1. Construction and solution of microscopic models of the high-temperature superconductors and other layered materials, focusing on the complex nature of the phase diagrams and the various types of  rich order that may arise.  Analytical methods such as the renormalization group, bosonization, and mean field theory, carried out in concert with numerical solutions, yield reliable insight into the phase diagrams.  I'm also studying the possible existence of deconfined fractionalized excitations in frustrated quantum antiferromagnets such as the layered Cs₂CuCl₄ material. 
 

2. Understanding the dynamics and transport of electrons in nanostructures such as quantum dots and wires by discovering new methods to treat quantum many body systems driven far away from equilibrium.  One promising approach that we've developed generalizes the density matrix renormalization group algorithm to time dependent problems (TDMRG).  This project, and the following one below, evolved out of my work of the past 12 years done in collaboration with Barbara Cooper's experimental group at Cornell working with quantum many-body descriptions of charge transfer between hyperthermal atoms and metallic surfaces, including the possibility of observing the Kondo effect.
 

3. Understanding the quantum chemistry of aqueous actinide complexes with application to the problem of environmental dispersal from nuclear waste storage sites such as the one proposed for Yucca Mountain, Nevada.  Disproportionation into multiple oxidation states, with widely varying solubilities, complicates geochemical transport mechanisms and is poorly understood at present.  Strong electronic correlations likely play an important role, due to the relatively localized nature of the actinide 5f orbitals. The conjunction of nanoscale complexification, an aqueous environment, and strong electronic correlations makes this a particularly fascinating and challenging problem.
 
 

4. Research into the possibility of applying statistical methods from theoretical physics to solve climate models in a much more direct manner than is currently done using huge supercomputers.  What we really want to do is to directly extract statistical information from the nonlinear equations of motion. (By way of analogy, we would not want to deduce the ideal gas law by following the individual motion of 10²³ molecules.) In other words, it is only the climate that is of interest, not the day-to-day weather, which in any case can't be predicted accurately more than a week in advance. One idea is to average analytically over initial conditions by mapping the problem into a framework similar to that used in quantum mechanics, with its linear operators, called the Liouville picture.

J. B. Marston, J. Fjærestad, and A. Sudbo, "Staggered Flux Phase in a Model of Strongly Correlated Electrons." Physical Review Letters 89, 056404 (2002).

M. A. Cazalilla and J. B. Marston, "Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Systems Out-of-Equilibrium." Physical Review Letters 88, 256403 (2002). 

J. O. Fjærestad and J. B. Marston, "Staggered Orbital Currents in the Half-Filled Two-Leg Ladder," Physical Review B65, 125106 (2002).

C. H. Chung, J. B. Marston, and Subir Sachdev, "Quantum Phases of the Shastry-Sutherland Antiferromagnet: Application to SrCu₂(BO₃)₂." Physical Review B64, 134407 (2001).

C. H. Chung, J. B. Marston, and Ross H. McKenzie, "Large-N Solutions of the Heisenberg and Hubbard-Heisenberg Models on the Anisotropic Triangular Lattice:  Application to Cs₂CuCl₄ and to the Layered Organic Superconductor k-(BEDT-TTF)₂X," Journal of Physics: Condensed Matter 13, 5159 (2001).

Shan-Wen Tsai and J. B. Marston, "Density-Matrix Renormalization-Group Analysis of Quantum Critical Points:  Quantum Spin Chains,'' Physical Review B62, 5546 (2000).

J. B. Marston, "Consilience of High-Tc Theories," Proceedings of the Third Rencontres du Vietnam:  Superconductivity, Magneto-Resistive Materials, and Strongly Correlated Systems, pages 23 to 32 (Vietnam National University Press, 2000).

T. Senthil, J. B. Marston, and M. P. A Fisher, "The Spin Quantum Hall Effect in Unconventional Superconductors," Physical Review B60, 4245--4254 (1999).

J. B. Marston and Shan-Wen Tsai, "Chalker-Coddington Network Model is Quantum Critical,'' Physical Review Letters 82, 4906 -- 4909 (1999).

A. Houghton, H.-J. Kwon, and J. B. Marston,  "Multidimensional Bosonization," Advances in Physics 49, 141-228 (2000).

A. V. Onufriev and J. B. Marston, "Enlarged symmetry and coherence in arrays of quantum dots," Physical Review B59, 12573 (1999).

J. Merino and J. B. Marston, "Room-temperature Kondo effect in atom-surface scattering: Dynamical 1/N approach," Physical Review B58, 6982 -- 6991 (1998).

A. V. Onufriev and J. B. Marston, "Memory Loss and Auger Processes in a Many Body Theory of Charge Transfer," Physical Review B53, 13,340 (1996).

H.-J. Kwon, A. Houghton, and J. B. Marston, "Gauge Interactions and Bosonized Fermi Liquids," Physical Review Letters 73, 284 -- 287 (1994).

A. Houghton, H.-J. Kwon, J. B. Marston, and R. Shankar, "Coulomb Interaction and the Fermi Liquid State: Solution by Bosonization,"  Journal of Physics: Condensed Matter 6, 4909 -- 4916 (1994).

J. B. Marston, M. Oppenheimer, R. M. Fujita, and S. R. Gaffin,"CO₂ and Temperature,"  Nature 349, 573 -- 574 (1991).  See also two popular articles about this work that appeared in The New York Times Tuesday, February 14, 1991, "Warming of Globe Could Build on Itself, Some Scientists Say" and Science News, March 9, 1991, p. 159, "CO₂ and Temperature: A pas de deux."

Copyright American Physical Society, American Institute of Physics, or Institute of Physics Publishing (as appropriate).  The above articles may be downloaded for personal use only.  Any other use requires permission of the author and the publisher.

Marston Group Web Pages

"This material is based upon work supported by the National Science Foundation under Grant No. 0213818.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation."