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Barry Martin Simon (born 16 April 1946) is an American
mathematical physicist Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...
and was the IBM professor of Mathematics and Theoretical Physics at
Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
, known for his prolific contributions in
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 ...
, functional analysis, and nonrelativistic quantum mechanics (particularly Schrödinger
operators Operator may refer to: Mathematics * A symbol indicating a mathematical operation * Logical operator or logical connective in mathematical logic * Operator (mathematics), mapping that acts on elements of a space to produce elements of another ...
), including the connections to atomic and molecular physics. He has authored more than 400 publications on mathematics and physics. His work has focused on broad areas of mathematical physics and
analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...
covering: quantum field theory,
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
,
Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position ins ...
,
random matrix theory In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...
, general nonrelativistic quantum mechanics (including
N-body In physics and astronomy, an ''N''-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity (see ''n''-body problem for other applications). ''N''-body simulations ar ...
systems and resonances), nonrelativistic quantum mechanics in
electric Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
and magnetic fields, the semi-classical limit, the singular
continuous spectrum In physics, a continuous spectrum usually means a set of attainable values for some physical quantity (such as energy or wavelength) that is best described as an interval of real numbers, as opposed to a discrete spectrum, a set of attainable ...
, random and ergodic Schrödinger operators, orthogonal polynomials, and non- selfadjoint spectral theory.


Early life

Barry Simon's mother was a school teacher, his father was an accountant. Simon attended James Madison High School in Brooklyn.


Career

During his high school years, Simon started attending college courses for highly gifted pupils at Columbia University. In 1962, Simon won a MAA mathematics competition. '' The New York Times'' reported that in order to receive full credits for a faultless test result he had to make a submission with MAA. In this submission he proved that one of the problems posed in the test was ambiguous. In 1962, Simon entered
Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher l ...
with a stipend. He became a
Putnam Fellow The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (rega ...
in 1965 at 19 years old. He received his AB in 1966 from Harvard College and his PhD in Physics at Princeton University in 1970, supervised by Arthur Strong Wightman. His dissertation dealt with ''Quantum mechanics for Hamiltonians defined as quadratic forms''. Following his doctoral studies, Simon took a professorship at Princeton for several years, often working with colleague
Elliott H. Lieb Elliott Hershel Lieb (born July 31, 1932) is an American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis. Lieb ...
on the
Thomas Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (disambiguation) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the A ...
-
Fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and t ...
Theory and
Hartree The hartree (symbol: ''E''h or Ha), also known as the Hartree energy, is the unit of energy in the Hartree atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is = The hartree energy is approxima ...
- Fock Theory of atoms in addition to phase transitions and mentoring many of the same students as Lieb. He eventually was persuaded to take a post at
Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
, from which he retired in the summer of 2016. 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 former graduate student of Simon's, in a tale revealing of his brilliance, once stated:


Honors and awards

*1974: Invited Speaker at the International Congress of Mathematicians in Vancouver *1981: Elected fellow of the
American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of k ...
*1990: Elected correspondent member of the Austrian Academy of Sciences *2005: Elected fellow of the
American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
*2012: Elected fellow of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
*2012: Awarded the
Henri Poincaré Prize The Henri Poincaré Prize is awarded every three years since 1997 for exceptional achievements in mathematical physics and foundational contributions leading to new developments in the field. The prize is sponsored by the Daniel Iagolnitzer Founda ...
*2015: Awarded the
Bolyai Prize The International János Bolyai Prize of Mathematics is an international prize founded by the Hungarian Academy of Sciences. The prize is named after János Bolyai and is awarded every five years to mathematicians for monographs with important new r ...
of the Hungarian Academy of Sciences *2016: Awarded the Steele Prize for Lifetime achievements *2018: Dannie Heineman Prize for Mathematical Physics from the
American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of k ...
*2019: Elected to the National Academy of Sciences


Selected publications


Articles

*Resonances in ''n''-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory, Annals of Mathematics 97 (1973), 247–274 (over 700 citations) *(with F. Guerra and L. Rosen) The P(φ)2 quantum theory as classical statistical mechanics, Annals of Mathematics 101 (1975), 111–259 *(with E. Lieb) The Thomas-Fermi theory of atoms, molecules and solids,
Advances in Mathematics ''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed a ...
23 (1977), 22–116 (over 700 citations) *(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. M. Sigal) Spectral analysis of multiparticle Schrödinger operators, Annals of Mathematics 114 (1981), 519–567 * Schrödinger semigroups, Bulletin of the American Mathematical Society 7 (1982), 447–526 (over 1500 citations) *(with M. Aizenman
Brownian motion and Harnack's inequality for Schrödinger operators
Commun. Pure Appl. Math. 35 (1982), 209–273 (over 600 citations) *Holonomy, the quantum adiabatic theorem and Berry's phase, Phys. Rev. Lett. 51 (1983), 2167–2170 (over 2050 citations) *(with Joseph E. Avron and Ruedi Seiler) Homotopy and quantization in condensed matter physics, Phys. Rev. Lett. 51 (1983) 51–53 (over 600 citations) *Semiclassical analysis of low lying eigenvalues, II. Tunneling, Annals of Mathematics 120 (1984), 89–118 *(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 Mathematics 141 (1995), 131–145


