Madan Lal Mehta

Madan Lal Mehta (1932 - December 10th, 2006) is a theoretical Physicien of Indian origin deceased today.

Course

Deceased with Udaipur, Indian city of the state of the the Rajasthan, Madan Lal Mehta was one of the pioneers of the theory of the random Matrices. Physicist theorist, former Research director at CNRS, it made most of his career to the Service of theoretical physics of ECA to Saclay.

Born in Relmagra, Udaipur on December 24th, 1932, Madan Lal Mehta off obtained in 1956 its Master Science in mathematics of the University of the Rajasthan, Jaipur. After two years with Touched Institute for Fundamental Research of Bombay, it came to France in November 1958 in the Service from Mathematical physics (today Service of Theoretical physics) from the Center from Nuclear Studies from Saclay.

Madan Lal Mehta remained in 1962-1963 in Princeton, establishing a durable collaboration with F.J. Dyson, which had generalized the original model of E.P. Wigner. It turned over to India to the University of Delhi before remaining again in the United States in 1966-1967 at the University of Princeton and the National laboratory of Argonne. It returned to France to the Service of Theoretical physics of the ECA Saclay in September 1967 when it remained until the end of its career and its return in its native land in January 2005. Recruited at CNRS in 1970, it acquired French nationality in 1971. Madan Lal Mehta made also various scientific stays in Mexico, in Australia, in Japan and in China. It practiced to differing degree, in addition to the Hindi and various languages of India, English, French, Russian, Japanese and Chinese.

Work in physics

M.L. Mehta is universally known for its work on the random matrices. It developed its work during the years 1959-1961 in Saclay, in the service directed by Claude Bloch. Considered since 1928 per John Wishart in statistics, the random Matrices were introduced in nuclear physics in 1951 per Eugene P. Wigner who put forth the assumption that energies of excitation of the heavy cores behave as the eigenvalues of a matrix whose elements are distributed randomly. The experimental and numerical results accumulated during the Fifties corroborated the advanced assumption without one managing to determine the distribution of these eigenvalues. In two articles published in 1960, Madan Lal Mehta and Michel Gaudin obtained the first analytical results, providing the foundations of the method known as of the orthogonal polynomials (of which the development allowed to determine exactly the statistical properties of fundamental whole of random matrices and to study of it the limit for matrices of big size). These decisive projections were worth in Madan Lal Mehta to be invited by E.P. Wigner in Institute for Advanced Studies of Princeton (the USA). Before answering this invitation, Madan Lal Mehta obtained its doctorate of state in Physical sciences of the University of Paris under the direction of Claude Bloch in December 1961 on a subject concerning the nuclear matter with low density.

While attacking various mathematical problems inspired of physics (theory of the groups, theory of the nodes, polynomials orthogonal,…), Madan Lal Mehta devoted the essence of its scientific activity to the random matrices. In addition to Mr. Gaudin and F.J. Dyson, his/her principal collaborators in this field were P.K. Srivastava, NR. Rozenzweig, J. of Cloizeaux, G. Mahoux, A. Pandey, J. - M. Norman and B. Eynard.

Work of Madan Lal Mehta inspired, in particular through direct contacts with J. - L. Pichard (ECA Saclay) and O. Bohigas (CNRS University of Orsay), many other developments, such as the study of the systems disordered and mesoscopic and quantum chaos. The applications of the random matrices extended to the atomic and molecular spectra. New methods of study were elaborate (developments perturbatifs, method of the collar, method of the counterparts, supersymmetric method, method of theory of the groups, method of renormalization,…). Ideas of G.T. Hooft in 1974, then the theoretical developments of the Eighties, highlighted the major relations between random matrices, topological developments in theory of the fields and random surfaces, opening new scopes of application. The random models of matrices are currently used in major problems, so much of the theoretical physics (disordered systems, systems mesoscopic, chaos quantum, turbulence, chromodynamic quantum in physics of the particles, random surfaces, quantum gravitation, theory of the cords, statistical mechanics on random networks, theories in conformity and integrable models,…), that mathematics (zeros of the function zéta, theory of the numbers, geometry algebraic, combinative,…). The work of Madan Lal Mehta continues to be used as a basis for good number of these applications and developments of the theory of the random matrices.

Madan Lal Mehta published two books on the random matrices, “Random Matrices” published in 1967 (with one 3rd in 2004, and a work on the matrices initially published in India in 1977, then in France in 1988.

Works

Madan Lal Mehta ; One the statistical properties off the level-spacings in nuclear will spectra , Nuclear Physics 18 (1960), 395-419.
Madan Lal Mehta ; Random matrices . This bible was the subject of three editions of volume growing:
Random Matrices and the Statistical Theory off Energy Levels , Academic Close (New York - 1967), 259 pp.
Random Matrices (2nd revised and increased edition), Academic Close (New York, San Diego - 1991), 562 pp.
Random matrices (3rd edition), Pure and Applied Mathematics Series 142, Elsevier (London - 2004), 688 pp. ISBN 0120884097.
Madan Lal Mehta; Random matrices in nuclear physics and number theory , in: J.E. Cohen, H. Kesten and C.M. Newman (eds.); Proceedings off the AMS-IMS-SIAM Joint Summer Conference, Bowdoin College, Brunswick, Maine, the USA (June 1984), Contemporary Mathematics 50 (1986), 295-309.

Dependant articles

random Matrices
Theoretical physics

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