Short talks and Posters

The world personal or individual income distribution, as constructed from the aggregated income distributions all of countries, was fitted to the lognormal and gamma functions up to 60K for some years between 1988 and 2018 measured by power parity exchange rates. Despite incomplete or lack of reliable datasets, in early years the available data included the vast majority of world’s population. Curves on the probability density functions (PDF) allowed easy identification of peaks in the distribution, and smoothed out curves of complementary cumulative distribution functions (CCDF) showed general trends in inequality distribution. The world distribution was bimodal in early years, but recent growing world middle classes in hugely populated countries like China and India are more recently producing a one-peak world distribution. When a single function was used to adjust the data, the fit quality is similar with gamma or log-normal functions, but the bimodal distribution constructed as sum of lognormals yielded almost perfect fits.

We will discuss some aspects of the dynamics of quantum systems composed of spin-1/2 particles, accommodated at each of the sites of a one-dimensional lattice of finite length, subject to a local random potential and that can interact between pairs. In particular, we study how time-independent properties, such as repulsion between energy levels and the structure of energy eigenstates, manifest themselves in time domain as the strength of the random potential changes. Our analysis considers the dynamics of observables, such as correlation functions, which are of interest for experiments on modern experimental platforms considered as quantum simulators. The emphasis will be on the so-called survival probability, which allows to distinguish between different phases of the system, a chaotic one (extended states), an intermediate one (extended but not ergodic states) and a localized one (localized states).

Multilayer networks represent complex systems, both natural and artificial, where groups or communities primarily interact in a linear manner. Increasingly sophisticated attempts to model real-world systems as multidimensional networks have yielded valuable insights in the fields of social network analysis, urban and international transportation, ecology, psychology, biology, physics, and computational neuroscience. Particularly, many real-world systems can be modeled using directed multilayer networks (those whose contained information follows a specific direction from one layer to another), which can be characterized through the properties of the eigenvalues and eigenvectors of the corresponding adjacency matrices. Therefore, in this work, we will use measures and techniques from random matrix theory to study some properties of the eigenvalues and eigenvectors of the adjacency matrices of directed multilayer networks.

Mexico is surrounded by five tectonic plates, making it a highly seismic country. Although earthquakes cannot currently be predicted, many scientists focus on developing methodologies to identify possible seismic precursors before the occurrence of an earthquake. Our team studies these phenomena using multifractal techniques. In this work, we present the results obtained by studying synthetic and real seismicity time series from Southern California. We used the model proposed by Olami, Feder, and Christensen (OFC) to generate a time series of synthetic earthquakes. Both the synthetic and real seismicity time series exhibit multifractal characteristics, which we analyzed using the Chhabra and Jensen methods to obtain their multifractal spectra. In both seismicity catalogues, we identified the major earthquakes and constructed overlapping time windows before and after their occurrence. For each window, we calculated its multifractal spectrum and measured the parameters of width, symmetry, and curvature, obtaining average values. We observed the evolution of these parameters before and after major synthetic earthquakes. The results show changes in the values of width, symmetry, and curvature of the multifractal spectra before and after large earthquakes. This suggests that multifractal techniques are sensitive to detecting the dynamic changes that precede and follow a major earthquake, making them promising candidates as seismic precursors.

The brain's complex structure supports functional dynamics that are difficult to understand. To unravel the principles underlying the brain's topology, we studied its state distribution. Maximum entropy determines the most likely state distribution for static systems, while maximizing path entropy (MaxCal) determines the most likely path distribution in both static and dynamic systems. The unique property of MaxCal led us to investigate path entropy as a potential explanatory principle for brain processes. We implemented MaxCal as a topological descriptor to analyze electroencephalographic (EEG) data from a cognitive inhibition task. By using MaxCal, we aimed to contribute to the understanding of brain dynamics and emphasize the fundamental role of entropy in explaining dynamic systems and life phenomena. This concept provides insights into the state and path distributions that govern complex systems such as the brain. Our approach allowed us to explore the potential of path entropy in elucidating brain processes through EEG analysis during a cognitive task. This work highlights the importance of entropy as a guiding principle for understanding dynamic systems and life phenomena, while advancing our understanding of brain dynamics.

