 103-114, Addendum 41 (1984) 333.
  11. (with E. Lieb, B. Simon and W. Thirring), Asymptotic bulk neutrality of large Z ions, Phys. Rev. Lett. 52 (1984) 994-996.
  12. A generalized Weyl theorem and Lp-spectral of Schrödinger operators, J. Oper. Theory 13 (1985) 119-129.
  13. (with A. Soffer), Asymptotic completeness of short-range many-body systems, Bull AMS 14 (1986) 107-110.
  14. Analytic properties of the scattering matrix of many particle systems, Int. Eq. Oper. Theory 9 (1986) 134-153.
  15. (with A. Soffer), The N-particle scattering problem: asymptotic completeness for short-range systems, Annal. Math. 125 (1987) 35-108.
  16. (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.
  17. (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.
  18. (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.
  19. Mathematical questions of Quantum many-body theory, Seminaire Eq. Deriv. Part., 1986-1987, Ecole Polytechnique.
  20. (with A. Soffer), Local decay and velocity bounds for time-independent and time-dependent Hamiltonians, Preprint, Princeton,1988.
  21. Lectures on scattering theory, preprint, Toronto 1988.
  22. Sharp exponential bounds on resonance states and width of resonances, Adv. in Appl. Math. 9 (1988) 127-166.
  23. Life-time of Stark resonances, in Proceedings of Conf. on Field Theory and Related Topics, CMS Conf. Proceedings 9 (1988) 233-246.
  24. Geometrical theory of Stark resonances in multielectron systems, Comm. Math. Phys. 119 (1988) 287-314.
  25. (with E. Lieb, S. Simon and W. Thirring), Approximate neutrality of large-Z ions, Comm. Math. Phys. 116 (1988) 635-649.
  26. Stark effect in multielectron systems: non-existence of bound states, Comm. Math. Phys. 122 (1989) 1-22.
  27. (with Hislop), Shape resonances, A Memoir AMS, 78, N399, 1989.
  28. 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.
  29. On long-range scattering, Duke Math. J. 60 N2, (1990), 473-496.
  30. (with A. Soffer), Long-range many-body scattering, asymptotic clustering for Coulomb-type potentials, Invent. Math. 99 (1990) 115-143.
  31. Many-body scattering problem, in Proceedings of the Nordic Summer School (H. Holden and A. Jensen, eds), Lecture Notes in Physics, Sringer-Verlag, 1990.
  32. (with L.A. Seco and J.P. Solovej), Bound on the ionization energy  . . . , Comm. Math. Phys. 131 (1990), 307-315.
  33. (with J.-M. Combes), Dynamical behaviour of multiple well Schrödinger operators, Proceedings in Quantum Mechanics, Poiana Brasov, Romania, Springer-Verlag, 1991.
  34. (with Yu. Ovchinnikov), The decay rate of metastable state, J. of Low Temp. Phys. 85 (1991), 125-135.
  35. Mathematical questions of quantum mechanics of many-particle systems, in Proceedings of the ICM, Kyoto, 1990, Springer-Verlag 1991.
  36. (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.
  37. (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.
  38. (with C. Gérard), Time-space picture of resonance, Comm. Math. Phys. 145 (1992), 281-328.
  39. (with A. Soffer), Asymptotic completeness for N=4 particle systems with the Coulomb-type interactions, Duke Math. J. 70 (1993), 243-298.
  40. (with V. Ivrii), Asymptotics of the ground state energies of large Coulomb systems, Annals of Mathematics 138 (1993), 243-335.
  41. Non-Linear wave and Schrödinger equations I, instability of periodic and quasiperiodic solutions, Comm. Math. Phys. 153 (1993) 297-320.
  42. (with Yu. N. Ovchinnikov), Decay of vortex states in superconductors, Phys. Rev. B. 48 (1993), 1085-1096.
  43. General characteristics of non-linear dynamics, in "Spectral and Scattering Theory" (M. Ikawa, ed.), Marcel Dekker, Inc. 1994.
  44. (with A. Soffer) Asymptotic completeness of N particle long range scattering, Journal of AMS 7 (1994), 307-334.
