Reference-less wavefront shaping in a Hopfield-like rough intensity landscape.

This study introduces a new digital-micromirror based binary-phase wavefront shaping technique, which allows the measurement of the full coupling matrix of a disordered medium without a reference and enables to focusing transmitted light. The coupling matrix takes on a bi-dyadic structure, similar to a Hopfield memory matrix containing two memory patterns. Sequential wavefront optimization in this configuration often stalls due to a rough intensity landscape, resulting in a non-optimal state. To overcome this issue, we propose the Complete Couplings Mapping method, which consistently reaches the theoretically expected maximum intensity.

Statistical mechanics of biomolecular condensates via cavity methods.

Physical mechanisms of phase separation in living systems play key physiological roles and have recently been the focus of intensive studies. The strongly heterogeneous nature of such phenomena poses difficult modeling challenges that require going beyond mean-field approaches based on postulating a free energy landscape. The pathway we take here is to calculate the partition function starting from microscopic interactions by means of cavity methods, based on a tree approximation for the interaction graph. We illustrate them on the binary case and then apply them successfully to ternary systems, in which simpler one-factor approximations are proved inadequate. We demonstrate the agreement with lattice simulations and contrast our theory with coacervation experiments of associative de-mixing of nucleotides and poly-lysine. Different types of evidence are provided to support cavity methods as ideal tools for modeling biomolecular condensation, giving an optimal balance between the consideration of spatial aspects and fast computational results.

Demonstration of Self-Starting Nonlinear Mode Locking in Random Lasers.

In ultrafast multimode lasers, mode locking is implemented by means of saturable absorbers or modulators, allowing for very short pulses. This occurs because of nonlinear interactions of modes with well equispaced frequencies. Though theory predicts that, in the absence of any device, mode locking would occur in random lasers, this has never been demonstrated so far. Through the analysis of multimode correlations we provide clear evidence for nonlinear mode coupling in random lasers. The behavior of multiresonance intensity correlations is tested against the nonlinear frequency matching condition equivalent to the one underlying phase locking in ordered ultrafast lasers. Nontrivially large correlations are clearly observed for spatially overlapping resonances that sensitively depend on the frequency matching condition to be satisfied, eventually demonstrating the occurrence of nonlinear mode-locked mode coupling. This is the first example, to our knowledge, of an experimental realization of self-starting mode locking in random lasers, allowing for many new developments in the design and use of nanostructured devices.

Reconstructing Nonparametric Productivity Networks.

Network models provide a general representation of inter-connected system dynamics. This ability to connect systems has led to a proliferation of network models for economic productivity analysis, primarily estimated non-parametrically using Data Envelopment Analysis (DEA). While network DEA models can be used to measure system performance, they lack a statistical framework for inference, due in part to the complex structure of network processes. We fill this gap by developing a general framework to infer the network structure in a Bayesian sense, in order to better understand the underlying relationships driving system performance. Our approach draws on recent advances in information science, machine learning and statistical inference from the physics of complex systems to estimate unobserved network linkages. To illustrate, we apply our framework to analyze the production of knowledge, via own and cross-disciplinary research, for a world-country panel of bibliometric data. We find significant interactions between related disciplinary research output, both in terms of quantity and quality. In the context of research productivity, our results on cross-disciplinary linkages could be used to better target research funding across disciplines and institutions. More generally, our framework for inferring the underlying network production technology could be applied to both public and private settings which entail spillovers, including intra- and inter-firm managerial decisions and public agency coordination. This framework also provides a systematic approach to model selection when the underlying network structure is unknown.

Spin Glasses in a Field Show a Phase Transition Varying the Distance among Real Replicas (And How to Exploit It to Find the Critical Line in a Field).

