Israel Michael Sigal
List of Publications
Updated July, 2019
ePrints available
 on arXiv.org
(Los Alamos Archive)
 on mp_arc (Mathematical Physics Preprint Archive)

Scattering theory in manybody quantum systems, analyticity
of the scattering matrix, in
Quantum Mechanics in Mathematics, Chemistry and Physics, Plenum Publ. Corp. N.Y. (1981),
pp. 307329.

(with P. Perry and B. Simon),
Spectral analysis of Nbody
Schrödinger operators,
Ann. of Math. 114 (1981) 519567.

Mathematical theory of singlechannel
systems. Analyticity of scattering matrix,
Trans. AMS 270 (1982) 409437.

Geometric methods in quantum manybody 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) 149156.

Geometric methods in the quantum manybody problem.
Nonexistence of very negative ions,
Comm. Math. Phys. 85 (1982) 309324.

Mathematical questions of quantum mechanical manybody
scattering theory.
Springer Lecture Notes in Math. N1011 (1983).

Geometric parametrices and the manybody BirmanSchwinger
principle,
Duke Math. J. 50 (1983) 517537.

How many electrons can a nucleus bind?
Annals of Phys. 157 (1984).

Asymptotic completeness of manybody shortrange systems,
Lett. in Math. Phys. 8 (1984) 181188.

Complex transformation method and resonances in onebody
systems,
Annal. Inst. H. Poincaré 41 (1984) 103114,
Addendum 41 (1984) 333.

(with E. Lieb, B. Simon and W. Thirring),
Asymptotic bulk neutrality of large Z ions,
Phys. Rev. Lett. 52 (1984) 994996.

A generalized Weyl theorem and L^{p}spectral
of Schrödinger operators,
J. Oper. Theory 13 (1985) 119129.

(with A. Soffer),
Asymptotic completeness of shortrange manybody systems,
Bull AMS 14 (1986) 107110.

Analytic properties of the scattering matrix of many
particle systems,
Int. Eq. Oper. Theory 9 (1986) 134153.

(with A. Soffer),
The Nparticle scattering
problem: asymptotic completeness for shortrange systems,
Annal. Math. 125 (1987) 35108.

(with A. Soffer),
Asymptotic completeness for Nbody quantum mechanics,
in VIII Int. Congr. on Math. Phys.
(M. Mebkhout and R. Seneor, eds) World Scientific
Publ. Co. 1987.

(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.

(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.

Mathematical questions of Quantum manybody theory, Seminaire Eq. Deriv. Part., 19861987,
Ecole Polytechnique.

(with A. Soffer),
Local decay and velocity bounds for timeindependent and
timedependent Hamiltonians, Preprint, Princeton,1988.

Lectures on scattering theory, preprint,
Toronto 1988.

Sharp exponential bounds on resonance states and
width of resonances,
Adv. in Appl. Math. 9 (1988) 127166.

Lifetime of Stark resonances, in
Proceedings of Conf. on Field Theory and Related Topics,
CMS Conf. Proceedings 9 (1988)
233246.

Geometrical theory of Stark resonances in multielectron
systems,
Comm. Math. Phys. 119 (1988) 287314.

(with E. Lieb, S. Simon and W. Thirring),
Approximate neutrality of largeZ ions,
Comm. Math. Phys. 116 (1988) 635649.

Stark effect in multielectron systems:
nonexistence of bound states,
Comm. Math. Phys. 122 (1989) 122.

(with Hislop),
Shape resonances,
A Memoir AMS, 78, N399, 1989.

Geometrical theory of resonances in multiparticle
systems,
Proceedings of the IX Congress on Mathematical Physics,
B. Simon, A. Truman and I. Davies, eds. U.K., Adam
Hilger 1989.

On longrange scattering,
Duke Math. J. 60 N2, (1990), 473496.

(with A. Soffer),
Longrange manybody
scattering, asymptotic clustering for Coulombtype
potentials,
Invent. Math. 99 (1990) 115143.

Manybody scattering problem, in Proceedings of the
Nordic Summer School (H. Holden and A. Jensen, eds),
Lecture Notes in Physics, SringerVerlag, 1990.

(with L.A. Seco and J.P. Solovej),
Bound on the ionization energy . . . ,
Comm. Math. Phys. 131 (1990), 307315.