  45. 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.
  46. (with W. Hunziker), On general theory of N-body quantum systems, CRM Proceedings and Lecture Notes, v. 7, AMS, 1995, 35-72.
  47. (with P. Hislop), Introduction to Spectral Theory with Applications to Schrödinger Operators, Springer-Verlag series of monographs on Applied Mathematical Sciences, 1996.
  48. (with V. Bach and J. Fröhlich), Mathematical theory of non-relativistic matter and radiation, Letters in Math. Phys. 34 (1995), 183-201.
  49. Asymptotic completeness, AMS Transl. 175 (1996), 199-206.
  50. (with Yu. N. Ovchinnikov), Ginzburg-Landau equation I. Static vortices. Part. Diff. Eqn and their Appl. CRM Proceedings 12 (1997), 199-220.
  51. (with R. Pyke), Nonlinear wave equations: Constraints on periods and exponential bounds for periodic solutions, Duke Math. J. 88 (1997), 133-180.
  52. (with V. Bach and J. Fröhlich), Mathematical Theory of Radiation, Foundations of Physics 178 (1997), 227-237.
  53. (with R. Pyke), Positive commutator methods for nonlinear wave equations, in Partial Differential Equations and their Applications, CRM Proceedings 12 (1997), 239-249.
  54. (with V. Bach and J. Fröhlich), Quantum electrodynamics of confined non-relativistic particles, Adv. Math. 137 (1998), 205-298.
  55. (with V. Bach and J. Fröhlich), The renormalization group approach to spectral problems in QFT, Adv. in Math. 137 (1998), 299-395.
  56. (with Yu. N. Ovchinnikov), The Landau-Ginzburg equation III. Vortex dynamics, Nonlinearity 11 No.5 (1998), 1277-1294.
  57. (with Yu. N. Ovchinnikov), Dynamics of localized structures, Physica A 261 (1998) 143-158.
  58. (with Yu. N. Ovchinnikov), On the Ginzburg-Landau and related equations, Ecole Polytechnique, Exposé nº XX1 (1998), 1-13.
  59. (with Yu. N. Ovchinnikov), Long-time behaviour of Ginzburg-Landau vortices, Nonlinearity 11 No.5 (1998), 1295-1309.
  60. (with M. Merkli), A time dependent theory of quantum resonance, Comm. Math. Phys. 201 No.3 (1999), 549-576.
  61. (with V. Bach, J. Fröhlich and A. Soffer), Positive commutators and spectrum of the radiation Hamiltonian, Comm. Math. Phys. 207 (1999), 557-587.
  62. (with W. Hunziker and A. Soffer), Minimal escape velocities revisited, Comm. in PDE 24 (1999), 2279-2295.
  63. (with V. Bach and J. Fröhlich), Mathematical theory of non-relativistic matter and radiation, Comm. Math. Phys. 207 No.2 (1999), 249-290.
  64. (with Yu. N. Ovchinnikov), Collapse in the nonlinear Schrödinger equation, J. Exp. Theor. Phys. 89 (1999), 35-40.
  65. (with S. Gustafson), The stability of magnetic vortices, Comm. Math. Phys. 210 No.2 (2000), 257-276.
  66. (with A. Laptev), Global Fourier integral operators and semiclassical asymptotics, Reviews in Math. Phys. 12 (2000), 749-766.
  67. (with V. Bach and J. Fröhlich), Return to equilibrium, J. Math. Phys.  41 (2000) 3985-4060.
  68. (with W. Hunziker), Quantum many-body problem, J. Math. Phys. 41 (2000), 3448-3510.
  69. (with Yu. N. Ovchinnikov), Asymptotic behaviour of solutions of Ginzburg-Landau and related equations, Rev. Math. Phys. 12 (2000), 287-299.
  70. (with W. Hunziker), Time-dependent scattering theory of N-body systems, Rev. Math. Phys. 12 No. 8 (2000), 1033-1084.
