Israel Michael Sigal

Israel Michael Sigal's AcademicInfluence.com Rankings

Mathematics

#1055

World Rank

#1808

Historical Rank

Group Theory

#96

World Rank

#122

Historical Rank

Number Theory

#248

World Rank

#315

Historical Rank

Algebra

#233

World Rank

#339

Historical Rank

mathematics Degrees

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Mathematics

Why Is Israel Michael Sigal Influential?

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According to Wikipedia, Israel Michael Sigal is a Canadian mathematician specializing in mathematical physics. He is a professor at the University of Toronto Department of Mathematics. He was an invited speaker at International Congress of Mathematicians, Kyoto—1990 and in International Congress on Mathematical Physics, Lausanne—1979, W. Berlin—1981, Marselle—1986.

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Israel Michael Sigal's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Introduction to Spectral Theory (1996) (672)
Introduction to Spectral Theory: With Applications to Schrödinger Operators (1995) (450)
QUANTUM ELECTRODYNAMICS OF CONFINED NONRELATIVISTIC PARTICLES (1998) (305)
Spectral analysis of N-body Schrodinger operators * (1981) (261)
Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field (1999) (236)
Return to equilibrium (2000) (203)
Renormalization Group Analysis of Spectral Problems in Quantum Field Theory (1998) (192)
The N-particle scattering problem: asymptotic completeness for short-range systems (1987) (190)
Solitary Wave Dynamics in an External Potential (2003) (175)
The quantum N-body problem (2000) (157)
Mathematical Concepts of Quantum Mechanics (2006) (144)
Geometric methods in the quantum many-body problem. Nonexistence of very negative ions (1982) (118)
Number of bound states of three-body systems and Efimov's effect (1979) (113)
Asymptotics of the ground state energies of large Coulomb systems (1993) (97)
Smooth Feshbach map and operator-theoretic renormalization group methods (2003) (96)
Positive Commutators and the Spectrum¶of Pauli--Fierz Hamiltonian of Atoms and Molecules (1999) (93)
Mathematical theory of nonrelativistic matter and radiation (1995) (89)
MINIMAL ESCAPE VELOCITIES (2000) (89)
Non-linear wave and Schrödinger equations (1993) (87)
A Time-Dependent Theory of Quantum Resonances (1999) (81)
Long Time Motion of NLS Solitary Waves in a Confining Potential (2005) (70)
The renormalized electron mass in non-relativistic quantum electrodynamics (2005) (64)
Long-range many-body scattering (1990) (63)
Time-Dependent Scattering Theory of N-Body Quantum Systems (2000) (58)
Spectral Theory for the Standard Model of Non-Relativistic QED (2006) (58)
The Stability of Magnetic Vortices (1999) (57)
Resonance theory of decoherence and thermalization (2007) (56)
Bound on the ionization energy of large atoms (1990) (50)
Effective dynamics of magnetic vortices (2003) (49)
Decoherence and thermalization. (2006) (49)
Asymptotic Neutrality of Large- Z Ions (1984) (48)
How many electrons can a nucleus bind (1984) (47)
Ginzburg-Landau equation I. Static vortices (1997) (47)
Approximate neutrality of large-Z ions (1988) (45)
Geometric methods in quantum many-body problem (1982) (43)
Instability of equilibrium states for coupled heat reservoirs at different temperatures (2005) (42)
Theory of Non-Equilibrium Stationary States as a Theory of Resonances (2006) (42)
Space-time picture of semiclassical resonances (1992) (41)
Long-time behaviour of Ginzburg-Landau vortices (1998) (38)
Ground State and Resonances in the Standard Model of the Non-Relativistic QED (2008) (38)
The Ginzburg-Landau equation III. Vortex dynamics (1998) (37)
Complex transformation method and resonances in one-body quantum systems (1984) (37)
Description of the spectrum of the energy operator of quantum-mechanical systems that is invariant with respect to permutations of identical particles (1970) (37)
