Incremental Principal Component Analysis Exact implementation and continuity corrections

This paper describes some applications of an incremental implementation of the principal component analysis (PCA). The algorithm updates the transformation coefficients matrix on-line for each new sample, without the need to keep all the samples in memory. The algorithm is formally equivalent to the usual batch version, in the sense that given a sample set the transformation coefficients at the end of the process are the same. The implications of applying the PCA in real time are discussed with the help of data analysis examples. In particular we focus on the problem of the continuity of the PCs during an on-line analysis.Comment: accepted at http://www.icinco.org

Scaling behaviour of trapped bosonic particles in two dimensions at finite temperature

In the framework of the trap-size scaling theory, we study the scaling properties of the Bose-Hubbard model in two dimensions in the presence of a trapping potential at finite temperature. In particular, we provide results for the particle density and the density-density correlator at the Mott transitions and within the superfluid phase. For the former quantity, numerical outcomes are also extensively compared to Local Density Approximation predictions.Comment: 8 pages, 9 figure

Shape dependence and anisotropic finite-size scaling of the phase coherence of three-dimensional Bose-Einstein condensed gases

We investigate the equilibrium phase-coherence properties of Bose-condensed particle systems, focusing on their shape dependence and finite-size scaling (FSS). We consider three-dimensional (3D) homogeneous systems confined to anisotropic L x L x L_a boxes, below the BEC transition temperature $T_c$. We show that the phase correlations develop peculiar anisotropic FSS for any $T<T_c$, in the large-$L$ limit keeping the ratio \lambda = L_a/L^2 fixed. This phenomenon is effectively described by the 3D spin-wave (SW) theory. Its universality is confirmed by quantum Monte Carlo simulations of the 3D Bose-Hubbard model in the BEC phase. The phase-coherence properties of very elongated BEC systems, \lambda>>1, are characterized by a coherence length \xi_a \sim A_t \rho_s/T where A_t is the transverse area and \rho_s is the superfluid density.Comment: 7 page

Bose-Einstein condensation and critical behavior of two-component bosonic gases

We study Bose-Einstein condensation (BEC) in three-dimensional two-component bosonic gases, characterizing the universal behaviors of the critical modes arising at the BEC transitions. For this purpose, we use field-theoretical (FT) renormalization-group (RG) methods and perform mean-field and numerical calculations. The FT RG analysis is based on the Landau-Ginzburg-Wilson Phi4 theory with two complex scalar fields which has the same symmetry as the bosonic system. In particular, for identical bosons with exchange Z_2,e symmetry, coupled by effective density-density interactions, the global symmetry is Z_2e X U(1) X U(1). At the BEC transition it may break into Z_2,e X Z_2 X Z_2 when both components condense simultaneously, or to U(1) X Z_2 when only one component condenses. This implies different universality classes for the corresponding critical behaviors. Numerical simulations of the two-component Bose-Hubbard model in the hard-core limit support the RG prediction: when both components condense simultaneously, the critical behavior is controlled by a decoupled XY fixed point, with unusual slowly-decaying scaling corrections arising from the on-site inter-species interaction.Comment: 13 page

Interplay between temperature and trap effects in one-dimensional lattice systems of bosonic particles

We investigate the interplay of temperature and trap effects in cold particle systems at their quantum critical regime, such as cold bosonic atoms in optical lattices at the transitions between Mott-insulator and superfluid phases. The theoretical framework is provided by the one-dimensional Bose-Hubbard model in the presence of an external trapping potential, and the trap-size scaling theory describing the large trap-size behavior at a quantum critical point. We present numerical results for the low-temperature behavior of the particle density and the density-density correlation function at the Mott transitions, and within the gapless superfluid phase.Comment: 9 page

Critical behavior of lattice gases in a trapping potential

The renormalization group theory is applied to study the scaling behavior of bosonic gases trapped in optical lattices. Quantum Monte Carlo simulations of the Bose-Hubbard model are made in one, two and three dimensions

Comportamento critico del modello di Ising in campo aleatorio

Studiamo il modello di Ising in campo aleatorio a temperatura finita con distribuzione bimodale con intensita' unitaria. Si analizza la possibilita' di una transizione di fase del secondo ordine governata da un punto fisso a temperatura nulla e si procede a uno studio Monte Carlo mediante la teoria del finite-size scaling

Stochastic model of solvent exchange in the first coordination shell of aqua Ions

Ion microsolvation is a basic, yet fundamental, process of ionic solutions underlying many relevant phenomena in either biological or nanotechnological applications, such as solvent reorganization energy, ion transport, catalytic activity, and so on. As a consequence, it is a topic of extensive investigations by various experimental techniques, ranging from X-ray diffraction to NMR relaxation and from calorimetry to vibrational spectroscopy, and theoretical approaches, especially those based on molecular dynamics (MD) simulations. The conventional microscopic view of ion solvation is usually provided by a "static" cluster model representing the first ion-solvent coordination shell. Despite the merits of such a simple model, however, ion coordination in solution should be better regarded as a complex population of dynamically interchanging molecular configurations. Such a more comprehensive view is more subtle to characterize and often elusive to standard approaches. In this work, we report on an effective computational strategy aiming at providing a detailed picture of solvent coordination and exchange around aqua ions, thus including the main structural, thermodynamic, and dynamic properties of ion microsolvation, such as the most probable first-shell complex structures, the corresponding free energies, the interchanging energy barriers, and the solvent-exchange rates. Assuming the solvent coordination number as an effective reaction coordinate and combining MD simulations with enhanced sampling and master-equation approaches, we propose a stochastic model suitable for properly describing, at the same time, the thermodynamics and kinetics of ion-water coordination. The model is successfully tested toward various divalent ions (Ca2+, Zn2+, Hg2+, and Cd2+) in aqueous solution, considering also the case of a high ionic concentration. Results show a very good agreement with those issuing from brute-force MD simulations, when available, and support the reliable prediction of rare ion-water complexes and slow water exchange rates not easily accessible to usual computational methods

Ferromagnetic-glassy transitions in three-dimensional Ising spin glasses

We investigate the ferromagnetic-glassy transitions which separate the low-temperature ferromagnetic and spin-glass phases in the temperature-disorder phase diagram of three-dimensional Ising spin-glass models. For this purpose, we consider the cubic-lattice +-J (Edwards-Anderson) Ising model with bond distribution $P(J) = p \delta(J - 1) + (1-p) \delta(J + 1)$, and present a numerical Monte Carlo study of the critical behavior along the line that marks the onset of ferromagnetism. The finite-size scaling analysis of the Monte Carlo data shows that the ferromagnetic-glassy transition line is slightly reentrant. As a consequence, for an interval of the disorder parameter p, around p=0.77, the system presents a low-temperature glassy phase, an intermediate ferromagnetic phase, and a high-temperature paramagnetic phase. Along the ferromagnetic-glassy transition line magnetic correlations show a universal critical behavior with critical exponents nu=0.96(2) and eta=-0.39(2). The hyperscaling relation beta/nu = (1 + eta)/2 is satisfied at the transitions, so that beta/nu = 0.305(10). This magnetic critical behavior represents a new universality class for ferromagnetic transitions in Ising-like disordered systems. Overlap correlations are apparently not critical and show a smooth behavior across the transition.Comment: 24 page