  71. Perron-Frobenius theory and symmetry of solutions to nonlinear PDE's, Letters Math Phys., 53 No.4 (2000), 313-320.
  72. (with Yu. N. Ovchinnikov), Optical bistability, Journal of Experimental and Theorretical Physics 93 (2001), 1004-1016
  73. Renormalization group approach in spectral analysis and problem of radiation, CMS Notes 33 (3) (2001), 3-9
  74. (with Yu. N. Ovchinnikov), The energy of Ginzburg-Landau vortex, European Journal of Applied Mathematics 13 (2002), 153-178.
  75. (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.
  76. (with B. Vasilijevic), Mathematical theory of tunneling at positive temperatures, Annales de l'Institut Henri Poincaré, 3 (2002), 1-41.
  77. (with Yu. Ovchinnikov), Collapse in the nonlinear Schrödinger equation, JETP, 89 (2002), 35-40.
  78. (with Yu. Ovchinnikov), Collape in critical nonlinear Schrödinger equation, JETP Letters, 75 (2002), 357-361.
  79. (with V. Bach, T. Chen and J. Fröhlich), Smooth Feshbach map, J. Funct. Anal., 203 (2003), 44-92.
  80. (with Yu. Ovchinnikov), Multiparameter family of collapsing solutions of the critical nonlinear Schrödingers equation, JETP. 97 (2003) 194-203.
  81. (with S. Gustafson), Mathematical Concepts of Quantum Mechanics, Springer, Universitext Series (2003).
  82. (with J. Fröhlich and M. Merkli), Ionization of Atoms in a Thermal Field, J. of Statistical Mechanics 116 (2004) 311-359.
  83. (with P. Bizon and Yu. Ovchinnikov), Collapse of an instanton Nonlinearity 17 (2004) 1179-1191
  84. (with F. Ting) Pinning of magnetic vortices, Algebra and Analysis 16 (2004) 239-268.
  85. (with Yu. Ovchinnikov), Symmetry Breaking Solutions to the Ginzburg-Landau Equations, JETP (2004), 1090-1108.
  86. (with J. Fröhlich, S. Gustafon and L. Jonsson) Dynamics of solitary waves external potentials, Commun Math Phys 250 (2004) 613-642.
  87. (with Zhou Gang), Asymptotic stability of nonlinear Schrödinger equations with potential, Reviews in Mathematical Physics, 17 (2005), 1193-1207.
  88. (with S. Gustafson), Mathematical Concepts of Quantum Mechanics Springer, 2nd enlarged printing, 2006. (One new chapter and several new or enlarged sections.)
  89. (with S. Gustafson), Dynamics of Magnetic Vortices, Advances in Mathematics, 199 (2006) 448-498.
  90. (with S. Dejak), Long time dynamics of KdV solitary waves over variable bottom, Commun in Pure and Applied Mathematics 59 (2006) 869-905.
  91. (with Y. Strauss), Effective Dynamics of a Magnetic Vortex in a Local potential, Journal of Nonlinear Science, 16 (2006) 123-157.
  92. (with J. Fröhlich, S. Gustafson and L. Jonsson) Long time motion of NLS solitary waves in a confining potential, Annales Henri Poincaré 7 (2006) 621-660.
  93. (with Zhou Gang) On Soliton Dynamics in Nonlinear Schrödinger Equations, GAFA, 16 (2006) 1377-1390.
  94. (with M. Merkli and M. Mück), Instability of equilibrium states for systems coupled to reservoirs at different temperatures, Journal of Functional Analysis, 243 (2007) 87-120.
  95. (with V. Bach, T .Chen, J. Fröhlich) The renormalized electron mass in non-relativistic quantum electrodynamics, Journal of Functional Analysis 243 2007 426-535.
  96. (with G. Berman and M. Merkli) Decoherence and Thermalization, Physical Review Letters Vol.98, No.13, 30 March 2007. (This article has been also selected for the April 2007 issue of Virtual Journal of Quantum Information.)
  97. (with M. Merkli and M. Mück) Theory of non-equilibrium stationary states as a theory of resonances, Annales Henri Poincaré 8 (2007), no. 8, 1539-1593.
  98. (with Zhou Gang) Relaxation of solitons in nonlinear Schrödinger equations with potentials, Adv Math, 216 (2007), no. 2, 443-490.
