Quantum quench influenced by an excited-state phase transition

We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear cut evidence of the ESQPT effects is presented in integrable models, while in the nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.Comment: submitted to Physical Review

The contribution of Real Madrid’s first five European Cups to the emergence of a common football space

Real Madrid won the first five editions of the European Champion Clubs’ Cup (now formally known as the UEFA Champions League, and to which we will refer hereon as the European Cup) between 1956 and 1960, contributing decisively to the competition’s consolidation. The tournament’s history started towards the end of 1954, when a journalist of the French sports daily L’Équipe, Gabriel Hanot, published an article arguing the need to organise a competition that could bring together the champions of every European league. However, this was not an original proposal. Thirty years before Hanot’s article proposals for such a football competition were circulated among the game’s ruling elite. Unfortunately, at that time the lack of a good transport infrastructure to travel through Europe discouraged the proposers which, instead, turned their attention to regional supranational competitions, such as the Mitropa Cup or the Latin Cup. The first five editions of the European Cup witnessed as many victories of Real Madrid, thus forging an indissoluble bond between the competition and the Spanish club. These five European titles did not only cement the supremacy of Real Madrid on the pitch as a great football team, but they also contributed to the consolidation of the European Cup itself in the public’s imaginary. We also argue that given the expectations raised by Real Madrid’s triumphs across Europe those matches might have contributed as well to the emergence of a European football space. Since 1955 Real Madrid occupied an ever increasing space in the press across Europe. Real Madrid was then considered as the best expression of modernity in football. This chapter aims to analyse the meaning of these five European Cup titles for the emergence and definition of a nascent European football space. We, of course, also question whether such a common space can be found. The chapter explores in depth the reasons behind Real Madrid’s enthusiasm with the new European competition. We also examine the social impact that Real Madrid’s hegemony in the European Cup had in the context of Spain’s international isolation during General Franco’s dictatorship (1939-1975). In order to achieve the above mentioned objectives, the chapter relies on thematic analysis of selected publications in the Spanish and British press during those years. Moreover, we have also relied on a review of academic literature on the role of Real Madrid during the Franco dictatorship years, mainly the 1950s and 60s. This chapter is part of wider on-going research. In this research we examine the content of two Spanish dailies (ABC and Marca) and three British newspapers (The Guardian, The Times and the Daily Mirror). We searched these newspapers for content related to Real Madrid on specific dates: The semifinal games (two legs) and the final of each one of the five years where Real Madrid won the European Cup. We searched for content the day of each match, the day before and two days after each one of the matches. This chapter is a presentation of the findings obtained through thematic analysis of the data obtained through those searches