From asking to observing. Behavioural measures of socio-emotional and motivational skills in large-scale assessments.

Socio-emotional and motivational skills are routinely measured using self-reports in large-scale educational assessments. Measures exploiting test-takers' behaviour during the completion of questionnaires or cognitive tests are increasingly used as alternatives to self-reports in the economics of education literature. We compute behavioural measures of socio-emotional and motivational skills using data from the Programme for International Student Assessment (PISA). We find that these measures capture important aspects of students' academic profiles: some are importantly associated with contemporaneous performance and educational attainment and most measures have a high degree of stability over time. However, these measures are only limitedly correlated among themselves and have low correlations with self-report measures of the same constructs. This is likely a reflection of the fact that behavioural measures are representations of the test taker current 'state', rather than descriptions of the participant view of their own 'trait' like the self-report measures. Moreover, the low correlation across measures suggests that they capture different behavioural responses to the test-taking situation. These differences are still limitedly understood because the measures are constructed ex-post using collateral information collected during the administration of assessments rather than developed ex ante in line with theoretical models of human cognition and affect.

Performance decline in a low-stakes test at age 15 and educational attainment at age 25: Cross-country longitudinal evidence.

INTRODUCTION: Educational attainment is associated with important life outcomes including labour market performance, health status, well-being, civic and political participation. An important question is whether it is possible to identify early those students who lack the achievement motivation that is needed to complete a higher education degree. METHODS: Longitudinal follow-ups of representative samples of participants in the 2000 and 2003 Programme for International Student Assessment (PISA) from Australia, Denmark and Switzerland (N = 3110; 1130; and 1962; age = 15 to 27; % females 51%, 51%, 49%; ethnicity/race unknown) were used to identify the association between a measure of effort on a cognitively demanding low-stake task at age 15 - performance decline during the test - and educational attainment at age 25-27. RESULTS: A one SD difference in performance decline was associated with a 5-6 percentage point difference in the probability of obtaining tertiary-level qualifications (r = -0.15 in Australia; -0.11 in Denmark and -0.11 in Switzerland). We find no evidence of differences in this relationship across genders, socio-economic status and baseline levels of ability in the three countries. The association between performance decline and educational attainment is homogeneous across these groups. Self-reported measures of achievement motivation were not predictive of educational attainment in the three countries. CONCLUSIONS: Our work contributes new longitudinal evidence to the body of research in education employing behavioural measures of motivation and engagement. It can be used to understand the potential long-term consequences of disparities in students' preparation to sustain effort over cognitively demanding tasks.

Chaos and statistical relaxation in quantum systems of interacting particles.

We study the transition to chaos and the emergence of statistical relaxation in isolated dynamical quantum systems of interacting particles. Our approach is based on the concept of delocalization of the eigenstates in the energy shell, controlled by the Gaussian form of the strength function. We show that, although the fluctuations of the energy levels in integrable and nonintegrable systems are different, the global properties of the eigenstates are quite similar, provided the interaction between particles exceeds some critical value. In this case, the statistical relaxation of the systems is comparable, irrespective of whether or not they are integrable. The numerical data for the quench dynamics manifest excellent agreement with analytical predictions of the theory developed for systems of two-body interactions with a completely random character.

Magnetic reversal time in open long-range systems.

Topological phase space disconnection has been recently found to be a general phenomenon in many-body spin system with anisotropic interaction. We show that the power law divergence of magnetic reversal time at the energy signaling such disconnection is generic for long-range interacting systems with an exponent proportional to the number of particles. We also study the modifications induced putting the system in contact with a thermal bath. Using the canonical formalism we analyze the magnetic reversal times at any temperature. Moreover, due to the divergence of reversal time at the energy disconnection threshold we can recover, using saddle point approximation, a simple exponential dependence on the inverse temperature showing the explicit relevance of the energy disconnection threshold for finite many-body interacting systems at finite temperature. This sets a general framework to understand the emergence of ferromagnetism in finite magnetic systems starting from microscopic models without phenomenological on-site barriers.

Time scale for magnetic reversal and the topological nonconnectivity threshold.

Anisotropic classical Heisenberg models with all-to-all spin coupling display a topological nonconnectivity threshold (TNT) for any number N of spins. Below this threshold, the energy surface is disconnected in two components with positive and negative total magnetizations, respectively, so that magnetization cannot reverse its sign and ergodicity is broken, even at finite N. Here, we solve the model in the microcanonical ensemble, using a recently developed method based on large deviation techniques, and show that a phase transition is present at an energy higher than the TNT energy. In the energy range between the TNT energy and the phase transition, magnetization changes sign stochastically and its behavior can be fully characterized by an average magnetization reversal time. The time scale for magnetic reversal can be computed analytically, using statistical mechanics. Numerical simulations confirm this calculation and further show that the magnetic reversal time diverges with a power law at the TNT threshold, with a size-dependent exponent. This exponent can be computed in the thermodynamic limit N-->(infinity), by the knowledge of entropy as a function of magnetization, and turns out to be in reasonable agreement with finite numerical simulations. We finally generalize our results to other models: Heisenberg chains with distance-dependent coupling, small 3D clusters with nearest-neighbor interactions, metastable states. We conjecture that the power-law divergence of the magnetic reversal time scale might be a universal signature of the presence of a TNT.