GLOBAL FOURIER INTEGRAL OPERATORS AND SEMICLASSICAL ASYMPTOTICS (2000) (36)
Asymptotic completeness of N-particle long-range scattering (1994) (36)
Statics and dynamics of magnetic vortices and of Nielsen–Olesen (Nambu) strings (2010) (35)
Sharp exponential bounds on resonances states and width of resonances (1988) (34)
Neck Pinching Dynamics under Mean Curvature Flow (2007) (33)
Effective Dynamics of an Electron Coupled to an External Potential in Non-relativistic QED (2012) (32)
Maximal velocity of photons in non-relativistic QED (2011) (31)
On Rayleigh Scattering in Non-Relativistic Quantum Electrodynamics (2012) (30)
Scattering Theory for the Wave Equation on Non-Compact Manifolds (1992) (30)
Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow (2011) (30)
Geometric theory of Stark resonances in multielectron systems (1988) (29)
The Stability of Magnetic VorticesRID="*"ID="*"Research on this paper was supported by NSERC under grant N7901 (2000) (28)
Scattering Theory for Many-Body Quantum Mechanical Systems--Rigorous Results (1983) (28)
Dynamics of collective decoherence and thermalization (2008) (27)
Blow-up in nonlinear heat equations (2006) (27)
Magnetic Vortices, Abrikosov Lattices, and Automorphic Functions (2013) (26)
Ionization of Atoms in a Thermal Field (2004) (26)
On soliton dynamics in nonlinear schrödinger equations (2006) (26)
Local Decay in Non-Relativistic QED (2009) (26)
On the discrete spectrum of the Schrödinger operators of multiparticle systems (1976) (26)
ON SPECTRAL RENORMALIZATION GROUP (2008) (25)
Colliding Solitons for the Nonlinear Schrödinger Equation (2008) (25)
Long‐time dynamics of KdV solitary waves over a variable bottom (2004) (23)
The Hartree-von Neumann limit of many body dynamics (2009) (23)
Semiclassical theory of shape resonances in quantum mechanics (1989) (23)
On the spectral properties of Hamiltonians without conservation of the particle number (2002) (22)
On long-range scattering (1990) (20)
Collapse of an instanton (2003) (20)
Symmetry-breaking solutions of the Ginzburg-Landau equation (2004) (20)
Mathematical foundations of quantum scattering theory for multiparticle systems (1978) (20)
Asymptotic completeness for $N \leq 4$ particle systems with the Coulomb-type interactions (1993) (19)
Shape resonances in quantum mechanics (1987) (19)
Stark effect in multielectron systems: Non-existence of bound states (1989) (18)
The energy of Ginzburg–Landau vortices (2002) (18)
Minimal Photon Velocity Bounds in Non-relativistic Quantum Electrodynamics (2014) (17)
Stability of Abrikosov lattices under gauge-periodic perturbations (2011) (16)
On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations (2009) (15)
On stability of Abrikosov vortex lattices (2013) (15)
Renormalization Group and Problem of Radiation (2011) (15)
On the theory of resonances in non-relativistic quantum electrodynamics and related models (2009) (15)
Stability of spheres under volume-preserving mean curvature flow (2010) (15)
Geometric parametrices and the many-body Birman-Schwinger principle (1983) (15)
Pinning of magnetic vortices by an external potential (2005) (15)
On quantum mechanics of many-body systems with dilation-analytic potentials (1978) (14)
Long‐Range Behavior of the van der Waals Force (2017) (13)
On Collapse of Wave Maps (2009) (13)
On spectra of linearized operators for Keller–Segel models of chemotaxis (2011) (12)
Maximal Speed for Macroscopic Particle Transport in the Bose-Hubbard Model. (2021) (12)
On blowup dynamics in the Keller-Segel model of chemotaxis (2013) (12)
Effective Dynamics of a Magnetic Vortex in a Local Potential (2006) (11)
Lectures on large Coulomb systems (1995) (11)
The time-dependent Hartree–Fock–Bogoliubov equations for Bosons (2016) (11)
Suppression of Decoherence by Periodic Forcing (2014) (11)
