We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using the example of massless scalar electrodynamics, we show how the radiatively induced spontaneous symmetry breaking stabilizes the vacuum state against chaos, and we speculate that monopole condensation can have the same effect in non-Abelian gauge theories.

Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of semiclassical recurrence functions. A band-limited periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. The frequencies of the periodic orbit signal are the semiclassical eigenvalues, and are determined by either linear predictor, Padé approximant, or signal diagonalization. The second method is based upon the direct application (...) of the Padé approximant to the periodic orbit sum. The Padé approximant allows the resummation of the, typically exponentially, divergent periodic orbit terms. Both techniques do not depend on the existence of a symbolic dynamics, and can be applied to bound as well as to open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard. (shrink)

This article aims to present the Georgian reality regarding the sharing economy and its future trends based on the market players and already appeared innovative businesses through sharing platforms. The sharing economy, with its in-depth context, is not developed in Georgia either at the national governance or the societal level. However, the sharing of goods and services to each other was a good habit between Georgians historically. Moreover, in the world of the Internet, personal computers, and smartphones, it is simplified (...) today for the parties of sharing to find and connect. However, may this kind of action be considered as a sharing economy, joint consumption, or collective economy? The present article discusses the issues about the sharing economy market in Georgia. There is an overview of the normative base and regulations referring to the sharing economy, expressed the readiness of sharing through people, describes the companies that operate in sharing market so far. There are recommendations for the government and the whole society for future development. (shrink)