Pasquale Calabrese - Università di Pisa #
Replica Bethe ansatz solutions to KPZ equation #
<p> The one-dimensional Kardar-Parisi-Zhang (KPZ) equation describes the 
scale-invariant stochastic motion of a line. I will report on the exact 
calculation of the height distribution at arbitrary time of the KPZ 
growth equation in one dimension with droplet and flat initial 
conditions obtained using the mapping to a directed polymer (DP) and the 
Bethe Ansatz for the replicated attractive boson model. The generating 
function of the moments of the DP partition sum is obtained as a 
Fredholm determinant/Pfaffian. The final result, valid for all times, 
exhibits convergence of the  KPZ height distribution to the GOE/GUE 
Tracy Widom distributions at large time.</p>
Based on:
<br/>
P Calabrese and P. Le Doussal, Phys. Rev. Lett. 106, 250603 (2011); J. 
Stat. Mech. (2012) P06001; P Calabrese, P Le Doussal, and A Rosso, 2010 
EPL 90 20002