Topics in Nonequilibrium Field Theory
S. Habib, L. Bettencourt, G. Lythe, and C. Molina-Paris, Los Alamos National Laboratory
H. Mabuchi, California Institute of Technology
K. Shizume, University of Tsukuba
B. Sundaram, City University of New York
Research Objectives
Nonequilibrium field theory covers a variety of topics such as transport theory of quantum fields, nonequilibrium phase transitions, the nucleation and transport of topological defects and other nonlinear coherent structures, as well as fundamental issues such as the quantum-classical transition and the coherent control of quantum systems. Specific examples of current interest involving nonequilibrium dynamics of field theories include electroweak baryogenesis and topological transition rates, post-inflationary reheating in the early universe, and chiral condensates and evolution of the quark-gluon plasma in heavy-ion collisions.
Due to advances in high-performance computing, quantitative attacks are now possible on a host of outstanding, but until recently quite intractable, problems in quantum field theories under nonequilibrium conditions. We are studying selected problems in the areas of baryon number violation, Relativistic Heavy Ion Collider physics, nonequilibrium phase transitions, quantum transport, and cavity quantum electrodynamics (QED), all of which share common features from the perspective of nonequilibrium quantum field theory.
Computational Approach
We use several computational techniques in our research effort. Homogeneous and inhomogeneous mean-field dynamics codes solve for the evolution of a mean field self-consistently coupled to quantum fluctuations. These codes exist for Landau-Ginzburg theories, QED and scalar QED, and the linear sigma model. Applications include dynamics of phase transitions, disoriented chiral condensates, and soliton transport.
The next class of codes are Langevin solvers for field theories in one, two, and three dimensions. They feature automatic inclusion of global and gauge constraints as well as extensive diagnostics for tracking nonlinear coherent structures such as domain walls and vortices.
Finally, we have a suite of Schrödinger and master equation solvers based mainly on spectral split-operator methods. Applications include fundamental studies of quantum dynamics, quantum chaos, soliton transport, decoherence, cavity QED, and atomic optics.
Accomplishments
In FY98, we concentrated to a large extent on porting code to the T3E. In addition, we completed three research projects on statistical mechanics of a new field theory, the quantum-classical transition in chaotic systems, and a new method to compute Lyapunov exponents.
Field intensity profiles of a model for a two-dimensional superfluid at low temperature. The quasi-circular features are vortices, which evolve in time under the effect of their own interactions and interactions with the surrounding heat bath. The two vortices closest to each other have opposite charges and will annihilate each other in the course of the evolution.
Significance
In our work to date, we have shown that very high resolution simulations allow for the possibility of using new methods to study statistical mechanics of field theories, demonstrated how the classical limit of certain chaotic systems is obtained from quantum dynamics via decoherence, and developed a new, accurate method for the characterization of classically chaotic systems.
Publications
A. Khare, S. Habib, and A. Saxena, "Exact thermodynamics of the Double Sinh-Gordon Theory in 1+1-dimensions," Phys. Rev. Lett. 79, 3797 (1997).
S. Habib, K. Shizume, and W. H. Zurek, "Decoherence, chaos, and the correspondence principle," Phys. Rev. Lett. 80, 4361 (1998)
G. Rangarajan, S. Habib, and R. D. Ryne, "Lyapunov exponents without rescaling and reorthogonalization," Phys. Rev. Lett. 80, 3747 (1998)