  99. (with S. Dejak, Zhou Gang and S. Wang), Blowup dynamics in nonlinear heat equations, Adv Appl Math 40 (2008), 433-481.
  100. (with G. Berman and M. Merkli) Resonance Theory of Decoherence and Thermalization, Annals Physics, 323(2) (2008) 373-412.
  101. (with J. Fröhlich and M. Griesemer) Spectral Theory for the Standard Model of Non-Relativistic QED, Comm. Math. Physics, 283(3) (2008) 613-646.
  102. (with G.P. Berman and M. Merkli), Dynamics of Collective Decoherence and Thermalization, Annals of Physics 323(12) (2008) 3091-3312.
  103. (with Zhou Gang), Neckpinching dynamics under mean curvature flow, J Geometric Analysis 19 (1) (2009) 36-80.
  104. (with W. K. Abou Salem, J. Faupin and J. Fröhlich), On the theory of resonances in non-relativistic QED and related models, Advances in Applied Mathematics 43 (2009), pp. 201-230.
  105. Ground State and Resonances in the Standard Model of the Non-Relativistic QED, J Statistical Mechanics, 134 Numbers 5-6, 2009, 899 - 939; arXiv:0806.3297.
  106. (with J. Fröhlich and M. Griesemer) On Spectral Renormalization Group, Rev Math Phys, 21 Issue: 4 (2009) pp. 511-548; arXiv:0811.2616.
  107. (with W. K. Abou Salem and J. Fröhlich), Colliding solitons for the nonlinear Schrödinger equation, Comm. Math. Physics, 291(1), 151--176, 2009; arXiv:0804.1608.
  108. (with S. Gustafson and T. Tzaneteas), Statics and dynamics of magnetic vortices and of Nielsen--Olesen (Nambu) strings, Journal of Mathematical Physics, 51, Issue 1, 2010.
  109. (with G.P. Berman and M. Merkli), Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits, Adv Math Phys, Vol. 2010, Article ID 169710, 20 pages, 2010.
  110. (with D. Antonopoulou and G. Karali) Stability of spheres under volume-preserving mean curvature flow, Dynamics of PDE 7(4):327-354, 2010.
  111. (with T. Tzaneteas), On Abrikosov lattices, in Spectral Theory and Geometric Analysis, M. Braverman, et al, editors, in Contemporary Mathematics, AMS 2011.
  112. (with J. Fröhlich and M. Griesemer) Spectral Renormalization Group and Local Decay in the Standard Model of the non-relativistic Quantum Electrodynamics, Rev. Math. Phys. 23(2):179-209, 2011. arXiv:0904.1014.
  113. (with Yu. Ovchinnikov) Long-time relaxation processes in the nonlinear Schrödinger equation, J. Exp. Theor. Phys, 112(3):469-478, 2011.
  114. (with Yu. Ovchinnikov) On collapse of wave maps, Physica D: Nonlinear Phenomena 240(17):1311-1324, 2011.
  115. (with B.L.G. Jonsson, Yu. Ovchinnikov and F.S.T. Ting) Dynamics of breakup of multiple vortices in Gross-Pitaevskii equations of superfluids, Journal of Mathematical Physics 52(9):093505-1--093505-16 (2011).
  116. (with S. Gustafson), Mathematical Concepts of Quantum Mechanics Springer, 3rd edition, 2011.
  117. Renormalization group and problem of radiation, published in Quantum Theory from Small to Large Scales Lecture Notes of the Les Houches Summer School Volume 95, 2013.
  118. (with T. Chen, J. Faupin and J. Fröhlich) Local decay in non-relativistic QED, Comm. in Mathematical Physics Volume 309, Number 2, Pages 543-582, 2012
  119. (with T. Tzaneteas), Stability of Abrikosov lattices under gauge-periodic perturbations, Nonlinearity 25: 1187-1210, 2012.
  120. (with S.I. Dejak, P.M. Lushnikov and Yu. Ovchinnikov) On spectra of linearized operators for Keller-Segel models of chemotaxis, Physica D, 241, 1245-1254, 2012.