Books

* ''Quantum mechanics for hamiltonians defined as quadratic forms.'' Princeton University Press, Princeton NJ 1971, . * with Michael C. Reed: ''Methods of Modern Mathematical Physics.'' 4 vols. Academic Press, New York, NY etc. 1972–1978; ** vol. 1: ''Functional Analysis.'' 1972, ; ** vol. 2: ''Fourier Analysis, Self-Adjointness.'' 1975, ; ** vol. 3: ''Scattering Theory.'' Academic Press, 1979, ; ** vol. 4: ''Analysis of Operators.'' Academic Press, 1978, . * ''The \Phi^2 Euclidean (Quantum) Field Theory.'' Princeton University Press, Princeton NJ 1974, . * as editor with Elliott H. Lieb and Arthur S. Wightman: ''Studies in mathematical physics. Essays in Honor of Valentine Bargmann.'' Princeton University Press, Princeton NJ 1976, , contributions by Barry Simon: ** pp. 305–326: ''On the number of bound states of two body Schrödinger operators – a review.'
online PDF; 377 kB.
** pp. 327–349: ''Quantum dynamics: from automorphism to hamiltonian.'
online PDF; 573 kB.
* ''Functional integration and quantum physics'' (= ''Pure and Applied Mathematics.'' 86). Academic Press, New York NY etc. 1979, ISBN 0-12-644250-9 (2nd edition: American Mathematical Society, Providence RI 2005, ). * ''Trace Ideals and their applications'' (= ''London Mathematical Society. Lecture Note Series.'' 35). Cambridge University Press, Cambridge etc. 1979, (2nd edition: (= ''Mathematical Surveys and Monographs.'' 120). American Mathematical Society, Providence RI 2005, ). * with Hans L. Cycon, Richard G. Froese, and Werner Kirsch: ''Schrödinger Operators.'' Springer, Berlin etc. 1987, (corrected and extended 2nd printing: Springer 2008, ). * ''The Statistical mechanics of lattice gases.'' vol. 1. Princeton University Press, Princeton NJ 1993, . * ''Orthogonal polynomials on the unit circle'' (= ''American Mathematical Society Colloquium Publications.'' 54, 1–2). 2 vols. American Mathematical Society, Providence RI 2005; ** vol. 1: ''Classical theory.'' 2005, ; ** vol. 2: ''Spectral theory.'' 2005, . * ''Convexity. An analytic viewpoint'' (= ''Cambridge Tracts in Mathematics.'' 187). Cambridge University Press, Cambridge etc. 2011, . * ''Szegő´s theorem and its descendants. Spectral theory for L^2 perturbations of orthogonal polynomials.'' Princeton University Press, Princeton NJ 2011, .
''A Comprehensive Course in Analysis''
4 vols. with vol. 2 published in 2 parts, American Mathematical Society, Providence RI 2015, . ** vol. 1: ''Real Analysis.'' ** vol. 2A: ''Basic Complex Analysis.'' ** vol. 2B: ''Advanced Complex Analysis.'' ** vol. 3: ''Harmonic Analysis.'' ** vol. 4: ''Operator Theory.''
''Loewner's theorem on monotone matrix functions''
Springer, 2019,


See also

* Simon problems


References


Further reading


Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday: Ergodic Schrödinger Operators, Singular Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory


External links





* * ttps://scholar.google.com/citations?user=OM0D_3wAAAAJ&oi=ao Publications and citationsat Google Scholar * * (KBS Fest at ISI Bangalore) * * * * * * Caltech Heritage Project, interviews from 2021 & 2022 ** (interview Thursday Nov. 18, 2021) ** ** (interview Friday Nov. 26, 2021) ** ** (interview Thursday Dec. 2, 2021) ** ** (interview Thursday Dec. 9, 2021) ** ** (interview Wednesday Dec. 15, 2021) ** ** (interview Thursday Dec. 23, 2021) ** (interview March 7, 2022) {{DEFAULTSORT:Simon, Barry 1946 births Living people 20th-century American mathematicians 21st-century American mathematicians 21st-century American physicists Jewish American physicists Harvard University alumni Princeton University alumni Princeton University faculty California Institute of Technology faculty Putnam Fellows Fellows of the American Mathematical Society Mathematical physicists Operator theorists James Madison High School (Brooklyn) alumni Mathematicians from New York (state) Members of the United States National Academy of Sciences Fellows of the American Physical Society 21st-century American Jews