Searcharxiv⌕ Search

arXiv subjects

Predrag Cvitanovic'

Publications and source records attributed to Predrag Cvitanovic'.

4 recordsLinked to original sources
arXiv2004

A Perturbative Analysis of Modulated Amplitude Waves in Bose-Einstein Condensates

We apply Lindstedt's method and multiple scale perturbation theory to analyze spatio-temporal structures in nonlinear Schrödinger equations and thereby study the dynamics of quasi-one-dimensional Bose-Einstein condensates with mean-field interactions. We determine the dependence of the intensity of modulated amplitude waves on their wave number. We also explore the band structure of Bose-Einstein condensates in detail using Hamiltonian perturbation theory and supporting numerical simulations.

nlin.CD↗
arXiv1998

Trace formulas for stochastic evolution operators: Weak noise perturbation theory

Periodic orbit theory is an effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory is cast in the standard field theoretic formalism, and weak noise perturbation theory written in terms of Feynman diagrams. The result is a stochastic analog of the next-to-leading hbar corrections to the Gutzwiller trace formula, with long time averages calculated from periodic orbits of the deterministic system. The perturbative corrections are computed analytically and tested numerically on a simple 1-dimensional system.

chao-dyn↗
arXiv1996

Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns

Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.

chao-dyn↗