(with J.M. Combes),
Dynamical behaviour of multiple well Schrödinger operators,
Proceedings in Quantum Mechanics,
Poiana Brasov, Romania, SpringerVerlag, 1991.

(with Yu. Ovchinnikov),
The decay rate of metastable state,
J. of Low Temp. Phys. 85 (1991), 125135.

Mathematical questions of quantum mechanics of
manyparticle systems, in
Proceedings of the ICM, Kyoto, 1990,
SpringerVerlag 1991.

(with S. DeBievre and P. Hislop),
Scattering theory for wave equation on noncompact
manifolds,
Reviews in Mathematical Physics Vol. 4, No. 4
(1992), 575618.

(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, SpringerVerlag 1992.

(with C. Gérard),
Timespace picture of resonance,
Comm. Math. Phys. 145 (1992), 281328.

(with A. Soffer),
Asymptotic completeness for N=4
particle systems with the Coulombtype interactions,
Duke Math. J. 70 (1993), 243298.

(with V. Ivrii),
Asymptotics of the ground
state energies of large Coulomb systems,
Annals of Mathematics 138 (1993), 243335.

NonLinear wave and Schrödinger equations I, instability
of periodic and quasiperiodic solutions,
Comm. Math. Phys. 153 (1993) 297320.

(with Yu. N. Ovchinnikov),
Decay of vortex states in superconductors,
Phys. Rev. B. 48 (1993), 10851096.

General characteristics of nonlinear dynamics,
in "Spectral and Scattering Theory"
(M. Ikawa, ed.), Marcel Dekker, Inc. 1994.

(with A. Soffer)
Asymptotic completeness of
N particle long range scattering,
Journal of AMS 7 (1994), 307334.

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, 73107.

(with W. Hunziker),
On general theory of Nbody quantum systems,
CRM Proceedings and Lecture Notes, v. 7, AMS,
1995, 3572.

(with P. Hislop),
Introduction to Spectral Theory with Applications to Schrödinger Operators,
SpringerVerlag series of monographs on Applied Mathematical Sciences, 1996.

(with V. Bach and J. Fröhlich),
Mathematical theory of nonrelativistic matter and
radiation, Letters in Math. Phys.
34 (1995), 183201.

Asymptotic completeness,
AMS Transl. 175 (1996), 199206.

(with Yu. N. Ovchinnikov),
GinzburgLandau equation I.
Static vortices.
Part. Diff. Eqn and their Appl.
CRM Proceedings 12 (1997), 199220.

(with R. Pyke),
Nonlinear wave equations:
Constraints on periods and exponential bounds for periodic
solutions,
Duke Math. J. 88 (1997), 133180.

(with V. Bach and J. Fröhlich),
Mathematical Theory of
Radiation, Foundations of Physics
178 (1997), 227237.

(with R. Pyke),
Positive commutator methods for nonlinear wave equations,
in Partial Differential Equations and their Applications,
CRM Proceedings 12 (1997), 239249.

(with V. Bach and J. Fröhlich),
Quantum electrodynamics of
confined nonrelativistic particles,
Adv. Math. 137 (1998), 205298.

(with V. Bach and J. Fröhlich),
The renormalization group approach to spectral
problems in QFT, Adv. in Math. 137 (1998), 299395.

(with Yu. N. Ovchinnikov),
The LandauGinzburg equation III.
Vortex dynamics,
Nonlinearity 11 No.5 (1998), 12771294.

(with Yu. N. Ovchinnikov),
Dynamics of localized
structures, Physica A 261 (1998)
143158.

(with Yu. N. Ovchinnikov),
On the GinzburgLandau and related equations,
Ecole Polytechnique, Exposé nº XX1 (1998),
113.

(with Yu. N. Ovchinnikov),
Longtime behaviour of
GinzburgLandau vortices,
Nonlinearity 11 No.5 (1998), 12951309.

(with M. Merkli),
A time dependent theory of
quantum resonance,
Comm. Math. Phys. 201 No.3 (1999), 549576.

(with V. Bach, J. Fröhlich and A. Soffer),
Positive commutators and
spectrum of the radiation Hamiltonian, Comm. Math. Phys.
207 (1999), 557587.

(with W. Hunziker and A. Soffer),
Minimal escape velocities revisited,
Comm. in PDE 24 (1999), 22792295.

