Joaquin Mazdak Luttinger Explained

Joaquin Mazdak Luttinger
Birth Date:	2 December 1923
Birth Place:	New York City, United States
Death Place:	New York City, US
Alma Mater:	Massachusetts Institute of Technology
Work Institutions:	University of Michigan, University of Pennsylvania, Columbia University
Field:	Physics of interacting particles
Known For:	Luttinger liquid Luttinger's theorem Luttinger parameter Luttinger–Kohn model Luttinger–Ward functional Anomalous Hall effect Kohn–Luttinger superconductivity
Prizes:	Guggenheim Fellowship (1974)
Notable Students:	T. V. Ramakrishnan

Joaquin (Quin) Mazdak Luttinger (December 2, 1923  - April 6, 1997) was an American physicist well known for his contributions to the theory of interacting electrons in one-dimensional metals^[1] (the electrons in these metals are said to be in a Luttinger-liquid state) and the Fermi-liquid theory. He received his BS and PhD in physics from MIT in 1947.^[2] His brother was the physical chemist Lionel Luttinger (1920–2009) and his nephew is the mathematician Karl Murad Luttinger (born 1961).

See also

• Negative mass
• Schrieffer–Wolff transformation
• Wiener sausage
• Fermi liquid
• Many-body problem
• Anomalous magnetic moment
• Effective mass theory
• k·p perturbation theory

Some publications

(Note: For a complete list, see J. Stat. Phys. 103, 641 (2001).)

• W. Kohn, and J. M. Luttinger, Quantum Theory of Electrical Transport Phenomena, Physical Review, Vol. 108, pp. 590–611 (1957). APS
• W. Kohn, and J. M. Luttinger, Quantum Theory of Electrical Transport Phenomena. II, Physical Review, Vol. 109, pp. 1892–1909 (1958). APS
• J. M. Luttinger, Theory of the Hall Effect in Ferromagnetic Substances, Physical Review, Vol. 112, pp. 739–751 (1958). APS
• W. Kohn, and J. M. Luttinger, Ground-State Energy of a Many-Fermion System, Physical Review, Vol. 118, pp. 41–45 (1960). APS
• J. M. Luttinger, and J. C. Ward, Ground-State Energy of a Many-Fermion System. II, Physical Review, Vol. 118, pp. 1417–1427 (1960). APS
• J. M. Luttinger, Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions, Physical Review, Vol. 119, pp. 1153–1163 (1960). APS
• J. M. Luttinger, Analytic Properties of Single-Particle Propagators for Many-Fermion Systems, Physical Review, Vol. 121, pp. 942–949 (1961). APS
• J. M. Luttinger, Theory of the de Hass-van Alphen Effect for a System of Interacting Fermions, Physical Review, Vol. 121, pp. 1251–1258 (1961). APS
• J. M. Luttinger, Derivation of the Landau Theory of Fermi Liquids. I. Formal Properties, Physical Review, Vol. 127, pp. 1423–1431 (1962). APS
• J. M. Luttinger, Derivation of the Landau Theory of Fermi Liquids. II. Equilibrium Properties and Transport Equation, Physical Review, Vol. 127, pp. 1431–1440 (1962). APS
• J. M. Luttinger, An exactly solvable model of a many-fermion system, Journal of Mathematical Physics, Vol. 4, No. 9, pp. 1154–1162 (1963).
• W. Kohn, and J. M. Luttinger, New Mechanism for Superconductivity, Physical Review Letters, Vol. 15, No. 12, pp. 524–526 (1965). APS
• R. Friedberg, and J. M. Luttinger, Density of electronic energy levels in disordered systems, Physical Review B, Vol. 12, pp. 4460–4474 (1975). APS
• J. M. Luttinger, Density of electronic energy levels in disordered systems. II, Physical Review B, Vol. 13, pp. 2596–2600 (1976). APS
• R. Tao, and J. M. Luttinger, Exact evaluation of Green's functions for a class of one-dimensional disordered systems, Physical Review B, Vol. 27, pp. 935–944 (1983). APS

Obituary

• Philip W. Anderson, Richard M. Friedberg, and Walter Kohn, Joaquin M. Luttinger, Physics Today, December 1997, pp. 89–90 (PDF).
  Note: This obituary is reprinted with permission in Journal of Statistical Physics, Vol. 103, Nos. 3/4, pp. 413–415 (2001) (Link).

External links

• Photograph of J.M. Luttinger: http://www.columbia.edu/cu/record/archives/vol22/vol22_iss21/record2221.27c.gif.
• Robert Nelson, Leading Physicist Joaquin Luttinger, 73, April 18, 1997, Columbia University, New York, http://www.columbia.edu/cu/record/archives/vol22/vol22_iss21/record2221.32.html.
• Walter Kohn, "Joaquin M. Luttinger", Biographical Memoirs of the National Academy of Sciences (2014)

Notes and References

1. The Luttinger model was introduced by Luttinger in 1963 (J. Math. Phys., Vol. 4, 1154 (1963)). Luttinger's solution of this model was however incorrect. The correct solution was later provided by D. C. Mattis and E. H. Lieb (J. Math. Phys., Vol. 6, 304 (1965)). The error by Luttinger consists of solving the problem without imposing an appropriate cut-off on sums over momenta, whereby he erroneously mapped the interacting problem onto a non-interacting one. The Luttinger model is akin, but not identical, to an earlier model introduced by Sin-Itiro Tomonaga (Progress of Theoretical Physics, Vol. 5, No. 4, pp. 544-569 (1950)).
2. Web site: Massachusetts Institute of Technology. Department of Physics. history.aip.org. 2020-01-04.