Asymptotic completeness of short-range many-body systems (1986) (10)
On the theory of resonances in non-relativistic QED and related models (2007) (10)
Positive commutators and spectrum of nonrelativistic QED (1997) (10)
Analytic properties of the scattering matrix of many particle systems (1986) (10)
Dynamics of localized structures (1998) (9)
Nonlinear wave equations: constraints on periods and exponential bounds for periodic solutions (1997) (8)
Maximal speed of quantum propagation (2020) (8)
Abrikosov Vortex Lattices at Weak Magnetic Fields (2011) (8)
Mathematical theory of single channel systems. Analyticity of scattering matrix (1982) (8)
Ginzburg–Landau equations on Riemann surfaces of higher genus (2017) (8)
On quantum Huygens principle and Rayleigh scattering (2012) (8)
On Stability of Abrikosov Lattices (2013) (7)
On Derivation of the Poisson–Boltzmann Equation (2020) (7)
Mathematical theory of radiation (1997) (7)
Comment on the photon number bound and Rayleigh scattering (2012) (7)
The Energy Asymptotics of Large Coulomb Systems (1992) (7)
On Effective PDEs of Quantum Physics (2019) (7)
Hamiltonian Dynamics of a Particle Interacting with a Wave Field (2012) (7)
On the Bogolubov-de Gennes Equations (2017) (6)
On Lieb–Robinson Bounds for the Bose–Hubbard Model (2021) (6)
Abrikosov Lattice Solutions of the Ginzburg-Landau Equations of Superconductivity (2009) (5)
The general theory of -body quantum systems (1995) (5)
Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits (2009) (5)
Stability of spherical collapse under mean curvature flow (2011) (5)
On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations (2018) (4)
Long-Time Behaviour of Time-Dependent Density Functional Theory (2019) (4)
Theory of Non-Equilibrium Sationary States as a Theory of Resonances. Existence and Properties of NESS (2006) (4)
Long Range Behaviour of van der Waals Force (2012) (4)
ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF GINZBURG–LANDAU AND RELATED EQUATIONS (2000) (4)
The Effective Dynamics of the Volume Preserving Mean Curvature Flow (2018) (4)
Absence of singular continuous spectrum in $N$-body quantum systems (1980) (4)
Asymptotic completeness of many-body short-range systems (1984) (3)
Scattering theory for N-body systems (1983) (3)
Spectral Deformation of Schrödinger Operators (1996) (3)
Perturbation Theory: Feshbach-Schur Method (2020) (3)
Asymptotic completeness of multiparticle scattering (1987) (3)
Analysis of the Feshbach-Schur method for the planewave discretizations of Schr{ö}dinger operators (2020) (3)
On the point spectrum of the Schrödinger operators of multiparticle systems (1976) (2)
Vortex lattices and the Bogoliubov-de Gennes equations (2020) (2)
On propagation of information in quantum many-body systems (2022) (2)
Number of eigenvalues of many-body Hamiltonians and Efimov's effect (1980) (2)
Spectrum and Dynamics (2020) (2)
Long-time relaxation processes in the nonlinear Schrödinger equation (2011) (2)
Mathematical Theory of Quantum Tunneling Decay at Positive Temperature (2002) (2)
From Gamow States to Resonances for Schrödinger Operators (2004) (2)
Scattering States (2020) (2)
Perron–Frobenius Theory and Symmetry of Solutions to Nonlinear PDE's (2000) (2)
Maximal Speed of Propagation in Open Quantum Systems (2022) (2)
Vortex lattice solutions of the ZHK Chern–Simons equations (2019) (2)
Maximal Speed of Quantum Propagation for the Hartree equation (2023) (2)
Multiparameter family of collapsing solutions to the critical nonlinear Schrödinger equation in dimension D=2 (2003) (2)
Lectures on Mean Curvature Flow (MAT 1063 HS) (2013) (2)
Analysis of the Feshbach–Schur method for the Fourier spectral discretizations of Schrödinger operators (2020) (1)
Collapse in the nonlinear Schrödinger equation of critical dimension {σ=1, D=2} (2002) (1)
