Spin dynamics and structure formation in a spin-1 condensate in a magnetic field

We study the dynamics of a trapped spin-1 condensate in a magnetic field. First, we analyze the homogeneous system, for which the dynamics can be understood in terms of orbits in phase space. We analytically solve for the dynamical evolution of the populations of the various Zeeman components of the homogeneous system. This result is then applied via a local-density approximation to trapped quasi-one-dimensional condensates. Our analysis of the trapped system in a magnetic field shows that both the mean-field and Zeeman regimes are simultaneously realized, and we argue that the border between these two regions is where spin domains and phase defects are generated. We propose a method to experimentally tune the position of this border

On the specification of spatial econometric models

In this paper we discuss the specification process of a spatial econometric model. There are a lot of results available in a time series context, which form a very well structured phase, but little has been said when the domain of the model is the Space in relation to this question. There are several points that merit some special attention. For example, it is not clear if the concepts of integration and cointegration are also relevant in a spatial context. Moreover, at this moment we do not have any specific criteria in order to solve the selection of the variables. This weakness lead us to another question, which is related to the correlation problem: Which kind of cross-sectional dynamics could be allowed in a spatial specification? At present, in case of finding spatial autocorrelation in a model we try to model it immediatly, without considerer that if it may reflect a previous specification error. Finally, there is the problem of the outliers which are of paramount importance in time series but just unkown in a spatial context. We will discuss each one of this topics making reference to a general specification and looking also at the final stage of model selection.

GEOGRAPHICAL LABOUR MOBILITY IN SPAIN - A PANEL DATA APPROACH

In this paper, we study geographical labour mobility taken by workers in Spain from a regional standpoint. Using a panel data set referred to the evolution of these decisions in the 1990-2003 period, the main objective is to determine what are the main variables that influence in labour mobility as well as to quantify their impact. To this respect, regional labour market status, spatial variations in employment opportunities and house prices have turned to be the main determinants. Furthermore, also certain socio-demographic characteristic of workers such as education, marital status and the presence of children in the household are also of great relevant.

Local weighting or the necessity of flexibility

The local estimation algorithms are well-known techniques in the current spatial econometric literature. The Geographically Weighted Regressions are very popular to estimate, locally, static models, whereas the SALE or the Zoom approaches are useful solutions in the case of dynamic models. These techniques are well founded from a methodological point of view and present interesting properties. However, Farber and Paez (2008) detect some inconsistencies in the behavior of some of these algorithms that claim for a further analysis. The point that we want to study in this paper refers to the role of the bandwith. This measure defines how many neighbors will be used in the estimation of the local parameters corresponding to each observation. The cross-validation is the most popular criteria to fix the bandwith, although there are several other criteria in the literature. We think that there is a basic problem with this approach. The objective of these algorithms is to relax the restriction of homogeneity of the parameters of the model allowing for local peculiarities; however the definition of local neighborhood is the same. It does not matter if the observation corresponds to an isolated and poorly communicated region or it belongs to a central and highly connected point. According to our view, this is a very restrictive decision that should be avoided. Specifically, we discuss the procedure of specifying the sequence of local weighting matrices that will be used in the analysis. Our purpose is to achieve that these matrices also reflect the local surrounding of each observation. We examine two different strategies in order to construct the local weighting matrices. The first is a parametric approach which involves the J test, as presented by Kelejian (2008), and the second is a nonparametric approach that uses the guidance of the symbolic entropy measures. The first part of the paper presents the overall problem, including a review of the literature; we discuss the solutions in the second part and the third part consists of a Monte Carlo simulation.

