Istituto Nazionale per la Fisica della Materia

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy \ensuremath{\Sigma} and the electron-hole interaction. A good approximation for \ensuremath{\Sigma} is obtained with Hedin's $\mathrm{GW}$ approach, using density-functional theory as a zero-order solution. First-principles $\mathrm{GW}$ calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of \ensuremath{\Sigma}. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional studies in metabolic and protein networks), or technological problems (optimization of large infrastructures). Several types of algorithms exist for revealing the community structure in networks, but a general and quantitative definition of community is not implemented in the algorithms, leading to an intrinsic difficulty in the interpretation of the results without any additional nontopological information. In this article we deal with this problem by showing how quantitative definitions of community are implemented in practice in the existing algorithms. In this way the algorithms for the identification of the community structure become fully self-contained. Furthermore, we propose a local algorithm to detect communities which outperforms the existing algorithms with respect to computational cost, keeping the same level of reliability. The algorithm is tested on artificial and real-world graphs. In particular, we show how the algorithm applies to a network of scientific collaborations, which, for its size, cannot be attacked with the usual methods. This type of local algorithm could open the way to applications to large-scale technological and biological systems.

This review presents in a comprehensive and tutorial form the basic principles of the Monte Carlo method, as applied to the solution of transport problems in semiconductors. Sufficient details of a typical Monte Carlo simulation have been given to allow the interested reader to create his own Monte Carlo program, and the method has been briefly compared with alternative theoretical techniques. Applications have been limited to the case of covalent semiconductors. Particular attention has been paid to the evaluation of the integrated scattering probabilities, for which final expressions are given in a form suitable for their direct use. A collection of results obtained with Monte Carlo simulations is presented, with the aim of showing the power of the method in obtaining physical insights into the processes under investigation. Special technical aspects of the method and updated microscopic models have been treated in some appendixes.

Numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional positions of individual birds in airborne flocks of a few thousand members, we show that the interaction does not depend on the metric distance, as most current models and theories assume, but rather on the topological distance. In fact, we discovered that each bird interacts on average with a fixed number of neighbors (six to seven), rather than with all neighbors within a fixed metric distance. We argue that a topological interaction is indispensable to maintain a flock's cohesion against the large density changes caused by external perturbations, typically predation. We support this hypothesis by numerical simulations, showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one.

We report on a quantum optical experimental implementation of teleportation of unknown pure quantum states. This realizes all of the nonlocal aspects of the original scheme proposed by Bennett et al. and is equivalent to it up to a local operation. We exhibit results for the teleportation of a linearly polarized state and of an elliptically polarized state. We show that the experimental results cannot be explained in terms of a classical channel alone. The Bell measurement in our experiment can distinguish between all four Bell states simultaneously allowing, in the ideal case, a 100% success rate of teleportation.

Abstract We present a dataset of daily resolution climatic time series that has been compiled for the European Climate Assessment (ECA). As of December 2001, this ECA dataset comprises 199 series of minimum, maximum and/or daily mean temperature and 195 series of daily precipitation amount observed at meteorological stations in Europe and the Middle East. Almost all series cover the standard normal period 1961–90, and about 50% extends back to at least 1925. Part of the dataset (90%) is made available for climate research on CDROM and through the Internet (at http://www.knmi.nl/samenw/eca ). A comparison of the ECA dataset with existing gridded datasets, having monthly resolution, shows that correlation coefficients between ECA stations and nearest land grid boxes between 1946 and 1999 are higher than 0.8 for 93% of the temperature series and for 51% of the precipitation series. The overall trends in the ECA dataset are of comparable magnitude to those in the gridded datasets. The potential of the ECA dataset for climate studies is demonstrated in two examples. In the first example, it is shown that the winter (October–March) warming in Europe in the 1976–99 period is accompanied by a positive trend in the number of warm‐spell days at most stations, but not by a negative trend in the number of cold‐spell days. Instead, the number of cold‐spell days increases over Europe. In the second example, it is shown for winter precipitation between 1946 and 1999 that positive trends in the mean amount per wet day prevail in areas that are getting drier and wetter. Because of its daily resolution, the ECA dataset enables a variety of empirical climate studies, including detailed analyses of changes in the occurrence of extremes in relation to changes in mean temperature and total precipitation. Copyright © 2002 Royal Meteorological Society.

We generated single-cycle isolated attosecond pulses around approximately 36 electron volts using phase-stabilized 5-femtosecond driving pulses with a modulated polarization state. Using a complete temporal characterization technique, we demonstrated the compression of the generated pulses for as low as 130 attoseconds, corresponding to less than 1.2 optical cycles. Numerical simulations of the generation process show that the carrier-envelope phase of the attosecond pulses is stable. The availability of single-cycle isolated attosecond pulses opens the way to a new regime in ultrafast physics, in which the strong-field electron dynamics in atoms and molecules is driven by the electric field of the attosecond pulses rather than by their intensity profile.

We report the production of matter-wave solitons in an ultracold lithium-7 gas. The effective interaction between atoms in a Bose-Einstein condensate is tuned with a Feshbach resonance from repulsive to attractive before release in a one-dimensional optical waveguide. Propagation of the soliton without dispersion over a macroscopic distance of 1.1 millimeter is observed. A simple theoretical model explains the stability region of the soliton. These matter-wave solitons open possibilities for future applications in coherent atom optics, atom interferometry, and atom transport.

The high performance of ceria (CeO2) as an oxygen buffer and active support for noble metals in catalysis relies on an efficient supply of lattice oxygen at reaction sites governed by oxygen vacancy formation. We used high-resolution scanning tunneling microscopy and density functional calculations to unravel the local structure of surface and subsurface oxygen vacancies on the (111) surface. Electrons left behind by released oxygen localize on cerium ions. Clusters of more than two vacancies exclusively expose these reduced cerium ions, primarily by including subsurface vacancies, which therefore play a crucial role in the process of vacancy cluster formation. These results have implications for our understanding of oxidation processes on reducible rare-earth oxides.

The concept of fast ignition with inertial confinement fusion (ICF) is a way to reduce the energy required for ignition and burn and to maximize the gain produced by a single implosion. Based on recent experimental findings at the PETAWATT laser at Lawrence Livermore National Laboratory, an intense proton beam to achieve fast ignition is proposed. It is produced by direct laser acceleration and focused onto the pellet from the rear side of an irradiated target and can be integrated into a hohlraum for indirect drive ICF.

Numerical investigations of dynamical systems allow one to give estimates of the rate of divergence of nearby trajectories, by means of a quantity which is usually assumed to be related to the Kolmogorov (or metric) entropy. In this paper it is shown first, on the basis of mathematical results of Oseledec and Piesin, how such a relation can be made precise. Then, as an example, a numerical study of the Kolmogorov entropy for the H\'enon-Heiles model is reported.

The macroscopic nonlinear pyroelectric polarization of wurtzite AlxGa1-xN, InxGa1-xN and Al(x)ln(1-x)N ternary compounds (large spontaneous polarization and piezoelectric coupling) dramatically affects the optical and electrical properties of multilayered Al(In)GaN/GaN hetero-, nanostructures and devices, due to the huge built-in electrostatic fields and bound interface charges caused by gradients in polarization at surfaces and heterointerfaces. Models of polarization-induced effects in GaN-based devices so far have assumed that polarization in ternary nitride alloys can be calculated by a linear interpolation between the limiting values of the binary compounds. We present theoretical and experimental evidence that the macroscopic polarization in nitride alloys is a nonlinear function of strain and composition. We have applied these results to interpret experimental data obtained in a number of InGaN/GaN quantum wells (QWs) as well as AlInN/GaN and AlGaN/GaN transistor structures. We find that the discrepancies between experiment and ab initio theory present so far are almost completely eliminated for the AlGaN/GaN-based heterostructures when the nonlinearity of polarization is accounted for. The realization of undoped lattice-matched AlInN/GaN heterostructures further allows us to prove the existence of a gradient in spontaneous polarization by the experimental observation of two-dimensional electron gases (2DEGs). The confinement of 2DEGs in InGaN/GaN QWs in combination with the measured Stark shift of excitonic recombination is used to determine the polarization-induced electric fields in nanostructures. To facilitate inclusion of the predicted nonlinear polarization in future simulations, we give an explicit prescription to calculate polarization-induced electric fields and bound interface charges for arbitrary composition in each of the tertiary III-N alloys. In addition, the theoretical and experimental results presented here allow a detailed comparison of the predicted electric fields and bound interface charges with the measured Stark shift and the sheet carrier concentration of polarization-induced 2DEGs. This comparison provides an insight into the reliability of the calculated nonlinear piezoelectric and spontaneous polarization of group III nitride ternary alloys.
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Over the last decade there have been spectacular developments in ultrafast laser technology, due to the introduction of solid state active materials and of new mode-locking and amplification techniques. These advances, together with the discovery of new nonlinear optical crystals, have fostered the introduction of ultrafast optical parametric amplifiers as a practical source of femtosecond pulses tunable across the visible and infrared spectral ranges. This article summarizes the recent progress in the development of ultrafast optical parametric amplifiers, giving the basic design principles for different frequency ranges and in addition presenting some advanced designs for the generation of ultrabroadband, few-optical-cycle pulses. Finally, we also briefly discuss the possibility of applying parametric amplification schemes to large-scale, petawatt-level systems.