We discuss a phase transition in spin glass models that have been rarely considered in the past, namely, the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e., at a smaller overlap) than the typical one. In the first part of the work, by solving analytically the Sherrington-Kirkpatrick model in a field close to its critical point, we show that, even in a paramagnetic phase, the forcing of two real replicas to an overlap small enough leads the model to a phase transition where the symmetry between replicas is spontaneously broken. More importantly, this phase transition is related to the de Almeida-Thouless (dAT) critical line. In the second part of the work, we exploit the phase transition in the overlap between two real replicas to identify the critical line in a field in finite dimensional spin glasses. This is a notoriously difficult computational problem, because of considerable finite size corrections. We introduce a new method of analysis of Monte Carlo data for disordered systems, where the overlap between two real replicas is used as a conditioning variate. We apply this analysis to equilibrium measurements collected in the paramagnetic phase in a field, h > 0 and T c ( h ) < T < T c ( h = 0 ) , of the d = 1 spin glass model with long range interactions decaying fast enough to be outside the regime of validity of the mean field theory. We thus provide very reliable estimates for the thermodynamic critical temperature in a field.

Inverse problem for multi-body interaction of nonlinear waves.

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable temperature-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems. The high versatility of the exposed techniques also concerns the number of expected interactions: results are presented for different graph topologies, ranging from sparse to dense graphs.

The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra.

The behavior of a newly introduced overlap parameter, measuring the correlation between intensity fluctuations of waves in random media, is analyzed in different physical regimes, with varying amount of disorder and non-linearity. This order parameter allows to identify the laser transition in random media and describes its possible glassy nature in terms of emission spectra data, the only data so far accessible in random laser measurements. The theoretical analysis is performed in terms of the complex spherical spin-glass model, a statistical mechanical model describing the onset and the behavior of random lasers in open cavities. Replica Symmetry Breaking theory allows to discern different kinds of randomness in the high pumping regime, including the most complex and intriguing glassy randomness. The outcome of the theoretical study is, eventually, compared to recent intensity fluctuation overlap measurements demonstrating the validity of the theory and providing a straightforward interpretation of qualitatively different spectral behaviors in different random lasers.

Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model.

The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-1 model with p-body quenched disordered interaction, with p>2, termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coexistence of low-density and high-density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be obtained by the one-step replica symmetry breaking ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include: (i) the usual random first-order transition (Kauzmann-like) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat, and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a nonzero complexity line. The latter inversion, though, turns out to be preceded by a dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode-coupling-theory equations near the boundaries of paramagnetic solutions and the relationship with the underlying statics is discussed.

Time-resolved dynamics of granular matter by random laser emission.

Because of the huge commercial importance of granular systems, the second-most used material in industry after water, intersecting the industry in multiple trades, like pharmacy and agriculture, fundamental research on grain-like materials has received an increasing amount of attention in the last decades. In photonics, the applications of granular materials have been only marginally investigated. We report the first phase-diagram of a granular as obtained by laser emission. The dynamics of vertically-oscillated granular in a liquid solution in a three-dimensional container is investigated by employing its random laser emission. The granular motion is function of the frequency and amplitude of the mechanical solicitation, we show how the laser emission allows to distinguish two phases in the granular and analyze its spectral distribution. This constitutes a fundamental step in the field of granulars and gives a clear evidence of the possible control on light-matter interaction achievable in grain-like system.

Shaken granular lasers.

Granular materials have been studied for decades, driven by industrial and technological applications. These very simple systems, composed of agglomerations of mesoscopic particles, are characterized, in specific regimes, by a large number of metastable states and an extreme sensitivity (e.g., in sound transmission) to the arrangement of grains; they are not substantially affected by thermal phenomena, but can be controlled by mechanical solicitations. Laser emission from shaken granular matter is so far unexplored. Here we provide experimental evidence that laser emission can be affected and controlled by the status of the motion of the granular material; we also find that competitive random lasers can be observed. We hence demonstrate the potentialities of gravity-affected moving disordered materials for optical applications, and open the road to a variety of novel interdisciplinary investigations, involving modern statistical mechanics and disordered photonics.

Stable solution of the simplest spin model for inverse freezing.

We analyze the Blume-Emery-Griffiths-Capel model with disordered interaction that displays the inverse freezing phenomenon. The behavior of this spin-1 model in crystal field is studied throughout the phase diagram, and the transition lines are computed using the full replica symmetry breaking ansatz. We compare the results both with the formulation of the same model in terms of Ising spins on lattice gas, where no reentrance takes place, and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. 93, 037202 (2004)], for which the reentrance is enhanced as the ratio between the degeneracy of full to empty sites increases. The simplest version of all these models, known as the Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase.