Center for Nonlinear Studies

Multi-scale modeling of strongly coupled systems (2007-2009)

Multi-scale systems present great scientific challenges. Some of the greatest advances in theoretical physics have involved these kinds of problems, e.g., disordered systems, phase transitions , quantum chromodynamics (limit of high energy), and conventional superconductivity. Although great progress was made on these problems using tools such as renormalization group analysis, variational techniques and other non-perturbative methods , significant challenges remain. These include fluid turbulence, the dynamics of materials, unconventional superconductivity, dark matter/energy problems, and emerging issues in nano-science and their applications in technology. We will focus on novel mathematical, theoretical and computational methods for treating strongly coupled multi-scale systems. Particular emphasis:

Strength of materials including elastic and plastic material response
Fluid turbulence and mixing
Macroscopic quantum systems: Superconductors and Bose-Einstein condensates.
Mathematical physics of multiscale problems.

Highlight Publications:

Batista, C.D., J. Schmalian, N. Kawashima, P. Sengupta, S. E. Sebastian, N. Harrison, M. Jaime, and I. R. Fisher. Geometric frustration and dimensional reduction at a quantum critical point. 2007. Physical Review Letters. 98 (25): 257201.
Bender, C.M. Making sense of non-Hermitian Hamiltonians. 2007. Reports on Progress in Physics. 70 (6): 947.
Chertkov, M., C. Connaughton, I. Kolokolov, and V. Lebedev. Dynamics of energy condensation in two-dimensional turbulence. 2007. Physical Review Letters. 99 (8): 084501.
Groger, R., and V. Vitek. Explanation of the discrepancy between the theoretical and measured yield stresses in body-centered cubic metals. 2007. Philosophical Magazine Letters. 87: 113.
Maniadis, P., T. Lookman, E. M. Kober, and K. O. Rasmussen. Stress distributions in diblock copolymers. 2007. Physical Review Letters. 99 (4): 048302.
Sengupta, P., and C. Batista. Spin supersolid in anisotropic spin-one Heisenberg chain. Physical Review Letters.
Sengupta, P., and C. D. Batista. Field-induced supersolid phase in spin-one Heisenberg models. 2007. Physical Review Letters. 98 (22): 227201.
Sengupta, P., and S. Haas. Quantum glass phases in the disordered Bose-Hubbard model. 2007. Physical Review Letters. 99 (5): 050403.