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Memory effects in Kardar Parisi Zhang growth: exact results via the by Pierre Le Doussal

Memory effects in Kardar Parisi Zhang growth: exact results via the by Pierre Le DoussalMemory effects in Kardar Parisi Zhang growth: exact results via the by Pierre Le Doussal

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Title :Memory effects in Kardar Parisi Zhang growth: exact results via the by Pierre Le Doussal
Duration : 1h 10m 44s
Uploader : International Centre for Theoretical Sciences
Added On: : 31 October, 2017
Views : 168 times
Likes : 2
Dislikes: : 0
Source : YouTube



Date: Thursday, October 12, 2017 Time: 11:00 AM Venue: Madhava Lecture Hall, ICTS Campus, Bangalore Abstract : We review recent progress in describing the statistics of height fluctuations in 1D Kardar Parisi Zhang (KPZ) growth, focusing on the KPZ equation and its integrability properties via the mapping onto the Lieb Liniger model of impenetrable bosons. We recall the replica Bethe Ansatz method and how it allows to calculate one time probabilities, and shows the emergence of the Tracy Widom distributions of random matrix theory. We then study the two-time problem, the so called aging problem, which is still outstanding: the aim is to obtain the joint probability distribution of heights at time t and t', in the limit of large times with fixed ratio t/t' 1. We provide a partial solution of this problem, exact in some limits. In particular we derive the exact form of the persistent correlations in the limit t/t' large, which quantifies the memory effect in the time evolution, also called ergodicity breaking. Comparison with experiments and numerics shows a very nice agreement. Most is joint work with J. de Nardis and K. Takeuchi. Table of Contents (powered by 0:00:00 Start 0:00:07 Memory in Kardar-Parisi-Zhang growth: exact results via the replica Bethe ansatz, and experiments P. 0:04:34 Collaborators 0:05:31 Why is it interesting? 0:10:10 Part I : one-time KPZ/DP: Replica Bethe Ansatz (RBA) 0:12:01 how to model a growing interface 0:17:34 Turbulent liquid crystals 0:19:24 Large N by N random matrices H, with Gaussian independent entries 0:21:17 What is a Fredholm determinant? 0:22:17 Calculation of F1(s) 0:22:40 Tracy Wisdom distributions Tracy Wisdom (1994) 0:23:12 Exact results for height distributions for some discrete models in KPZ class 0:28:19 part I 0:29:29 Droplet (Narrow wedge) KPZ/Continuum DP fixed endpoints 0:30:22 Cole Hopf mapping 0:32:03 initial conditions 0:33:40 Schematically 0:34:26 Quantum mechanics and Replica.. 0:38:27 What do we need to solve KPZ with droplet initial condition eigenstates Eu eigen-energies 0:39:56 LL model: bosons on a ring with local delta attraction 0:45:00 Integer moments of partition sum: fixed endpoints (droplet IC) 0:46:31 how to get P( In Z) i.e. P(h) 0:48:58 Results: 1) g(x) is a Fredholm determinant at any time 0:50:45 Summary: one-time observables for models in KPZ class and a tale of tails 0:51:31 GUE-Tracy Wisdom distribution 0:53:26 Part II: two-time KPZ via RBA 0:53:34 two-time problem: - KPZ equation w. droplet initial conditions 0:54:30 Other works on two times 0:55:32 Main result: tail approximate of the joint PDF 0:56:35 Limits of the JPDF 0:59:17 Part II: tow-time KPZ via RBA 0:59:37 general initial condition 1:01:27 Two time KPZ via Airy processes 1:03:36 Explicit formula for JCDF 1:03:47 Consequence for 2-time KPZ: persistent correlations 1:05:23 Conclusions 1:06:33 Q&A

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