• B.S., 1953, Massachusetts Institute of Technology
• M.S., 1954; Ph.D., 1957, University of Illinois, Urbana

Research Interests:

Condensed matter theory is a rapidly evolving discipline combined from solid state theory, statistical mechanics, field theory and mathematics. Examples of recent advances in which Dr. Mattis has participated include the "few-body problem" in solids, detailed calculation of the normal modes in glasses and amorphous materials, and high-temperature superconductivity. His 1984 work on the mass of an exciton (an electron-hole bound complex found in insulators), in which it was shown that the mass of the complex exceeds the sum of the electron and hole masses by an amount related to the binding energy of the complex, was soon confirmed experimentally by Cafolla et al., Phys. Rev. Lett. 55, 2818 (1985). His recent work includes a contribution to the study of the diffusion-controlled chemical reactions. Applications range from fluorescence phenomena (diffusion and recombination of electrons and holes) to chemical explosions. The work resulted in a review article illustrating and summarizing the uses of quantum-field theory as a method for solving the complicated problems involving the diffusive motion of "classical" particles (e.g., atoms and molecules or even larger objects) while they are undergoing chemical or "scavenging" reactions.

His recent research (1998-2001) includes a microscopic, first-principles derivation of the electronic properties of a layered copper-oxide-type superconductor. Starting from the atomic properties, the work identified the composite charge carriers and their interactions. This work is a contribution to the theory of the exciting new phenomenon, "high-temperature superconductivity." Other recent research of Dr. Mattis and his collaboratores deals with the statistical mechanics of glassy materials, including a publication on the exact free energy of a "spin ladder" with frozen-in defects (also known as "frustration") using the "hyper-transfer matrix, an approach which was developed here.

Current research (2003-) is concentrated in the new field of submicron nanotechnology. This work is focused on the theoretical design and construction of artificial nano-ferromagnetic and nano-superconductors, through novel architectures of nanodots and manipulation of their electrical charges.

New books include a revised edition of The Many-body Problem (World Scientific Publ. Co., Singapore 1993), a book entitled Statistical Mechanics Made Simple (2003) and a revised version (and new edition) of his book The Theory of Magnetism which is under preparation. Dr. Mattis contributed the article on "The Many-Body Theory" found in various editions of the Encyclopedia of Physics, Lerner and Trigg, eds. and co-authored the article "Magnetic Semiconductors" in the Handbuch der Physik, vol. 18.

Selected Recent Publications

• The Theory of Magnetism, Vol. I: Statics and Dynamics, Springer-Verlag Series in Solid State Sciences (Berlin-New York, 1981), and revised (paperback) (1988); Vol. II: Thermodynamics and Statistical Mechanics (1985).
• "Decay of Electron Waves in a Random Medium," Phys. Rev. Lett. 48, 1857 (1982).
• "Application of Tridiagonalization to the Many-Body Problem" (with J. Mancini), Phys. Rev. B 28, (1983).
• "Roughening Transition of Surfaces," Phys. Lett. 104A, 361 (1984).
• "Transfer Matrix in Plane Rotator Model," Phys. Lett. 104A, 357 (1984).
• "What is the Effective Mass of an Exciton?" (with J.-P. Gallinar), Phys. Rev. Lett. 53, 1391 (1984).
• "Phonon Model of Vacancy-Interstitial Pair Formation in Solids," Phys. Rev. Lett. 53, 568 (1984).
• "Three-Body Bound States on a Lattice" (with S. Rudin), Phys. Rev. Lett. 52, 755 (1984).
• "Phonons in Disordered Solids. I," Phys. Lett. A 117, 297 (1986), II. Phys. Lett. A 120, 349 (1987).
• "Theory of Glass Dynamics," Phys. Rev. Lett. 58, 2470 (1987).
• "Bond Asymmetry and High-Tc Superconductivity" (with M. Mattis) Phys. Rev. Lett. 59, 2780 (1987).
• "The Few-Body Problem on a Lattice," Revs. Mod. Phys. 58, 361 (1986).
• "Dynamics of Quasiparticles in the Two-Dimensional Hubbard Model" (with M. Dzierzawa and X. Zotos), Phys. Rev. B 42, 6787 (1990).
• "Review and Theory of Oxygen Ordering in the High-Temperature Superconductor YBCO" (with A. Szpilka, M.L. Glasser and M.P. Mattis), Phase Transitions 22, 185 (1990).
• "States of a Few Holes in a t-J Model" (with Hua Chen), Int. J. Mod. Phys. B5, 1401 (1991).
• "Phonons in Disordered, Anharmonic Solids" (with M. Molina), Phys. Lett. A 159, 337 (1991).
• "New Mapping for 'Hard Core Interactions," Phys. Rev. Lett. 76, 692 (1996).
• "'Limit Model' of CuO₂ Planes: Exact Results" Phys. Rev. Lett. 74, 3676 (1995).
• "The Uses of Quantum Field Theory in Diffusion-Limited Reactions" (with M.L. Glasser), Rev. of Mod. Phys. 70, 979 (1998).
• "Statistical Transfer Matrix of a Spin-Glass Ladder" (with P. Paul), Phys. Rev. Lett. 83, 3733 (1999).
• "Accuracy of Bosonization for Localized Interaction" Phys. Rev. B 61, 7169 (2000)
• "Design of a Nanomagnet," J. Statistical Phys. 116, 773 (tentatively) (August 2004), in press.