80,441 research outputs found
Exponential moments for disk counting statistics of random normal matrices in the critical regime
We obtain large asymptotics for the -point moment generating function
of the disk counting statistics of the Mittag-Leffler ensemble. We focus on the
critical regime where all disk boundaries are merging at speed
, either in the bulk or at the edge. As corollaries,
we obtain two central limit theorems and precise large asymptotics of all
joint cumulants (such as the covariance) of the disk counting function. Our
results can also be seen as large asymptotics for determinants
with merging planar discontinuities.Comment: 23 pages, 1 figur
Interaction Quench in Nonequilibrium Luttinger Liquids
We study the relaxation dynamics of a nonequilibrium Luttinger liquid after a
sudden interaction switch-on ("quench"), focussing on a double-step initial
momentum distribution function. In the framework of the non-equilibrium
bosonization, the results are obtained in terms of singular Fredholm
determinants that are evaluated numerically and whose asymptotics are found
analytically. While the quasi-particle weights decay exponentially with time
after the quench, this is not a relaxation into a thermal state, in view of the
integrability of the model. The steady-state distribution emerging at infinite
times retains two edges which support Luttinger-liquid-like power-law
singularities smeared by dephasing. The obtained critical exponents and the
dephasing length are found to depend on the initial nonequilibrium state.Comment: 11 pages, 5 figure
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