Barry Simon
Encyclopedia
Barry Simon is an eminent American
mathematical physicist and the IBM
Professor
of Mathematics
and Theoretical Physics
at Caltech, known for his prolific contributions in spectral theory
, functional analysis
, and nonrelativistic
quantum mechanics
(particularly Schrödinger operators), including the connections to atomic and molecular physics
. He has authored more than 300 publications on mathematics and physics.
More particularly, his work has focused on broad areas of mathematical physics and analysis
covering: quantum field theory
, statistical mechanics
, Brownian motion
, random matrix theory
, general nonrelativistic quantum mechanics (including N-body
systems and resonance
s), nonrelativistic quantum mechanics in electric
and magnetic field
s, the semi-classical limit, the singular
continuous spectrum
, random and ergodic
Schrödinger operators, orthogonal polynomials
, and non-selfadjoint spectral theory.
and his Ph.D.
in Physics
at Princeton University
in 1970.
Following his doctoral studies, Simon took professorship at Princeton for many years, often working with colleague Elliott H. Lieb
on the Thomas
-Fermi
Theory and Hartree-Fock
Theory of atom
s in addition to phase transition
s and mentoring many of the same students as Lieb. He eventually was persuaded to take a post at Caltech, which he still holds.
A colleague of his, in a tale revealing of his brilliance, once stated:
Barry has always been remarkable for his vast knowledge of mathematics, so it was many years before I can recall ever telling him a published theorem he didn't already know. One day I saw Barry in Princeton shortly after a meeting and told him about an old inequality for PDEs, which, as I could tell from his intent look, was new to him. I said, "It seems to be useful. Do you want to see the proof?" His response "No, that's OK." Then he went to the board and wrote down a flawless proof on the spot.
There is a similar account of how the mathematical physics seminars at Princeton were conducted while Simon was in residence.
There was an outside speaker most of the time. Wigner would usually show up and ask his typical "Wignerian" questions. Barry would sit in the audience and write a paper. From time to time he would look up from his notes and ask a question that would unsettle most speakers: someone in the audience seemed to know more about what he was talking about than himself. Sometimes, at the end of the talk, Barry would go to the board and give his version of the proof, which was always slick.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematical physicist and the IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...
Professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
of Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and Theoretical Physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
at Caltech, known for his prolific contributions in spectral theory
Spectral theory
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of...
, functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, and nonrelativistic
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
(particularly Schrödinger operators), including the connections to atomic and molecular physics
Atomic, molecular, and optical physics
Atomic, molecular, and optical physics is the study of matter-matter and light-matter interactions on the scale of single atoms or structures containing a few atoms. The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of the...
. He has authored more than 300 publications on mathematics and physics.
More particularly, his work has focused on broad areas of mathematical physics and analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
covering: quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, Brownian motion
Brownian motion
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
, random matrix theory
Random matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable. Many important properties of physical systems can be represented mathematically as matrix problems...
, general nonrelativistic quantum mechanics (including N-body
Many-body problem
The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of a large number of interacting particles. Microscopic here implies that quantum mechanics has to be used to provide an accurate description of the system...
systems and resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
s), nonrelativistic quantum mechanics in electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s, the semi-classical limit, the singular
Mathematical singularity
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability...
continuous spectrum
Continuous spectrum
The spectrum of a linear operator is commonly divided into three parts: point spectrum, continuous spectrum, and residual spectrum.If H is a topological vector space and A:H \to H is a linear map, the spectrum of A is the set of complex numbers \lambda such that A - \lambda I : H \to H is not...
, random and ergodic
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
Schrödinger operators, orthogonal polynomials
Orthogonal polynomials
In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...
, and non-selfadjoint spectral theory.
Early career
Simon became a Putnam Fellow in 1965 at 19 years old. He received his A.B. in 1966 from Harvard CollegeHarvard College
Harvard College, in Cambridge, Massachusetts, is one of two schools within Harvard University granting undergraduate degrees...
and his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in Physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1970.
Following his doctoral studies, Simon took professorship at Princeton for many years, often working with colleague Elliott H. Lieb
Elliott H. Lieb
Elliott H. Lieb is an eminent American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis....
on the Thomas
Llewellyn Thomas
Llewellyn Hilleth Thomas was a British physicist and applied mathematician. He is best known for his contributions to atomic physics, in particular:...