(with V. Bach and J. Fröhlich),
Mathematical theory of nonrelativistic matter and radiation,
Comm. Math. Phys. 207 No.2 (1999), 249290.

(with Yu. N. Ovchinnikov),
Collapse in the nonlinear Schrödinger equation,
J. Exp. Theor. Phys. 89 (1999), 3540.

(with S. Gustafson),
The stability of magnetic
vortices,
Comm. Math. Phys. 210 No.2 (2000), 257276.

(with A. Laptev),
Global Fourier
integral operators and semiclassical asymptotics,
Reviews in Math. Phys. 12 (2000), 749766.

(with V. Bach and J. Fröhlich),
Return to equilibrium,
J. Math. Phys. 41 (2000) 39854060.

(with W. Hunziker),
Quantum manybody
problem,
J. Math. Phys. 41 (2000), 34483510.

(with Yu. N. Ovchinnikov),
Asymptotic behaviour of solutions of GinzburgLandau and related equations,
Rev. Math. Phys. 12 (2000), 287299.

(with W. Hunziker),
Timedependent scattering
theory of Nbody systems,
Rev. Math. Phys. 12 No. 8 (2000), 10331084.

PerronFrobenius theory and
symmetry of solutions to nonlinear PDE's,
Letters Math Phys., 53 No.4 (2000), 313320.

(with Yu. N. Ovchinnikov),
Optical bistability, Journal of Experimental and
Theorretical Physics 93 (2001), 10041016

Renormalization group approach in spectral analysis and problem of radiation, CMS
Notes 33 (3) (2001), 39

(with Yu. N. Ovchinnikov),
The energy of GinzburgLandau vortex, European Journal
of Applied Mathematics 13 (2002), 153178.

(with A. Soffer and L. Zielinski),
On the spectral properties of Hamiltonians without
conservation of the particle number,
J. Math. Phys. 43 (2002), 18441855.

(with B. Vasilijevic),
Mathematical theory of tunneling at positive temperatures,
Annales de l'Institut Henri Poincaré,
3 (2002), 141.

(with Yu. Ovchinnikov),
Collapse in the nonlinear Schrödinger equation,
JETP,
89 (2002), 3540.

(with Yu. Ovchinnikov),
Collape in critical nonlinear Schrödinger equation,
JETP Letters,
75 (2002), 357361.

(with V. Bach, T. Chen and J. Fröhlich),
Smooth Feshbach map,
J. Funct. Anal., 203 (2003), 4492.

(with Yu. Ovchinnikov),
Multiparameter family of collapsing solutions of the
critical nonlinear Schrödingers equation,
JETP. 97
(2003) 194203.

(with S. Gustafson),
Mathematical Concepts of Quantum Mechanics,
Springer, Universitext Series (2003).

(with J. Fröhlich and M. Merkli),
Ionization of
Atoms in a Thermal Field,
J. of Statistical Mechanics 116 (2004) 311359.

(with P. Bizon and Yu. Ovchinnikov),
Collapse of an instanton Nonlinearity
17 (2004) 11791191

(with F. Ting)
Pinning of magnetic vortices, Algebra and Analysis
16 (2004) 239268.

(with Yu. Ovchinnikov),
Symmetry Breaking Solutions to the GinzburgLandau Equations,
JETP (2004), 10901108.

(with J. Fröhlich, S. Gustafon and L. Jonsson)
Dynamics of solitary waves external potentials,
Commun Math Phys 250 (2004) 613642.

(with Zhou Gang),
Asymptotic stability of nonlinear Schrödinger equations with
potential, Reviews in Mathematical Physics, 17
(2005), 11931207.

(with S. Gustafson),
Mathematical Concepts of Quantum Mechanics
Springer, 2nd enlarged printing, 2006. (One new chapter and several new or enlarged sections.)

(with S. Gustafson), Dynamics of Magnetic Vortices,
Advances in Mathematics, 199 (2006) 448498.

(with S. Dejak), Long time dynamics of KdV solitary
waves over variable bottom,
Commun in Pure and Applied Mathematics
59 (2006) 869905.

(with Y. Strauss), Effective Dynamics of a Magnetic Vortex in a Local potential,
Journal of Nonlinear Science,
16 (2006) 123157.