Theory of Quantum Resonances I: The Aguilar-Balslev-Combes-Simon Theorem (1996) (1)
The Essential Spectrum: Weyl’s Criterion (1996) (1)
Radiation and Scattering in Non-relativistic Quantum Electrodynamics (2016) (1)
On Blowup in Nonlinear Heat Equations (2011) (1)
On Rayleigh Scattering in Non-Relativistic Quantum Electrodynamics (2014) (1)
Mean curvature flow of a hyperbolic surface (2011) (1)
The Feshbach–Schur map and perturbation theory (2021) (1)
Nonlinear Dynamics and Renormalization Group (2001) (1)
Dynamics of breakup of multiple vortices in Gross-Pitaevskii equations of superfluids (2011) (1)
The Feynman Path Integral (2020) (1)
Relatively Compact Operators and the Weyl Theorem (1996) (1)
Scattering Theory in Many-Body Quantum Systems. Analyticity of the Scattered Matrix (1981) (1)
Instability of a triangular Abrikosov lattice at values of the Ginzburg–Landau parameter κ close to unity (2016) (1)
Mathematical questions of quantum many-body theory (1987) (1)
The Effective Dynamics of the Volume Preserving Mean Curvature Flow (2018) (0)
Semiclassical Analysis of Schrödinger Operators I: The Harmonic Approximation (1996) (0)
Observables (2020) (0)
Quasibound states and the finiteness of the discrete spectrum (1983) (0)
Ginzburg-Landau Equations on Non-compact Riemann Surfaces (2022) (0)
Many-particle Systems (2003) (0)
Dynamics (2020) (0)
Comments on Missing Topics, Literature, and Further Reading (2003) (0)
On dynamics of a soliton in an external potential (2003) (0)
Riesz Projections and Isolated Points of the Spectrum (1996) (0)
Instability of quasibound-state and embedded eigenvalues (1983) (0)
Self-Consistent Approximations (2020) (0)
Renormalization Group (2020) (0)
Operators on Hilbert Spaces (1996) (0)
Instability of electroweak homogeneous vacua in strong magnetic fields (2022) (0)
Positive commutator methods for nonlinear wave equations. Constraints on periods and exponential decay of periodic solutions (1997) (0)
A P ] 6 S ep 2 00 6 Blow-up in Nonlinear Heat Equations (2008) (0)
Mathematical Supplement: Elements of Operator Theory (2020) (0)
Spectral Deformation Theory (1996) (0)
On long time dynamics for KdV solitons (2003) (0)
Two-space scattering theory (1983) (0)
Special Cases and Extensions (2020) (0)
Ginzburg – Landau equations on Riemann surfaces , April 23 , 2019 2 1 The Ginzburg – Landau Equations (2019) (0)
A pr 2 00 8 Dynamics of Collective Decoherence and Thermalization (2008) (0)
Theory of Quantum Resonances II: The Shape Resonance Model (1996) (0)
Mathematical questions of quantum mechanics of many-body systems (1980) (0)
The prefactor in the expression of the decay rate of a metastable state (1991) (0)
Semiclassical Analysis of Schrödinger Operators II: The Splitting of Eigenvalues (1996) (0)
Quantization (2020) (0)
Semi-Classical Analysis (2020) (0)
02 20 7 v 1 2 2 Fe b 20 07 Resonance Theory of Decoherence and Thermalization (2008) (0)
Theory of Quantum Resonances III: Resonance Width (1996) (0)
The Energy Asymptotics of Large Coulomb Systems Introduction. Consider a Molecule Consisting of N Quantized Electrons at Positions (2007) (0)
Partial Differential Equations Ii Mat1061 * (0)
Physical Background (2020) (0)
Uncertainty Principle and Stability of Atoms and Molecules (2020) (0)
Resonances (2021) (0)
The Geometry of a Hilbert Space and Its Subspaces (1996) (0)
Propagation of information in long-range quantum systems (2023) (0)
Quantum Nontrapping Estimates (1996) (0)
Other Topics in the Theory of Quantum Resonances (1996) (0)
General Theory of Many-Particle Systems (2020) (0)
0 30 90 53 v 1 2 3 Se p 20 03 Solitary wave dynamics in an external potential (2008) (0)
Optical bistability (2001) (0)
Suppression of Decoherence by Periodic Forcing (2014) (0)
The Ginzburg-Landau Equation Ii. The Energy Of Vortex Configurations (1997) (0)
Quantum Electro-Magnetic Field – Photons (2020) (0)
