Nonlinear Coherent Structures      

Nonlinear coherent structures such as kinks, solitons, sphalerons, vortices, and instantons arise in the study of a variety of interesting and important physical situations such as baryon number violation, properties of materials, optical communications, dynamics of phase transitions, and the physics of the early universe. My main interest has been the study of the equilibrium and nonequilibrium statistical mechanics of these fascinating objects using both analytical and numerical techniques. I have studied kinks with Frank Alexander (CCS-3), Luis Bettencourt (CCS-3), Alex Kovner (Connecticut), and Grant Lythe (Leeds), all one-time LANL post-docs. With Avinash Khare (IOP) and Avadh Saxena (T-11) I have applied techniques from quantum mechanics (quasi-exactly solvable systems) to these problems. I have investigated sphaleron and periodic instanton physics with Emil Mottola (T-8) and Peter Tinyakov (INR Moscow), more recently also with Gian Franco Bonini and Claudio Rebbi (BU) and Robert Singleton (X-7). Vortex transport in two dimensions was studied with Luis Bettencourt and Roman Sasik (UCSD) (another ex-LANL post-doc).

Present interests include application of techniques developed with Grant Lythe to reaction-diffusion systems in collaboration with Carmen Molina-Paris (Leeds) and Katja Lindenberg (UCSD) and the construction and application of an improved inhomogeneous mean field theory to study quantum transport of nonlinear coherent structures. Also, along with Carmen and Tom Deisboeck (Harvard), I have been modeling cell transport using reaction-diffusion ideas.

Links are to the Los Alamos eprint server:

1. Kink Stochastics, Grant Lythe and Salman Habib, Computing in Science and Engineering 8, 10 (2006)
2. Complex Dynamics of Tumors: Modeling an Emerging Brain Tumor System with Coupled Reaction-Diffusion Equations, Salman Habib, Carmen Molina-Paris, and Thomas S. Deisboeck, Physica A 327, 501 (2003)
3. Kinks in a Stochastic PDE, Grant Lythe and Salman Habib, Proceedings, IUTAM Symposium on Nonlinear Stochastic Dynamics (Monticello, August 2002), Solid Mechanics and its Applications 110, 435 (2003)
4. Diffusion-Limited Reaction in One Dimension: Paired and Unpaired Nucleation, Salman Habib, Katja Lindenberg, Grant Lythe, and Carmen Molina-Paris, J. Chem. Phys. 115, 73 (2001) cond-mat/0102270
5. Thermal Vortex Motion in a Two-Dimensional Condensate, R. Sasik, Luis M.A. Bettencourt, and Salman Habib, Phys. Rev. B 62, 1238 (2000) cond-mat/9907501
6. Dynamics of Kinks: Nucleation, Diffusion and Annihilation, Salman Habib and Grant Lythe, Phys. Rev. Lett. 84, 1070 (2000) cond-mat/9911228
7. Periodic Instantons in SU(2) Yang-Mills-Higgs Theory, G. Bonini, S. Habib, E. Mottola, C. Rebbi, R. Singleton, and P. Tinyakov, Phys. Lett. B 474, 113 (2000) hep-ph/9905243
8. Statistical Mechanics of Double sinh-Gordon Kinks, Salman Habib, Avinash Khare, and Avadh Saxena, Physica D 123, 341 (1998) cond-mat/9808008
9. Exact Thermodynamics of the Double sinh-Gordon Theory in 1+1-Dimensions, Avinash Khare, Salman Habib, and Avadh Saxena, Phys. Rev. Lett. 79, 3797 (1997) cond-mat/9707222
10. Statistical Mechanics of Kinks for Quasi-Exactly-Solvable Potentials, Avadh Saxena and Salman Habib, Physica D 107, 338 (1997)
11. Winding Transitions at Finite Energy and Temperature: An O(3) Model, Salman Habib, Emil Mottola, and Peter Tinyakov, Phys. Rev. D 54, 7774 (1996) hep-ph/9608327
12. Statistical Mechanics of Nonlinear Coherent Structures: Kinks in the Phi^6 Model, Salman Habib and Avadh Saxena, Proceedings, NEEDS'94 cond-mat/9502004
13. Phi^4 Kinks: Statistical Mechanics, Salman Habib, Proceedings, NEEDS'94 cond-mat/9411058
14. Finite Energy Instantons in the O(3) Non-Linear Sigma Model, Peter G. Tinyakov, Emil Mottola, and Salman Habib, Proceedings, Quarks'94 hep-ph/9411251
15. Statistical Mechanics of Kinks in (1+1)-Dimensions: Numerical Simulations and Double Gaussian Approximation, Francis J. Alexander, Salman Habib, and Alex Kovner, Phys. Rev. E 48, 4284 (1993) hep-th/9308103
16. Statistical Mechanics of Kinks in (1+1)-Dimensions, Francis J. Alexander and Salman Habib, Phys. Rev. Lett. 71, 955 (1993) hep-th/9212059

Salman Habib / LANL / revised February 2005