arXiv subjects

Isaac Pérez Castillo

Publications and source records attributed to Isaac Pérez Castillo.

At least 37 records · Page 2Linked to original sources

arXiv2020

Quantum quench in a driven Ising chain

We consider the Ising chain driven by oscillatory transverse magnetic fields. For certain parameter regimes, we reveal a hidden integrable structure in the problem, which allows access to the \textit{exact time-evolution} in this driven quantum system. We compute time-evolved one- and two-point functions following a quench that activates the driving. It is shown that this model does not heat up to infinite temperature, despite the absence of energy conservation, and we further discuss the generalization to a family of driven Hamiltonians that do not suffer heating to infinite temperature, despite the absence of integrability and disorder. The particular model studied in detail also presents a route for realising exotic physics (such as the E8 perturbed conformal field theory) via driving in quantum chains that could otherwise never realise such behaviour. In particular we numerically confirm that the ratio of the meson excitations masses is given by the golden ratio.

cond-mat.other↗

arXiv2020

Analytic approach for the number statistics of non-Hermitian random matrices

We introduce a powerful analytic method to study the statistics of the number $\mathcal{N}_{\textbf{A}}(γ)$ of eigenvalues inside any contour $γ\in \mathbb{C}$ for infinitely large non-Hermitian random matrices ${\textbf A}$. Our generic approach can be applied to different random matrix ensembles, even when the analytic expression for the joint distribution of eigenvalues is not known. We illustrate the method on the adjacency matrices of weighted random graphs with asymmetric couplings, for which standard random-matrix tools are inapplicable. The main outcome is an effective theory that determines the cumulant generating function of $\mathcal{N}_{\textbf{A}}$ via a path integral along $γ$, with the path probability distribution following from the solution of a self-consistent equation. We derive the expressions for the mean and the variance of $\mathcal{N}_{\textbf{A}}$ as well as for the rate function governing rare fluctuations of ${\mathcal{N}}_{\textbf{A}}{(γ)}$. All theoretical results are compared with direct diagonalization of finite random matrices, exhibiting an excellent agreement.

cond-mat.dis-nn↗

arXiv2020

Out-of-equilibrium phase transitions induced by Floquet resonances in a periodically quench-driven XY spin chain

We consider the dynamics of an XY spin chain subjected to an external transverse field which is periodically quenched between two values. By deriving an exact expression of the Floquet Hamiltonian for this out-of-equilibrium protocol with arbitrary driving frequencies, we show how, after an unfolding of the Floquet spectrum, the parameter space of the system is characterized by alternations between local and non-local regions, corresponding respectively to the absence and presence of Floquet resonances. The boundary lines between regions are obtained analytically from avoided crossings in the Floquet quasi-energies and are observable as phase transitions in the synchronized state. The transient behaviour of dynamical averages of local observables similarly undergoes a transition, showing either a rapid convergence towards the synchronized state in the local regime, or a rather slow one exhibiting persistent oscillations in the non-local regime, where explicit decay coefficients are presented.

cond-mat.stat-mech↗

arXiv2020

The exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model

Inelastic neutron scattering experiments are commonly used to unveil how excitations on Heisenberg spin models play a role in dynamical correlations functions. For a certain class of materials, like CsCoCl$_3$ or CsCoBr$_3$ salts, it turns out that their magnetic properties are fairly well approximated by quasi-one dimensional XXZ models, which enjoy the property of quantum integrability. In these instances, one can in principle use their underlying algebraic structure to describe very precisely how excitations, the so-called spinons, participate in dynamical correlations functions. Even though the available theories (either algebraic Bethe ansatz or quantum group approach) provide all the needed physical quantities such as form factors, complete set of eigenstates and spectrum, it is typically a rather daunting task, however, to obtain sufficiently simple analytical expressions for computing Dynamical Structure Factors (DSFs), valuable, e.g., for parameters estimation based on experimental data. This is particularly the case for the longitudinal DSF of the XXZ model, which has eluded a formal mathematical treatment thus far. Using the quantum group approach, we present here an exact and simple expression of the 2-spinon longitudinal DSF and show our results to be consistent with the expected sum rules and the isotropic and Ising antiferromagnet limiting cases.

cond-mat.str-el↗

arXiv2020

Using posterior predictive distributions to analyse epidemic models: COVID-19 in Mexico City

Epidemiological models contain a set of parameters that must be adjusted based on available observations. Once a model has been calibrated, it can be used as a forecasting tool to make predictions and to evaluate contingency plans. It is customary to employ only point estimators for such predictions. However, some models may fit the same data reasonably well for a broad range of parameter values, and this flexibility means that predictions stemming from such models will vary widely, depending on the particular parameter values employed within the range that give a good fit. When data are poor or incomplete, model uncertainty widens further. A way to circumvent this problem is to use Bayesian statistics to incorporate observations and use the full range of parameter estimates contained in the posterior distribution to adjust for uncertainties in model predictions. Specifically, given the epidemiological model and a probability distribution for observations, we use the posterior distribution of model parameters to generate all possible epidemiological curves via the posterior predictive distribution. From the envelope of all curves one can extract the worst-case scenario and study the impact of implementing contingency plans according to this assessment. We apply this approach to the potential evolution of COVID-19 in Mexico City and assess whether contingency plans are being successful and whether the epidemiological curve has flattened.

