Rapidly Rotating Bose-Einstein Condensates in Homogeneous Traps

We extend the results of a previous paper on the Gross-Pitaevskii description of rotating Bose-Einstein condensates in two-dimensional traps to confining potentials of the form V(r) = r^s, $2<s <\infty$. Writing the coupling constant as $1/\epsilon^2$ we study the limit $\epsilon \to 0$. We derive rigorously the leading asymptotics of the ground state energy and the density profile when the rotation velocity \Omega tends to infinity as a power of $1/\epsilon$. The case of asymptotically homogeneous potentials is also discussed.Comment: LaTex2e, 16 page

Experimentally Induced Language Modes and Regular Code-Switching Habits Boost Bilinguals’ Executive Performance: Evidence From a Within-Subject Paradigm

Bilingualism may modulate executive functions (EFs), but the mechanisms underlying this phenomenon are poorly understood. In this study, we investigated two potential sources of variability in bilinguals’ EF performance: (1) interactional contexts and code-switching, and (2) dominance profiles. Previous research on code-switching often relied on self-reports of regular code-switching habits. In this study, we investigated the effects of experimentally induced language modes (single language versus code-switching modes) on bilinguals’ EF performance. Crucially, in the bilingual conditions, we differentiated between different types of intra-sentential code-switching (Insertion, Alternation, and Dense code-switching). Moreover, we investigated the interaction of the effects of temporary language modes with bilinguals’ sociolinguistic code-switching habits. All our participants were L1-dominant German–English bilinguals (N = 29) immersed in an L2 context. We assessed the effects of dominance by correlating individual bilinguals’ L1-dominance with their EF performance. In addition, we investigated whether language modes activate different EF patterns in bilinguals, as opposed to monolinguals, i.e., individuals who have no additional language to suppress. Based on models of bilingual language processing, we predicted our bilinguals to display the best EF performance in L2 single language contexts, as these require them to activate inhibitory schemata to suppress their dominant L1. Indeed, bilinguals performed better in the single language than in the code-switching conditions. The results also suggested that bilinguals activated more inhibitory control compared to monolinguals, supporting the notion that bilingual processing involves inhibition. The task conditions inducing different code-switching modes differed only in terms of the predictors explaining EF performance in the regression. We observed negative correlations between the frequency of engaging in a given type of code-switching and performance in language modes inducing non-corresponding control modes. The results suggested that Dense code-switching draws upon proactive control modes that differ from the reactive control involved in Alternation. Importantly, bilinguals’ dominance profiles played a crucial role in explaining EF performance. The more balanced individuals in our overall L1-dominant sample displayed better EF performance in the bilingual conditions, suggesting that more balanced bilingualism trains the control modes involved in code-switching. This highlights the importance of assessing bilinguals’ sociolinguistic profiles in bilingualism research

Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps

We study a rotating Bose-Einstein Condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of 2D Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as $1/\epsilon^2$ and we are interested in the limit $\epsilon\to 0$ (TF limit) with the angular velocity $\Omega$ depending on $\epsilon$. We derive rigorously the leading asymptotics of the ground state energy and the density profile when $\Omega$ tends to infinity as a power of $1/\epsilon$. If $\Omega(\epsilon)=\Omega_0/\epsilon$ a ``hole'' (i.e., a region where the density becomes exponentially small as $1/\epsilon\to\infty$) develops for $\Omega_0$ above a certain critical value. If $\Omega(\epsilon)\gg 1/\epsilon$ the hole essentially exhausts the container and a ``giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyse the detailed vortex structure we prove that rotational symmetry is broken in the ground state for ${\rm const.}|\log\epsilon|<\Omega(\epsilon)\lesssim \mathrm{const.}/\epsilon$.Comment: LaTex2e, 28 pages, revised version to be published in Journal of Mathematical Physic

Effects of dense code-switching on executive control

Bilingualism is reported to re-structure executive control networks, but it remains unknown which aspects of the bilingual experience cause this modulation. This study explores the impact of three code-switching types on executive functions: (1) alternation, (2) insertion, and (3) dense code-switching or congruent lexicalisation. Current models hypothesise that different code-switching types challenge different aspects of the executive system because they vary in the extent and scope of language separation. Two groups of German-English bilinguals differing in dense code-switching frequency participated in a flanker task under conditions varying in degree of trial-mixing and resulting demands to conflict-monitoring. Bilinguals engaging in more dense code-switching showed inhibitory advantages in the condition requiring most conflict-monitoring. Moreover, dense code-switching frequency correlated positively with monitoring skills. This suggests that dense code-switching is a key experience shaping bilinguals’ executive functioning and highlights the importance of controlling for participants’ code-switching habits in bilingualism research

Predicting executive functions in bilinguals using ecologically valid measures of code-switching behaviour

The study of bilingualism has charted a dramatically new, important, and exciting course in the 21st century, benefiting from the integration in cognitive science of theoretical linguistics, psycholinguistics, and cognitive psychology (especially work on the higher-level cognitive processes often called executive function or executive control). Current research, as exemplified in this book, advances the study of the effects of bilingualism on executive function by identifying many different ways of being bilingual, exploring the multiple facets of executive function, and developing and analyzing tasks that measure executive function. The papers in this volume (21 chapters), by leading researchers in bilingualism and cognition, investigate the mechanisms underlying the effects (or lack thereof) of bilingualism on cognition in children, adults, and the elderly. They take us beyond the standard, classical, black-and-white approach to the interplay between bilingualism and cognition by presenting new methods, new findings, and new interpretations

Explaining Individual Differences in Executive Functions Performance in Multilinguals: The Impact of Code-Switching and Alternating Between Multicultural Identity Styles

This study sheds new light on the relative impact of switching between languages and switching between cultures on Executive Functions (EFs) in bilinguals. Several studies have suggested that bilingualism has a measurable impact on executive functioning, presumably due to bilinguals’ constant practice in dealing with two languages, or two cultures. Yet, the evidence on the relative contribution of culture and bilingualism to EFs is not well understood, because disentangling language, culture and immigration status is very difficult. The novelty of our approach was to keep the language pair and immigration status constant, whilst the cultural identity of participants was systematically varied, and measured at the individual level (not just at group level). Two groups of Turkish–English bilinguals, all adult immigrants to the United Kingdom, took part in the study, but one group (n = 29) originated from mainland Turkey and the other (n = 28) from Cyprus. We found that the bilinguals experienced smaller Conflict Effects on a Flanker task measuring inhibition, by comparison with monolingual British participants (n = 30). The key variable explaining EF performance variance at the individual level turned out to be bilinguals’ Multicultural Identity Style. In particular those who indicated that they attempted to alternate between different British and Turkish (Cypriot) identity styles were found to have shorter RTs on incongruent trials of the Flanker task. The two multicultural identity variables, Alternating and Hybrid Identity Styles, together explained 32% in RTs over and above Education, Working Memory and Nonverbal reasoning (overall explained variance 49%). Thus, the data provide strong evidence for the impact of culture on EFs. We suggest that, as a result of their daily practice in recognizing cultural cues which highlight the need to switch to a different cultural frame, multicultural bilinguals develop a heightened context-sensitivity, and this gives them an advantage over monolinguals in a Flankers task. Our approach, which draws on models from cross-cultural psychology, bilingualism and executive functioning, illustrates the importance of theory building in which sociolinguistic and cultural variables are integrated into models of EFs