(with J. Fröhlich, S. Gustafson and L. Jonsson)
Long time motion of NLS solitary waves in a confining potential,
Annales Henri Poincaré
7 (2006) 621660.

(with Zhou Gang) On Soliton Dynamics in Nonlinear Schrödinger Equations,
GAFA,
16 (2006) 13771390.

(with M. Merkli and M. Mück),
Instability of equilibrium states for systems coupled to reservoirs at different
temperatures,
Journal of Functional Analysis,
243 (2007) 87120.

(with V. Bach, T .Chen, J. Fröhlich)
The renormalized electron mass in nonrelativistic quantum electrodynamics,
Journal of Functional Analysis
243 2007 426535.

(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.)

(with M. Merkli and M. Mück) Theory of
nonequilibrium stationary states as a theory of resonances,
Annales Henri Poincaré
8 (2007), no. 8, 15391593.

(with Zhou Gang) Relaxation of solitons in nonlinear Schrödinger equations with potentials,
Adv Math,
216 (2007), no. 2, 443490.

(with S. Dejak, Zhou Gang and S. Wang), Blowup dynamics in nonlinear heat equations,
Adv Appl Math
40 (2008), 433481.

(with G. Berman and M. Merkli) Resonance Theory of Decoherence and Thermalization,
Annals Physics,
323(2) (2008) 373412.

(with J. Fröhlich and M. Griesemer) Spectral Theory for the Standard Model of NonRelativistic QED,
Comm. Math. Physics,
283(3) (2008) 613646.

(with G.P. Berman and M. Merkli), Dynamics of Collective Decoherence and Thermalization,
Annals of Physics
323(12) (2008) 30913312.

(with Zhou Gang), Neckpinching dynamics under mean curvature flow,
J Geometric Analysis
19 (1) (2009) 3680.

(with W. K. Abou Salem, J. Faupin and J. Fröhlich),
On the theory of resonances in nonrelativistic QED and related models,
Advances in Applied Mathematics
43 (2009), pp. 201230.

Ground State and Resonances in the Standard Model of the NonRelativistic QED,
J Statistical Mechanics,
134 Numbers 56, 2009, 899  939; arXiv:0806.3297.

(with J. Fröhlich and M. Griesemer) On Spectral Renormalization Group,
Rev Math Phys,
21 Issue: 4 (2009) pp. 511548; arXiv:0811.2616.

(with W. K. Abou Salem and J. Fröhlich),
Colliding solitons for the nonlinear Schrödinger equation,
Comm. Math. Physics,
291(1), 151176, 2009; arXiv:0804.1608.

(with S. Gustafson and T. Tzaneteas),
Statics and dynamics of magnetic vortices and of NielsenOlesen (Nambu) strings,
Journal of Mathematical Physics,
51, Issue 1, 2010.

(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.

(with D. Antonopoulou and G. Karali)
Stability of spheres under volumepreserving mean curvature flow,
Dynamics of PDE
7(4):327354, 2010.

(with T. Tzaneteas), On Abrikosov lattices, in
Spectral Theory and Geometric Analysis,
M. Braverman, et al, editors, in Contemporary Mathematics, AMS 2011.

(with J. Fröhlich and M. Griesemer)
Spectral Renormalization Group and Local Decay in the Standard Model of the nonrelativistic Quantum Electrodynamics,
Rev. Math. Phys.
23(2):179209, 2011. arXiv:0904.1014.

(with Yu. Ovchinnikov) Longtime relaxation processes in the nonlinear Schrödinger equation,
J. Exp. Theor. Phys,
112(3):469478, 2011.

(with Yu. Ovchinnikov) On collapse of wave maps,
Physica D: Nonlinear Phenomena
240(17):13111324, 2011.

(with B.L.G. Jonsson, Yu. Ovchinnikov and F.S.T. Ting)
Dynamics of breakup of multiple vortices in GrossPitaevskii equations of superfluids,
Journal of Mathematical Physics
52(9):093505109350516 (2011).

(with S. Gustafson), Mathematical Concepts of Quantum Mechanics
Springer, 3rd edition, 2011.

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. http://arxiv.org/abs/1110.3841.

(with T. Chen, J. Faupin and J. Fröhlich)
Local decay in nonrelativistic QED,
Comm. in Mathematical Physics
Volume 309, Number 2, Pages 543582, 2012
https://arxiv.org/abs/0911.0828v1.