TheH-value orHurst exponentis used as a measure of long-term memory of time series. If H is in the interval (0.5, 1], then the time series has long-term positive self-correlations or persistence. A value in the range [0, 0.5) indicates anti-persistence. The primary goal of this study is to ascertain the efficacy of employing four Hurst exponent estimators on heartbeat time series for signal analysis. We analyzed heartbeat time series or tachograms of healthy people and CHF patients both awake and asleep, and healthy young people at rest and performing exercise. We used the Hurst exponent to determine cardiac stress and physical condition of healthy young subjects with a sedentary lifestyle and healthy subjects who exercise regularly. With this qualitative and quantitative analysis, it is possible to have information on the health status of the patients or the physical condition of any subject. The use of the Hurst exponent, even calculated by different methodologies, could be an auxiliary tool, to analyze heartbeat time series of subjects with some heart disease. H-values can also be used to characterize the physical condition of any person, and qualitatively measure the cardiac stress of a subject. The results indicate that, ifthe tachograms are persistent,they correspond to healthy subjects, butifthe seriesinvolves anti-persistence, they correspond totally to subjects with heart failure, but the heartbeat time series of sedentary young subjects that exercise show also anti-persistence. There is a relationship between the complexity of the series and the H-value because the persistent series are more complex than the antipersistent ones, for this reason the time series, when they lose complexity, reduce their Hurst exponent values.

We propose a model to represent the motility of social elements. The model is completely deterministic, possesses a small number of parameters, and exhibits a series of properties that are reminiscent of the behavior of communities in social-ecological competition; these are:

- Similar individuals attract each other;

- Individuals can form stable groups;

- A group of similar individuals breaks into subgroups if it reaches a critical size;

- Interaction between groups can modify the distribution of the elements as a result of fusion, fission, or pursuit;

- Individuals can change their internal state by interaction with their neighbors.

The simplicity of the model and its richness of emergent behaviors, such as, for example, pursuit between groups, make it a useful toy model to explore a diversity of situations by changing the rule by which the internal state of individuals is modified by the interactions with the environment.

We study the evolution of the one dimensional Ising spin system under a zero-temperature quenching from infinite temperature. In our model, each spin interact with its two nearest domains. The energy of the system is reduced by exchanging the position of two randomly selected spins. This dynamics models the social segregation under social pressure. We study the evolution of both, the average domain sizes and the persistent probability, defined as the probability that a site remain unaffected by exchanges until certain time t. It has been observed that both, the average domain sizes and the correlation length for the two-point correlation of the persistent sites grow in a power law with the same exponent. However, for our model these two measurables are not related.

We study the zero-temperature quenching of Ising spin systems under the influence of an external magnetic field. We subject a spin system with nearest neighbor interaction to a binary random field and we study the relation between the average of the magnetic field and the saturation value of the measurements. We also study spin systems with domain size dependent dynamics under an external magnetic field. Studies in these dynamic rules are already made in the context of binary opinion models without external field. This motivates the study of these models under the influence of external fields as the influence of external factors such as social media, news, social norms or marketing campaigns. To understand the dynamics of these different systems, we are measuring persistence, autocorrelation, magnetization, and exit probability.

In this work, we study random walkers that utilize memory-based strategies for resource searching on a two-dimensional lattice in the presence of trapping sites. If a walker reaches a trapping site, it will get trapped with a certain probability. One can say that the regular sites of the lattice have zero trapping probability. Doing simulations, we explore the dynamics of the walkers whose relocation strategies are based either on their own memory or the history of the entire community or a combination of both rules. We compute different observables like the fraction of population at and around the trapping sites, the persistence probability for lattice sites under different boundary conditions (open and reflective). We found that walkers with collective memory are more efficient in achieving higher localization under open boundary conditions, while those with a combined memory are more efficient under reflective conditions.

