Session A8: APS/GSNP/DCMP Prize Session: Heineman, Onsager, IUPAP/C10

Dannie Heineman Prize for Mathematical Physics Talk: Shape fluctuations of growing droplets and random matrix theory

In 1986 Kardar, Parisi, and Zhang (KPZ) proposed a stochastic evolution equation for growing interfaces, thereby triggering an intense study of growth processes with local growth rules. Specifically we have in mind the recent spectacular experiment of Takeuchi and Sano [1] on droplet growth in a thin film of turbulent liquid crystal. Over the last ten years one has studied universal probability density functions on the basis of simplified lattice growth models. Surprisingly enough the one-point shape fluctuations are governed by the same statistical laws as the largest eigenvalue of a random matrix, Gaussian Unitary Ensemble (GUE) in case of a curved front and Gaussian Orthogonal Ensemble (GOE) for a flat front. Recently we obtained the first exact solution of the KPZ equation for initial conditions corresponding to droplet growth, thereby providing the probability density function for the height at any time [2]. For long times we recover the universal statistical properties as computed from lattice growth models. \medskip\\ {[1]} K.Takeuchi and M.Sano, Phys. Rev. Lett. \textbf{104}, 230601 (2010).\\ {[2]} T.Sasamoto and H.Spohn, Phys. Rev. Lett. \textbf{104}, 230602 (2010).   

Lars Onsager Prize Talk I

This abstract not available.   

Lars Onsager Prize Talk II

This abstract not available.   

IUPAP C10 2011 Young Scientist Prize in the Structure and Dynamics of Condensed Matter Talk: Breakdown of thermalization in finite one-dimensional systems

Little more than fifty years ago, Fermi, Pasta, and Ulam set up a numerical experiment to prove the ergodic hypothesis for a one-dimensional lattice of harmonic oscillators when nonlinear couplings were added. Much to their surprise, the system exhibited long-time periodic dynamics with no signals of ergodic behavior. Those results motivated intense research, which ultimately gave rise to the modern chaos theory and to a better understanding of the basic principles of classical statistical mechanics. More recently, experiments with ultracold gases in one-dimensional geometries have challenged our understanding of the quantum domain. After bringing a nearly isolated system out of equilibrium, no signals of relaxation to the expected thermal equilibrium distribution were observed. Some of those results can be understood in the framework of integrable quantum systems, but then it remains the question of why thermalization did not occur even when the system was supposed to be far from integrability. In the latter regime, thermalization is expected to occur and can be understood on the basis of the eigenstate thermalization hypothesis. In this talk, we utilize quantum quenches to study how thermalization breaks down in finite one-dimensional lattices as one approaches an integrable point. We establish a direct connection between the presence or absence of thermalization and the validity or failure of the eigenstate thermalization hypothesis, respectively. {\bf References:}\\[4pt] [1] M. Rigol, V. Dunjko, and M. Olshanii, Nature {\bf 452}, 854 (2008).\\[0pt] [2] M. Rigol, Phys. Rev. Lett. {\bf 103}, 100403 (2009); Phys. Rev. A {\bf 80}, 053607 (2009).\\[0pt] [3] M. Rigol and L. F. Santos, Phys. Rev. A {\bf 82}, 011604(R) (2010).\\[0pt] [4] L. F. Santos and M. Rigol, Phys. Rev. E {\bf 81}, 036206 (2010); Phys. Rev. E {\bf 82}, 031130 (2010).