1,720,982 research outputs found
The glassy random laser: Replica symmetry breaking in the intensity fluctuations of emission spectra
Full text linkThe 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
Calcolo delle probabilità. Un trattatello per principianti volenterosi.
No full textCalcolo delle probabilità presenta la probabilità e la statistica in modo originale e profondo, pur restando intuitivo e facilmente accessibile. Anche quando elabora, e lo fa di frequente, argomenti intellettualmente sofisticati che sono spesso alla base di queste discipline, sceglie di appoggiarsi ai molti esempi svolti, a figure significative e ben scelte, e di esporre la teoria in un linguaggio di elegante essenzialità. Il testo copre tutti gli argomenti fondamentali, sempre con approfondimenti mirati a inserire sviluppi delicati ma cruciali in una comprensione di base. Gli strumenti matematici necessari a impadronirsi della teoria sono discussi in modo chiaro e originale, in nove appendici dedicate a questo scopo. Esempi di stime usano questioni e dati attuali e aggiornati: alcune argomentazioni si riferiscono per esempio all’analisi della recente pandemia di Covid-19. Il capitolo finale Entropia, probabilità e meccanica statistica introduce a una dimensione che richiama esplicitamente il mondo della fisica caro agli autori
Glassiness and lack of equipartition in random lasers: The common roots of ergodicity breaking in disordered and nonlinear systems
No full textWe present here a unifying perspective for the lack of equipartition in nonlinear ordered systems and the low-temperature phase-space fragmentation in disordered systems. We demonstrate that they are just two manifestation of the same underlying phenomenon: ergodicity breaking. Inspired by recent experiments suggesting that lasing in optically active disordered media is related to an ergodicity-breaking transition, we studied numerically a statistical mechanics model for the nonlinearly coupled light modes in a disordered medium under external pumping. Their collective behavior appears to be akin to that displayed around the ergodicity-breaking transition in glasses, as we show measuring the glass order parameter of the replicasymmetry-breaking theory. Most remarkably, we also find that at the same critical point a breakdown of energy equipartition among light modes occurs, the typical signature of ergodicity breaking in nonlinear systems as the celebrated Fermi-Pasta-Ulam model. The crucial ingredient of our system that allows us to find equipartition breakdown together with replica symmetry breaking is that the amplitudes of light modes are locally unbounded, i.e., they are only subject to a global constraint. The physics of random lasers appears thus as a unique test-bed to develop under a unifying perspective the study of ergodicity breaking in statistical disordered systems and nonlinear ordered ones
Regularization and decimation pseudolikelihood approaches to statistical inference inXYspin models
Full text linkWe implement a pseudolikelihood approach with l1 and l2 regularizations as well as the recently introduced pseudolikelihood with decimation procedure to the inverse problem in continuous spin models on arbitrary networks, with arbitrarily disordered couplings. Performances of the approaches are tested against data produced by Monte Carlo numerical simulations and compared also to previously studied fully connected mean-field-based inference techniques. The results clearly show that the best network reconstruction is obtained through the decimation scheme, which also allows us to make the inference down to lower temperature regimes. Possible applications to phasor models for light propagation in random media are proposed and discusse
Solving the spherical p -spin model with the cavity method: equivalence with the replica results
No full textThe spherical p-spin is a fundamental model for glassy physics, thanks to its analytical solution achievable via the replica method. Unfortunately, the replica method has some drawbacks: it is very hard to apply to diluted models and the assumptions beyond it are not immediately clear. Both drawbacks can be overcome by the use of the cavity method; however, this needs to be applied with care to spherical models. Here, we show how to write the cavity equations for spherical p-spin models, both in the replica symmetric (RS) ansatz (corresponding to belief propagation) and in the one-step replica-symmetry-breaking (1RSB) ansatz (corresponding to survey propagation). The cavity equations can be solved by a Gaussian RS and multivariate Gaussian 1RSB ansatz for the distribution of the cavity fields. We compute the free energy in both ansatzes and check that the results are identical to the replica computation, predicting a phase transition to a 1RSB phase at low temperatures. The advantages of solving the model with the cavity method are many. The physical meaning of the ansatz for the cavity marginals is very clear. The cavity method works directly with the distribution of local quantities, which allows us to generalize the method to diluted graphs. What we are presenting here is the first step towards the solution of the diluted version of the spherical p-spin model, which is a fundamental model in the theory of random lasers and interesting per se as an easier-to-simulate version of the classical fully connected p-spin model
Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model
No full textThe 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
Intensity pseudo-localized phase in the glassy random laser
Full text linkEvidence of an emergent pseudo-localized phase characterizing the low-temperature replica symmetry breaking phase of the complex disordered models for glassy light is provided in the mode-locked random laser model. A pseudo-localized phase corresponds to a state in which the intensity of light modes is neither equipartited among all modes nor really localized on few of them. Such a hybrid phase has been recently characterized in other models, such as the Discrete Non-Linear Schrödinger equation, just as a finite size effect, while in the low temperature phase of the glassy random laser it seems to be robust in the limit of large size.21 pages, 6 figure
Universality class of the mode-locked glassy random laser
Full text linkBy means of enhanced Monte Carlo numerical simulations parallelized on GPU's
we study the critical properties of the spin-glass-like model for the
mode-locked glassy random laser, a -spin model with complex spins with a
global spherical constraint and quenched random interactions. Using two
different boundary conditions for the mode frequencies we identify the critical
points and the critical indices of the random lasing phase transition using ,
with finite size scaling techniques. The outcome of the scaling analysis is
that the mode-locked random laser is in a mean-field universality class, though
different from the mean-field class of the Random Energy Model and the glassy
random laser in the narrow band approximation, that is, the fully connected
version of the present model. The low temperature (high pumping) phase is
finally characterized by means of the overlap distribution and evidence for the
onset of replica symmetry breaking in the lasing regime is provided.Comment: 17 pages, 11 figure
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
- …
