6,232 research outputs found
Linear degree growth in lattice equations
We conjecture recurrence relations satisfied by the degrees of some
linearizable lattice equations. This helps to prove linear growth of these
equations. We then use these recurrences to search for lattice equations that
have linear growth and hence are linearizable
Dynamics of horizontal-like maps in higher dimension
We study the regularity of the Green currents and of the equilibrium measure
associated to a horizontal-like map in C^k, under a natural assumption on the
dynamical degrees. We estimate the speed of convergence towards the Green
currents, the decay of correlations for the equilibrium measure and the
Lyapounov exponents. We show in particular that the equilibrium measure is
hyperbolic. We also show that the Green currents are the unique invariant
vertical and horizontal positive closed currents. The results apply, in
particular, to Henon-like maps, to regular polynomial automorphisms of C^k and
to their small pertubations.Comment: Dedicated to Professor Gennadi Henkin on the occasion of his 65th
birthday, 37 pages, to appear in Advances in Mat
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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