(with T. Tzaneteas), Stability of Abrikosov lattices under gaugeperiodic perturbations,
Nonlinearity
25: 11871210, 2012.

(with S.I. Dejak, P.M. Lushnikov and Yu. Ovchinnikov)
On spectra of linearized operators for KellerSegel models of chemotaxis,
Physica D, 241, 12451254, 2012.
https://arxiv.org/abs/1110.6393.

(with T. Tzanateas) Abrikosov lattices at weak magnetic fields,
J. Functional Analysis,
263(3): 675702, 2012.
https:https://doi.org/10.1016/j.jfa.2012.04.018.

(with W. Kong) On collapse of surfaces under mean curvature flow, 2012.
https://arxiv.org/abs/1110.5378

(with J.F. Bony and J. Faupin) Maximal velocity of photons in nonrelativistic QED,
Adv in Mathematics 231(5):30543078, 2012.
https://doi.org/10.1016/j.aim.2012.07.019

(with V. Bach, Th. Chen, J. Faupin, J. Fröhlich)
Effective dynamics of an electron coupled to an external potential in nonrelativistic QED,
Annales Henri Poincaré, 14(6):15731597, 2013.
https://doi.org/10.1007/s0002301202228

(with J. Faupin)
On quantum Huygens principle and Rayleigh scattering, 2012, submitted.

(with J. Faupin)
Minimal Photon Velocity Bounds in Nonrelativistic Quantum Electrodynamics.
J. Stat Physics, 154(12): 5890, 2014.
https://doi.org/10.1007/s1095501308621

(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): 21552198, 2013.
https://doi.org/10.1080/03605302.2013.816857

(with T. Tzanateas)
On Abrikosov Lattice Solutions of the GinzburgLandau Equation.
Math. Model Nat. Phenom., 8(5): 190205, 2013.
https://doi.org/10.1051/mmnp/20138512

(with J. Faupin)
On Rayleigh scattering in nonrelativistic quantum electrodynamics.
Comm. Math. Phys., 328(3): 11991254, 2014.
https://doi.org/10.1007/s0022001418836

(with S. I. Dejak, D. Egli, P.M. Lushnikov)
On blowup dynamics in the KellerSegel model of chemotaxis. St. Petersburg
Math Journal, 25(4): 547574, 2013.
https://doi.org/10.1090/S106100222014013064

(with V. Bach, W. Pedra, M. Merkli)
Suppression of decoherence by periodic forcing.
J Stat Phys, 155(6): 12711298, 2014.
https://doi.org/10.1007/s1095501409528

(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.
https://doi.org/10.1142/9789814618144_0003

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.

Radiation and Scattering in Nonrelativistic Quantum Electrodynamics, in
Mathematical Physics: A Bridge Between Mathematics and Physics,
Springer, 2016.

(with Yu. Ovchinnikov)
Instability of a triangular Abrikosov lattice at values of the GinzburgLandau
parameter κ close to unity,
J Exp Theor Phys, 123(1): 119, 2016.
https://doi.org/10.1134/S1063776116050083

(with I. Anapolitanos)
Long range behavior of van der Waals forces,
Comm Pure Appl Math, 70(9): 16331671, 2017
https://doi.org/10.1002/cpa.21695

(with T. Tzaneteas)
On stability of Abrikosov vortex lattices,
Adv Math, 326: 108199, 2018
https://doi.org/10.1016/j.aim.2017.11.031

(with I. Chenn and P. Smyrnelis)
On Abrikosov Lattice Solutions of the GinzburgLandau Equations,
Math Phys Analy Geom, 21: 7, 2018
https://doi.org/10.1007/s110400179257x

(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.
https://doi.org/10.1090/memo/1210

(with V. Bach, S. Breteaux, T. Chen and J. Frölich)
The timedependent HartreeFockBogolubov equations for bosons,
J Evol Eqn, To Appear, 2019.
arXiv:1602.05171v2.

(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).

(with D. Chouchkov N.M. Ercolani and S. Rayan)
GinzburgLandau equations on Riemann surfaces of higher genus,
Annales IHP, in press, 2019.
https://doi.org/10.1016/j.anihpc.2019.04.002.

(with I. Chenn)
On the Bogolubovde Gennes equations.
Adv in Math, under revision, 2019.
arXiv:11701.06080v2.
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