  121. (with T. Tzanateas) Abrikosov lattices at weak magnetic fields, J. Functional Analysis, 263(3): 675-702, 2012. https:
  122. (with W. Kong) On collapse of surfaces under mean curvature flow, 2012.
  123. (with J.-F. Bony and J. Faupin) Maximal velocity of photons in non-relativistic QED, Adv in Mathematics 231(5):3054-3078, 2012.
  124. (with V. Bach, Th. Chen, J. Faupin, J. Fröhlich) Effective dynamics of an electron coupled to an external potential in non-relativistic QED, Annales Henri Poincaré, 14(6):1573-1597, 2013.
  125. (with J. Faupin) On quantum Huygens principle and Rayleigh scattering, 2012, submitted.
  126. (with J. Faupin) Minimal Photon Velocity Bounds in Non-relativistic Quantum Electrodynamics. J. Stat Physics, 154(1-2): 58-90, 2014.
  127. (with D. Egli, J. Fröhlich, Zhou Gang, A. Shao) Hamiltonian Dynamics of a Particle Interacting with a Wave Field. Comm. Partial Differential Equations, 338(12): 2155-2198, 2013.
  128. (with T. Tzanateas) On Abrikosov Lattice Solutions of the Ginzburg-Landau Equation. Math. Model Nat. Phenom., 8(5): 190-205, 2013.
  129. (with J. Faupin) On Rayleigh scattering in non-relativistic quantum electrodynamics. Comm. Math. Phys., 328(3): 1199-1254, 2014.
  130. (with S. I. Dejak, D. Egli, P.M. Lushnikov) On blowup dynamics in the Keller-Segel model of chemotaxis. St. Petersburg Math Journal, 25(4): 547-574, 2013.
  131. (with V. Bach, W. Pedra, M. Merkli) Suppression of decoherence by periodic forcing. J Stat Phys, 155(6): 1271-1298, 2014.
  132. (with I. Anapolitanos) Long distance behaviour of van der Waals forces, in Mathematical Results in Quantum Mechanics: Proceedings of the QMath12 Conference World Scientific, 2014.
  133. Magnetic Vortices, Abrikosov Lattices and Automorphic Functions, in Mathematical and Computational Modeling (With Applications in Natural and Social Sciences, Engineering and the Arts), Wiley, 2015.
  134. Radiation and Scattering in Non-relativistic Quantum Electrodynamics, in Mathematical Physics: A Bridge Between Mathematics and Physics, Springer, 2016.
  135. (with Yu. Ovchinnikov) Instability of a triangular Abrikosov lattice at values of the Ginzburg-Landau parameter κ close to unity, J Exp Theor Phys, 123(1): 119, 2016.
  136. (with I. Anapolitanos) Long range behavior of van der Waals forces, Comm Pure Appl Math, 70(9): 1633-1671, 2017
  137. (with T. Tzaneteas) On stability of Abrikosov vortex lattices, Adv Math, 326: 108-199, 2018
  138. (with I. Chenn and P. Smyrnelis) On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations, Math Phys Analy Geom, 21: 7, 2018
  139. (with Zhou Gang and D. Knopf) Neckpinching under mean curvature flow for asymmetric surfaces evolving by mean curvature flow, Memoirs of the AMS, 253(1210), 2018.
  140. (with V. Bach, S. Breteaux, T. Chen and J. Frölich) The time-dependent Hartree-Fock-Bogolubov equations for bosons, J Evol Eqn, To Appear, 2019. arXiv:1602.05171v2.
  141. (with I. Chenn) On Effective PDEs of Quantum Physics, in New Tools for Nonlinear PDEs and Application, D'Abbico, et al, editors, Birkhäuser series on Trends in Mathematics, (2019).
  142. (with D. Chouchkov N.M. Ercolani and S. Rayan) Ginzburg-Landau equations on Riemann surfaces of higher genus, Annales IHP, in press, 2019.
  143. (with I. Chenn) On the Bogolubov-de Gennes equations. Adv in Math, under revision, 2019. arXiv:11701.06080v2.