RENORMALIZATION GROUP APPROACH IN SPECTRAL ANALYSIS AND PROBLEM OF RADIATION (2000) (0)
Quasi-classical Analysis (2012) (0)
Standard Model of Non-relativistic Matter and Radiation (2020) (0)
Long Time Motion of NLS Solitary Wavesin a Con ning PotentialB (2009) (0)
Perturbation Theory: Relatively Bounded Perturbations (1996) (0)
Bound States and Variational Principle (2020) (0)
Differential equations of quantum mechanics (2022) (0)
Locally Compact Operators and Their Application to Schrödinger Operators (1996) (0)
Light cones for open quantum systems (2023) (0)
Self-Adjointness: Part 2. The Kato-Rellich Theorem (1996) (0)
O ct 2 00 6 Blow-up in Nonlinear Heat Equations (2008) (0)
Effective Dynamics of an Electron Coupled to an External Potential in Non-relativistic QED (2012) (0)
The Uncertainty Principle (2003) (0)
Addendum “Complex transformation method and resonances in one-body quantum systems” (1984) (0)
“Soft” modes of the excitation spectrum constructed on perturbations of the Abrikosov lattice with a single flux quantum in the unit cell (2017) (0)
Mathematical Supplement: Spectral Analysis (2012) (0)
The Spectrum of Linear Operators and Hilbert Spaces (1996) (0)
On the Hartree-Fock-Bogoliubov equations (2018) (0)
Quantum Electro-Magnetic Field - Photons (2012) (0)
The Second Quantization (2020) (0)
The General Theory of Spectral Stability (1996) (0)
Theory of Radiation (2020) (0)
FORMATION OF PROFESSIONAL COMPETENCIES SOLOISTS-VOCALISTS IN THE PROCESS OF TRAINING AT THE UNIVERSITY (2020) (0)
Boundary values of the resolvent. The general case (1983) (0)
Open Quantum Systems (2020) (0)
A P ] 2 8 A pr 1 99 9 The stability of magnetic vortices ∗ (2000) (0)
Born–Oppenheimer Approximation and Adiabatic Dynamics (2020) (0)
The low temperature creep of the vortex lattice (1994) (0)
Existence of Atoms and Molecules (2020) (0)
Quantum Statistics (2020) (0)
Exponential Decay of Eigenfunctions (1996) (0)
Minimal Photon Velocity Bounds in Non-relativistic Quantum Electrodynamics (2013) (0)
Self-Adjointness: Part 1. The Kato Inequality (1996) (0)
Supplement: Renormalization Group (2003) (0)
Many-body scattering problem (1989) (0)
On the Ginzburg-Landau and related equations (1998) (0)
Boundary values of the resolvent. General single-channel case (1983) (0)
Reduction to diagonal form of the Schrödinger operator in Fok space (1972) (0)
Non-dilation-analytic potentials (1983) (0)
On dynamics of a NLS-soliton in an external potential (2003) (0)
Comments on Literature, and Further Reading (2020) (0)
Mathematical Supplement: The Calculus of Variations (2020) (0)
Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications (2018) (0)
General Characteristics of Non-Linear Dynamics (2020) (0)
Introduction to Quantum Field Theory (2003) (0)
Quantum Electrodynamics of Non-relativistic Particles: the Theory of Radiation (2003) (0)
0 60 30 06 v 1 1 M ar 2 00 6 Theory of Non-Equilibrium Stationary States as a Theory of Resonances . Existence and Properties of NESS (2009) (0)
Self-Adjoint Operators (1996) (0)
0 A pr 2 00 8 COLLIDING SOLITONS FOR THE NONLINEAR SCHRÖDINGER EQUATION (2021) (0)
“Soft” modes of the excitation spectrum constructed on perturbations of the Abrikosov lattice with a single flux quantum in the unit cell (2017) (0)
Local Decay in Non-Relativistic QED (2011) (0)
Near-Pulse Solutions of the FitzHugh–Nagumo Equations on Cylindrical Surfaces (2020) (0)
On Derivation of the Poisson–Boltzmann Equation (2020) (0)
Equationswith Potential (2022) (0)
Instability of a triangular Abrikosov lattice at values of the Ginzburg–Landau parameter κ close to unity (2016) (0)
Collapse in the nonlinear Schrödinger equation (1999) (0)

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Published Works

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What Schools Are Affiliated With Israel Michael Sigal?

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