Topological nonconnectivity threshold in long-range spin systems.

We demonstrate the existence of a topological disconnection threshold, recently found by Borgonovi [J. Stat. Phys. 116, 1435 (2004)], for generic 1-d anisotropic Heisenberg models interacting with an interparticle potential R(-alpha) when 0

Avoiding quantum chaos in quantum computation.

We study a one-dimensional chain of nuclear 1/2 spins in an external time-dependent magnetic field, considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos that can destroy the stability of quantum operations. The standard viewpoint is that the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a nonhomogeneous magnetic field can strongly reduce quantum chaos effects. We give analytical estimates that explain this effect, together with numerical data supporting our analysis.

Delocalization border and onset of chaos in a model of quantum computation.

We study the properties of spectra and eigenfunctions for a chain of 1/2 spins (qubits) in an external time-dependent magnetic field and under the conditions of nonselective excitation (when the amplitude of the magnetic field is large). This model is known as a possible candidate for experimental realization of quantum computation. We present the theory for finding delocalization transitions and show that for the interaction between nearest qubits, the transition is very different from that in quantum chaos. We explain this phenomena by showing that in the considered region of parameters our model is close to an integrable one. According to a general opinion, the threshold for the onset of quantum chaos due to the interqubit interaction decreases with an increase of the number of qubits. Contrary to this expectation, for a magnetic field with constant gradient we have found that chaos border does not depend on the number of qubits. We give analytical estimates that explain this effect, together with numerical data supporting our analysis. Random models with long-range interactions have been studied as well. In particular, we show that in this case the delocalization and quantum chaos borders coincide.

Dynamical fidelity of a solid-state quantum computation.

In this paper we analyze the dynamics in a spin model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows us to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to a quantum protocol. Specifically, we analyze, both analytically and numerically, how the fidelity decreases in dependence on the model parameters.

Enhancement of the magnetic anisotropy barrier in critical long range spin systems.

Magnetic materials are usually characterized by anisotropy energy barriers which dictate the timescale of the magnetization decay and consequently the magnetic stability of the sample. Here we consider magnetization decay for spin systems in a d = 3 cubic lattice with an isotropic Heisenberg interaction decaying as a power law with a critical exponent α = d and on-site anisotropy. We show that the anisotropy energy barrier can be determined from the ergodicity breaking energy of the corresponding isolated system and that, unlike in the case of nearest neighbour interaction, the anisotropy energy barrier grows as the particle volume, V, and not as the cross-sectional area.

Focusing in multiwell potentials: applications to ion channels.

We investigate nonequilibrium stationary distributions induced by stochastic dichotomous noise in double-well and multiwell models of ion channel gating kinetics. The channel kinetics is analyzed using both overdamped Langevin equations and master equations. With the Langevin equation approach we show a nontrivial focusing effect due to the external stochastic noise, namely, the concentration of the probability distribution in one of the two wells of a double-well system or in one or more of the wells of the multiwell model. In the multiwell system, focusing in the outer wells is shown to be achievable under physiological conditions, while focusing in the central wells has proved possible so far only at very low temperatures. We also discuss the strength of the focusing effect and obtain the conditions necessary for maximal focusing to appear. These conditions cannot be predicted by a simple master equation approach.

Onset of chaos and relaxation in isolated systems of interacting spins: energy shell approach.

We study the onset of chaos and statistical relaxation in two isolated dynamical quantum systems of interacting spins 1/2, one of which is integrable and the other chaotic. Our approach to identifying the emergence of chaos is based on the level of delocalization of the eigenstates with respect to the energy shell, the latter being determined by the interaction strength between particles or quasiparticles. We also discuss how the onset of chaos may be anticipated by a careful analysis of the Hamiltonian matrices, even before diagonalization. We find that despite differences between the two models, their relaxation processes following a quench are very similar and can be described analytically with a theory previously developed for systems with two-body random interactions. Our results imply that global features of statistical relaxation depend on the degree of spread of the eigenstates within the energy shell and may happen to both integrable and nonintegrable systems.

Classical statistical mechanics of a few-body interacting spin model

We study the emergence of Boltzmann's law for the "single-particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction is very strong. Specific attention is paid to classical analogs of the average shape of quantum eigenstates and "local density of states," which are very important in quantum chaology. Analytical predictions are then compared with numerical data.

Semiquantal approach to finite systems of interacting particles.

A novel approach is suggested for the statistical description of quantum systems of interacting particles. We show that the occupation numbers for single-particle states can be represented as a convolution of a classical analog of the eigenstate, with the quantum occupation number for noninteracting particles. The latter takes into account the wave function symmetry and depends on the unperturbed energy spectrum only. As a result, the distribution of occupation numbers n(s) can be found even for a large number of interacting particles. Using the model of interacting spins, we demonstrate that this approach gives a correct description of n(s) even in deep quantum regions with few single-particle orbitals.

Irregular dynamics in a one-dimensional Bose system.

We study many-body quantum dynamics of delta-interacting bosons confined in a one-dimensional ring. Main attention is paid to the transition from the mean-field to the Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wave function and the momentum distribution depend on time for weak and strong interactions. We show that the transition from regular (quasiperiodic) to irregular ("chaotic") dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime, the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.