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Dynamical scaling in Smoluchowski's coagulation equations: uniform convergence

Menon, Govind; Pego, Robert L.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.48%
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's coagulation equations for the solvable kernels K(x,y)=2, x+y and xy. We prove the uniform convergence of densities to the self-similar solution with exponential tails under the regularity hypothesis that a suitable moment have an integrable Fourier transform. For the discrete equations we prove uniform convergence under optimal moment hypotheses. Our results are completely analogous to classical local convergence theorems for the normal law in probability theory. The proofs rely on the Fourier inversion formula and the solution by the method of characteristics for the Laplace transform.; Comment: Latex2e, 31 pages with 1 figure. Revised per referee's suggestions

Eigenvalue statistics as indicator of integrability of non-equilibrium density operators

Prosen, Tomaz; Znidaric, Marko
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/07/2013
Relevância na Pesquisa
45.53%
We propose to quantify the complexity of non-equilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of level spacing distribution of their spectra. Based on extensive numerical studies in a variety of models, some solvable and some unsolved, we conjecture that integrability of density operators (e.g., existence of an algebraic procedure for their construction in finitely many steps) is signaled by a Poissonian level statistics, whereas in the generic non-integrable cases one finds level statistics of a Gaussian unitary ensemble of random matrices. Eigenvalue statistics can therefore be used as an efficient tool to identify integrable quantum non-equilibrium systems.; Comment: 4+eps pages in RevTeX, with 5 eps-figures