CP, T and fundamental interactions

We discuss the importance of the CP (simultaneous particle-antiparticle and left-right permutation) and T (time reversal) symmetries in the context of fundamental interactions. We show that they may provide clues to go beyond the 4-D gauge interactions. We insist on the fact that T violation is not associated to a degradation (like in entropy), but simply characterized by different trajectories.Comment: This is a "basic" introduction (non-technical) aimed at showing the importance of CP violation wrt gauge theorie

Hierarchical relaxation dynamics in a tilted two-band Bose-Hubbard model

We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the eigenstate thermalization hypothesis for relevant physical observables is demonstrated for certain parameter regimes. Using the truncated Wigner representation in the semiclassical limit of the system, dynamics of relevant observables reveal hierarchical relaxation and the appearance of prethermalized states is studied from the perspective of statistics of the underlying mean-field trajectories. The observed prethermalization scenario can be attributed to different stages of glassy dynamics in the mode-time configuration space due to dynamical phase transition between ergodic and nonergodic trajectories.Comment: 13 pages, 15 figure

Multi Product Market Equilibrium with Sequential Search

In this paper I investigate whether, in market equilibrium, one observes price dispersion and search when buyers intend to acquire several products whose price is unknown and exists a positive search cost. Although that seems fruitful, I prove that in market equilibrium it is not observed neither price dispersion nor search and shops act as if they where monopolists. Nevertheless, there is one property of the theory that is in accordance with empirical data, namely the continuous increase in the number and dimension of larger shops.Search, Price Dispersion, Market Equilibrium, Multi-products

When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?

For a set of sorts $S$ and an $S$-sorted signature $\Sigma$ we prove that a profinite $\Sigma$-algebra, i.e., a projective limit of a projective system of finite $\Sigma$-algebras, is a retract of an ultraproduct of finite $\Sigma$-algebras if the family consisting of the finite $\Sigma$-algebras underlying the projective system is with constant support. In addition, we provide a categorial rendering of the above result. Specifically, after obtaining a category where the objects are the pairs formed by a nonempty upward directed preordered set and by an ultrafilter containing the filter of the final sections of it, we show that there exists a functor from the just mentioned category whose object mapping assigns to an object a natural transformation which is a retraction