We investigate the role of topology in space-time scaling limit quantum quench dynamics, where both time and system size tend to infinity at a constant ratio. There, while standard topological characterization relying on local unitary transformations becomes ill defined, we show how different dynamical notion naturally arises through winding number encoding linear response Berry phase magnetic ...

The Kesten-Stigum Theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and subcritical cases, results of Kolmogorov and later authors give the rate of decay of the probability that the process survives at least n generations. We give conceptual proofs of these theorems based on comparisons of G...

Abstract In this paper we study a second-order mean-field stochastic differential systems describing the movement of particle under influence time-dependent force, friction, interaction and space noise. Using techniques from Malliavin calculus, establish explicit rates convergence in zero-mass limit (Smoluchowski-Kramers approximation) $$L^p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/Ma...

The functional central limit theorem (FCLT) version of Little’s law (L = λW ) established by Glynn and Whitt is extended to show that a bivariate FCLT for the number in the system and the waiting times implies the joint FCLT for all processes. It is based on a converse to the preservation of convergence by the composition map with centering on the function space containing the sample paths, exp...

The functional central limit theorem (FCLT) version of Little’s law (L = λW ) established by Glynn and Whitt is extended to show that a bivariate FCLT for the number in system and the waiting times implies the joint FCLT for all processes. It is based on a converse to the preservation of convergence by the composition map with centering on the function space containing the sample paths, exploit...