q-bio.PE↗

arXiv2020

Optical Tweezers: A Comprehensive Tutorial from Calibration to Applications

Since their invention in 1986 by Arthur Ashkin and colleagues, optical tweezers have become an essential tool in several fields of physics, spectroscopy, biology, nanotechnology, and thermodynamics. In this Tutorial, we provide a primer on how to calibrate optical tweezers and how to use them for advanced applications. After a brief general introduction on optical tweezers, we focus on describing and comparing the various available calibration techniques. Then, we discuss some cutting-edge applications of optical tweezers in a liquid medium, namely to study single-molecule and single-cell mechanics, microrheology, colloidal interactions, statistical physics, and transport phenomena. Finally, we consider optical tweezers in vacuum, where the absence of a viscous medium offers vastly different dynamics and presents new challenges. We conclude with some perspectives for the field and the future application of optical tweezers. This Tutorial provides both a step-by-step guide ideal for non-specialists entering the field and a comprehensive manual of advanced techniques useful for expert practitioners. All the examples are complemented by the sample data and software necessary to reproduce them.

physics.optics↗

arXiv2019

Phase transitions in atypical systems induced by a condensation transition on graphs

Random graphs undergo structural phase transitions that are crucial for dynamical processes and cooperative behavior of models defined on graphs. In this work we investigate the impact of a first-order structural transition on the thermodynamics of the Ising model defined on Erdös-Rényi random graphs, as well as on the eigenvalue distribution of the adjacency matrix of the same graphical model. The structural transition in question yields graph samples exhibiting condensation, characterized by a large number of nodes having degrees in a narrow interval. We show that this condensation transition induces distinct thermodynamic first-order transitions between the paramagnetic and the ferromagnetic phases of the Ising model. The condensation transition also leads to an abrupt change in the global eigenvalue statistics of the adjacency matrix, which renders the second moment of the eigenvalue distribution discontinuous. As a side result, we derive the critical line determining the percolation transition in Erdös-Rényi graph samples that feature condensation of degrees.

cond-mat.dis-nn↗

arXiv2019

Condensation of degrees emerging through a first-order phase transition in classical random graphs

Due to their conceptual and mathematical simplicity, Erdös-Rényi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely considered in complex network theory, the condensation of degrees has hitherto eluded a careful study. Here we show that the degree statistics of the classical random graph model undergoes a first-order phase transition between a Poisson-like distribution and a condensed phase, the latter characterized by a large fraction of nodes having degrees in a limited sector of their configuration space. The mechanism underlying the first-order transition is discussed in light of standard concepts in statistical physics. We uncover the phase diagram characterizing the ensemble space of the model and we evaluate the rate function governing the probability to observe a condensed state, which shows that condensation of degrees is a rare statistical event akin to similar condensation phenomena recently observed in several other systems. Monte Carlo simulations confirm the exactness of our theoretical results.

cond-mat.dis-nn↗

arXiv2019

Dynamical signatures of topological order in the driven-dissipative Kitaev chain

We investigate the effects of dissipation and driving on topological order in superconducting nanowires. Rather than studying the non-equilibrium steady state, we propose a method to classify and detect dynamical signatures of topological order in open quantum systems. Bulk winding numbers for the Lindblad generator $\hat{\mathcal{L}}$ of the dissipative Kitaev chain are found to be linked to the presence of Majorana edge master modes -- localized eigenmodes of $\hat{\mathcal{L}}$. Despite decaying in time, these modes provide dynamical fingerprints of the topological phases of the closed system, which are now separated by intermediate regions where winding numbers are ill-defined and the bulk-boundary correspondence breaks down. Combining these techniques with the Floquet formalism reveals higher winding numbers and different types of edge modes under periodic driving. Finally, we link the presence of edge modes to a steady state current.

cond-mat.str-el↗

arXiv2018

Testing Randomness in Quantum Mechanics

Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this review, we briefly discuss two such tests, point out the challenges that we have encountered and finally present a fairly simple method that successfully generates non-deterministic maximally random sequences.

quant-ph↗

arXiv2018

Non-convex image reconstruction via Expectation Propagation

Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as smoothness or sharpness. This maximization can be performed with standard local optimization tools when the function is concave, but it is generally intractable for realistic priors, which are non-concave. We introduce a new method to reconstruct images obtained from Radon projections by using Expectation Propagation, which allows us to reframe the problem from an Bayesian inference perspective. We show, by means of extensive simulations, that, compared to state-of-the-art algorithms for this task, Expectation Propagation paired with very simple but non log-concave priors, is often able to reconstruct images up to a smaller error while using a lower amount of information per pixel. We provide estimates for the critical rate of information per pixel above which recovery is error-free by means of simulations on ensembles of phantom and real images.