Chiral bound states in the continuum

We present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by the chiral symmetry. When the system is coupled to leads with a continuum energy band, part of these states remain bound. We derive some algebraic rules for the number of these states depending on the dimensionality and rank of the total Hamiltonian. We examine the transport properties of such systems including the appearance of Fano resonances in some limiting cases. Finally, we discuss experimental setups based on microwave dielectric resonators and atoms in optical lattices where these predictions can be tested.Comment: 9 pages, 8 figures. v2: includes results specific to honeycomb lattice; matches published versio

Intermunicipal cooperation and privatization of solid waste services among small municipalities in Spain

The aim of this paper is to analyze the effects of intermunicipal cooperation and privatization on the delivery costs of urban solid waste services. The results of our empirical analysis, which we conducted among a sample of very small municipalities, indicate that small towns that cooperate incur lower costs for their waste collection service. Cooperation also raises collection frequency and improves the quality of the service in small towns. By contrast, the form of production, whether it is public or private, does not result in systematic differences in costs. Interestingly, the degree of population dispersion has a significant positive relation with service costs.No evidence of scale economies is found because, it would seem, small municipalities exploit them by means of intermunicipal cooperation.local government, intermunicipal cooperation,privatization, contracting-out, solid waste collection.

Vuong and Wald tests. Simplicity vs. Complexity

The specification of cross-sectional models is usually solved following a traditional procedure, highly supported by practitioners. In the first step, a simple model is proposed that will be subsequently improved with different elements if the evidence so advises. This procedure expedites the econometric solution and fits well into the Lagrange Multiplier approach, which contributes to explain its current popularity. However, there are other methods that could also be used, and some of them are considered in this paper. Specifically, we turn our attention to the Vuong test, developed in the context of the Kullback-Leibler information measure. This test represents an intermediate solution between the complexity inherent in the Wald test and the simplicity of the Lagrange Multiplier principle.

Outliers in Cross-Sectional Regression

The robustness of the results coming from an econometric application depends to a great extent on the quality of the sampling information. This statement is a general rule that becomes especially relevant in a spatial context where data usually have lots of irregularities. The purpose of our paper is to examine more closely this question paying attention to one point in particular, namely outliers. The presence of outliers in the sample may be useful, for example in order to break some multicollinearity relations but they may also result in other inconsistencies. The main aspect of our work is that we resolve the discussion in a spatial context, looking closely into the behaviour shown, under several unfavourable conditions, by the most outstanding misspecification tests. For this purpose, we plan and solve a Monte Carlo simulation. The conclusions point to the fact that these statistics react in a different way to the problems posed.

Spectral statistics of molecular resonances in erbium isotopes: How chaotic are they?

We perform a comprehensive analysis of the spectral statistics of the molecular resonances in $^{166}$Er and $^{168}$Er observed in recent ultracold collision experiments [Frisch et al., Nature {\bf 507}, 475 (2014)] with the aim of determining the chaoticity of this system. We calculate different independent statistical properties to check their degree of agreement with random matrix theory (RMT), and analyze if they are consistent with the possibility of having missing resonances. The analysis of the short-range fluctuations as a function of the magnetic field points to a steady increase of chaoticity until $B \sim 30$ G. The repulsion parameter decreases for higher magnetic fields, an effect that can be interpreted as due to missing resonances. The analysis of long-range fluctuations allows us to be more quantitative and estimate a $20-25\%$ fraction of missing levels. Finally, a study of the distribution of resonance widths provides additional evidence supporting missing resonances of small width compared with the experimental magnetic field resolution. We conclude that further measurements with increased resolution will be necessary to give a final answer to the problem of missing resonances and the agreement with RMT.Comment: 9 pages, 6 figure

Measuring molecular electric dipoles using trapped atomic ions and ultrafast laser pulses

We study a hybrid quantum system composed of an ion and an electric dipole. We show how a trapped ion can be used to measure the small electric field generated by a classical dipole. We discuss the application of this scheme to measure the electric dipole moment of cold polar molecules, whose internal state can be controlled with ultrafast laser pulses, by trapping them in the vicinity of a trapped ion.Comment: 13 pages, 6 figures. Substantially modified version, with 4 new appendices; matches published versio