-Fermi
Enrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...
Theory and Hartree-Fock
Fock
Fock can refer to:* Vladimir Fock , a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics** Fock space, an algebraic system used in quantum mechanics for a variable or unknown number of particles...
Theory of atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s in addition to phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
s and mentoring many of the same students as Lieb. He eventually was persuaded to take a post at Caltech, which he still holds.
Anecdotes
His status is legendary in mathematical physics and he is renowned for his ability to write scientific manuscripts "in five percent of the time ordinary mortals need to write such papers."A colleague of his, in a tale revealing of his brilliance, once stated:
Barry has always been remarkable for his vast knowledge of mathematics, so it was many years before I can recall ever telling him a published theorem he didn't already know. One day I saw Barry in Princeton shortly after a meeting and told him about an old inequality for PDEs, which, as I could tell from his intent look, was new to him. I said, "It seems to be useful. Do you want to see the proof?" His response "No, that's OK." Then he went to the board and wrote down a flawless proof on the spot.
There is a similar account of how the mathematical physics seminars at Princeton were conducted while Simon was in residence.
There was an outside speaker most of the time. Wigner would usually show up and ask his typical "Wignerian" questions. Barry would sit in the audience and write a paper. From time to time he would look up from his notes and ask a question that would unsettle most speakers: someone in the audience seemed to know more about what he was talking about than himself. Sometimes, at the end of the talk, Barry would go to the board and give his version of the proof, which was always slick.
Family
Barry is married to Martha (née Katzin) who obtained her PhD in Mathematics from Princeton Graduate School. They married in January 1971, shortly after Barry became an Assistant Professor at Princeton. Martha has taught in a variety of schools in the New York/New Jersey area and California and is currently a Lecturer in Mathematics at CalState Northridge. Barry and Martha have five children and, so far, thirteen grandchildren.Quotes
- "To first approximation, the human brain is a harmonic oscillatorHarmonic oscillatorIn classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....
." Professor Simon made this remark in private conversation to Charles FeffermanCharles FeffermanCharles Louis Fefferman is an American mathematician at Princeton University. His primary field of research is mathematical analysis....
while walking around the Princeton campus. - "If you don't know how to add fractions, you don't know how to think." This was stated by Professor Simon while lecturing to a freshman mathematics class at the California Institute of TechnologyCalifornia Institute of TechnologyThe California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
.
Selected publications
- Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory, Annals of Math. 97 (1973), 247-274
- (with M. Reed) Methods of Modern Mathematical Physics, Vol. I: Functional Analysis, Academic Press, 1972; Vol. II: Fourier Analysis, Self-Adjointness, Academic Press, 1975; Vol. III: Scattering Theory, Academic Press, 1978; Vol. IV: Analysis of Operators, Academic Press, 1977
- (with F. Guerra and L. Rosen) The P(φ)2 quantum theory as classical statistical mechanics, Annals of Math. 101 (1975), 111-259
- (with E. Lieb) The Thomas-Fermi theory of atoms, molecules and solids, Advances in Math. 23 (1977), 22-116
- (with J. Fröhlich and T. Spencer) Infrared bounds, phase transitions and continuous symmetry breaking, Commun. Math. Phys. 50 (1976), 79-85
- (with P. Perry and I. Sigal) Spectral analysis of multiparticle Schrödinger operators, Annals of Math. 114 (1981), 519-567
- (with M. Aizenman) Brownian motion and Harnack's inequality for Schrödinger operators, Commun. Pure Appl. Math.Communications on Pure and Applied MathematicsCommunications on Pure and Applied Mathematics is a scientific journal which is associated with the Courant Institute of Mathematical Sciences. It publishes original research originating from or solicited by the institute, typically in the fields of applied mathematics, mathematical analysis, or...
35 (1982), 209-273 - Semiclassical analysis of low lying eigenvalues, II. Tunneling, Annals of Math. 120 (1984), 89-118
- Holonomy, the quantum adiabatic theorem and Berry's phase, Phys. Rev. Lett. 51 (1983), 2167–2170
- (with T. Wolff) Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Commun. Pure Appl. Math. 39 (1986), 75-90
- Operators with singular continuous spectrum: I. General operators, Annals of Math. 141 (1995), 131-145