eess.IV↗

arXiv2018

Theory for the conditioned spectral density of non-invariant random matrices

We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution conditioned to have a fixed fraction $k$ of eigenvalues smaller than $x \in \mathbb{R}$, provides the spectrum of random matrix samples that deviate atypically from the average behavior. We apply our theory to sparse random matrices and unveil strikingly new and generic properties, namely: (i) their conditioned spectral density has compact support; (ii) it does not experience any abrupt transition for $k$ around its typical value; (iii) its eigenvalues do not accumulate at $x$. Moreover, our work points towards other types of transitions in the conditioned spectral density for values of $k$ away from its typical value. These properties follow from the weak or absent eigenvalue repulsion in sparse ensembles and they are in sharp contrast to those displayed by classic or rotationally invariant random matrices. The exactness of our theoretical findings are confirmed through numerical diagonalization of finite random matrices.

cond-mat.dis-nn↗

arXiv2018

Motion of a Brownian molecule in the presence of reactive boundaries

We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics, chemistry and biology. We compute the probability density of the particle displacement exactly, from which we derive expressions for the survival probability and the mean absorption time as a function of the reactive coefficients. Furthermore, using the Feynman-Kac formalism, we investigate the reaction time profile, which is the fluctuating time spent by the particle at a given location, both till a fixed observation time and till the absorption time. Our analytical results are compared to numerical simulations showing perfect agreement.

cond-mat.stat-mech↗

arXiv2018

Universal behavior of the full particle statistics of one-dimensional Coulomb gases with an arbitrary external potential

We present a complete theory for the full particle statistics of the positions of bulk and extremal particles in a one-dimensional Coulomb Gas (CG) with an arbitrary potential, in the typical and large deviations regimes. Typical fluctuations are described by a universal function which depends solely on general properties of the external potential. The rate function controlling large deviations is, rather unexpectedly, not strictly convex and has a discontinuous third derivative around its minimum for both extremal and bulk particles. This implies, in turn, that the rate function cannot predict the anomalous scaling of the typical fluctuations with the system size. Moreover, its asymptotic behavior for extremal particles differs from the predictions of the Tracy-Widom distribution. Thus many of the paradigmatic properties of the full particle statistics of two-dimensional systems do \emph{not} carry out into their one-dimensional counterparts, hence proving that 1d CG belongs to a different universality class. Our analytical expressions are thoroughly compared with Monte Carlo simulations showing excellent agreement.

cond-mat.stat-mech↗

arXiv2018

Intermittent dynamics in complex systems driven to depletion

When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To understand and ultimately be able to predict such dynamics, we propose an underlying mechanism based on sharp thresholds of a local generalized energy density that naturally leads to negative feedback. We find a transition from a continuous regime to an intermittent one, in which avalanches can be predicted despite the stochastic nature of the process. This model may have applications in many natural and social complex systems where a rapid depletion of resources or generalized energy drives the dynamics. In particular, we show how this model accurately describes the time evolution and avalanches present in a real social system.

physics.soc-ph↗

arXiv2018

Large deviation theory for diluted Wishart random matrices

Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology and economy. In this work we develop a theory for the eigenvalue fluctuations of diluted Wishart random matrices, based on the replica approach of disordered systems. We derive an analytical expression for the cumulant generating function of the number of eigenvalues $\mathcal{I}_N(x)$ smaller than $x\in\mathbb{R}^{+}$, from which all cumulants of $\mathcal{I}_N(x)$ and the rate function $Ψ_{x}(k)$ controlling its large deviation probability $\text{Prob}[\mathcal{I}_N(x)=kN] \asymp e^{-NΨ_{x}(k)}$ follow. Explicit results for the mean value and the variance of $\mathcal{I}_N(x)$, its rate function, and its third cumulant are discussed and thoroughly compared to numerical diagonalization, showing a very good agreement. The present work establishes the theoretical framework put forward in a recent letter [Phys. Rev. Lett. 117, 104101] as an exact and compelling approach to deal with eigenvalue fluctuations of sparse random matrices.

cond-mat.dis-nn↗

arXiv2017

Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase

We calculate the level compressibility $χ(W,L)$ of the energy levels inside $[-L/2,L/2]$ for the Anderson model on infinitely large random regular graphs with on-site potentials distributed uniformly in $[-W/2,W/2]$. We show that $χ(W,L)$ approaches the limit $\lim_{L \rightarrow 0^+} χ(W,L) = 0$ for a broad interval of the disorder strength $W$ within the extended phase, including the region of $W$ close to the critical point for the Anderson transition. These results strongly suggest that the energy levels follow the Wigner-Dyson statistics in the extended phase, consistent with earlier analytical predictions for the Anderson model on an Erdös-Rényi random graph. Our results are obtained from the accurate numerical solution of an exact set of equations valid for infinitely large regular random graphs.

cond-mat.dis-nn↗

arXiv2017

Improving randomness characterization through Bayesian model selection

Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We have applied our method to an experimental device based on the process of spontaneous parametric downconversion, implemented in our laboratory, to confirm that it behaves as a genuine quantum random number generator (QRNG). As our approach relies on Bayesian inference, which entails model generalizability, our scheme transcends individual sequence analysis, leading to a characterization of the source of the random sequences itself.

physics.data-an↗