The structure of RuO(2)(110) and the mechanism for catalytic carbon monoxide oxidation on this surface were studied by low-energy electron diffraction, scanning tunneling microscopy, and density-functional calculations. The RuO(2)(110) surface exposes bridging oxygen atoms and ruthenium atoms not capped by oxygen. The latter act as coordinatively unsaturated sites-a hypothesis introduced long ago to account for the catalytic activity of oxide surfaces-onto which carbon monoxide can chemisorb and from where it can react with neighboring lattice-oxygen to carbon dioxide. Under steady-state conditions, the consumed lattice-oxygen is continuously restored by oxygen uptake from the gas phase. The results provide atomic-scale verification of a general mechanism originally proposed by Mars and van Krevelen in 1954 and are likely to be of general relevance for the mechanism of catalytic reactions at oxide surfaces.

We investigate the low energy excitations of a dilute atomic Bose gas confined in a harmonic trap of frequency ${\ensuremath{\omega}}_{0}$ and interacting with repulsive forces. The dispersion law $\ensuremath{\omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\omega}}_{0}({2n}^{2}+2n\ensuremath{\ell}+3n+\ensuremath{\ell}{)}^{1/2}$ for the elementary excitations is obtained for large numbers of atoms in the trap, to be compared with the prediction $\ensuremath{\omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\omega}}_{0}(2n+\ensuremath{\ell})$ of the noninteracting harmonic oscillator model. Here $n$ is the number of radial nodes and $\ensuremath{\ell}$ is the orbital angular momentum. The effects of the kinetic energy pressure are estimated using a sum rule approach. Results are also presented for deformed traps and attractive forces.

Activated processes can be studied in the molecular dynamics (MD) approach by imposing a mechanical constraint on the corresponding reaction coordinate and by performing a kind of thermodynamic integration. The blue-moon ensemble method provides us with the correct algorithm for computing the potential of mean force and the transmission coefficient. Here we show a procedure for obtaining the mean force directly from the average force of constraint and a geometric correction term which is easy to compute in MD simulations. Previous work on the same problem will be also discussed.

The measurements of the hyperfine structure of free, naturally occurring, alkali atoms are reviewed. The experimental methods are discussed, as are the relationships between hyperfine structure data and other atomic constants.

We report on the direct observation of an oscillating atomic current in a one-dimensional array of Josephson junctions realized with an atomic Bose-Einstein condensate. The array is created by a laser standing wave, with the condensates trapped in the valleys of the periodic potential and weakly coupled by the interwell barriers. The coherence of multiple tunneling between adjacent wells is continuously probed by atomic interference. The square of the small-amplitude oscillation frequency is proportional to the microscopic tunneling rate of each condensate through the barriers and provides a direct measurement of the Josephson critical current as a function of the intermediate barrier heights. Our superfluid array may allow investigation of phenomena so far inaccessible to superconducting Josephson junctions and lays a bridge between the condensate dynamics and the physics of discrete nonlinear media.

We provide explicit rules to calculate the nonlinear polarization for nitride alloys of arbitrary composition, and hence, the bound sheet charge induced by polarization discontinuity at the interfaces between different alloy and binary (epi)layers. We then present experimental results and simulations of polarization-related quantities in selected nitride-alloy-based heterostructure systems. The agreement of experiment and simulation, also in comparison to previous approaches, strongly suggests that the macroscopic polarization of nitride alloys is indeed nonlinear as a function of composition.