The random walk remains a concept widely employed in phenomena modeling and in search algorithms. We study two cases of this walk, the random walk with the relocation of a particle to a certain place with a constant rate, and the random walk with memory, where a particle can visit a previous position of its path with a constant rate, involving both analytical and numerical approaches. The relocation of the particle along its previous trajectory results in slow diffusion dynamics, which increase when collective memory is considered, allowing information transfer. In our future work, we will be examining the diffusion annihilation process of these kinds of walks.

In this work, we perform a spectral correlation analysis to the data of the daily incidence of the SARS-CoV2 during the COVID-19 pandemia developed in the different federal entities of Mexico (Mexican states). For doing this analysis we first removed suspected spurious correlations appearing at the Fourier transform spectrum of the time series and then proceed to apply noice reduction and return series techniques. Within this framework we found that the highest correlation eigenvalues seems to be well connected to the pandemic waves (increments and decrements of the infected cases) while also observing and additional invariant structure in the correlation spectrum, possible related to the contagious network, i.e. interconnectivity between the Mexican states. We aim with this study to extract the underlying information about possible internal structure within the dynamics of the COVID-19 dispersion, that could be related to the mobility patterns of the country, whether by air, sea, land, or a combination thereof, or some additional underlying characteristic in the dynamics of the disease contagion."

This work is focused on numerical simulations of the learning process in two artificial networks. The first network studied is the Hopfield Network. It is a model for associative memory, where neurons have binary states, and it is used for recovering and recognizing of patterns. We want to evaluate if, and if so, how many patterns (information) are stored on an unknown Hopfield network. For this purpose, we study the correlation matrix made with a set of completely random initials states and their evolution through the recovery algorithm. We show that one can classify these correlation matrices with the help of the k-means algorithm, and thereby obtain at least a rough estimate of the number of patterns stored in the network. In the second part of our investigation, we compare the elemental and non-elemental olfactory learning of Drosophila fruitflies with a perceptron. For this, we adjust the network size and learning rate. Our simulations reproduce relatively well, the experimental results, and numerical simulations of a semi-realistic brain model constructed from Izhikevich neurons. We discuss the meaning of our findings.

We analyze the cooperative effects induced by ultraviolet (UV) excitation of several biologically relevant Trp mega-networks, thus giving insights into novel mechanisms for cellular signaling and control. Our theoretical analysis in the single-excitation manifold predicts the formation of strongly superradiant states due to collective interactions among organized arrangements of up to >105 Trp UV-excited transition dipoles in microtubule architectures, which leads to an enhancement of the fluorescence quantum yield (QY) that is confirmed by our experiments. Trp networks as microtubules MTs are crucial to cytoskeletal regulation and form complex bundles in neuronal tissue. Our studies of axonal MT bundles may have implications for both neuroscience and quantum optics research.

The intricate tapestry of the world around us can be surprisingly well-described by the language of networks. Understanding these patterns is no easy feat, but a powerful tool emerges from the realm of statistics: Exponential Random Graph Models (ERGMs). The ERGMs are a statistical tool for modeling the formation and evolution of networks. ERGMs are based on the idea that the probability of a tie forming between two actors depends on network statistics. Fitness Exponential Random Graph Models (FERGMs) offer a window into the hidden forces shaping interconnected systems. Unlike traditional models that treat ties as random occurrences, FERGMs recognize the inherent biases and preferences that govern network formation. At their core, these models introduce the concept of fitness, a quantifiable measure of a node’s attractiveness, which plays a pivotal role in attracting new connections. In this work, we discuss the statistical properties of complex networks with a fixed number of vertices and varying links, described by the Exponential Random Graph Models (ERGMs). We show that the proposed ERGM agrees with weakly scale-free networks that exhibit some characteristics of scale-free networks but do not adhere strictly to the power-law degree distribution across their entire range. We also compare our findings with some real-world networks and show that our model describes them better than the scale-free network’s approach does.

We study the time dynamics of random density matrices generated by evolving the same pure state using a Gaussian orthogonal ensemble (GOE) of Hamiltonians. We show that the spectral statistics of the resulting mixed state is well described by random matrix theory (RMT) and undergoes a crossover from the GOE to the Gaussian unitary ensemble (GUE) for short and large times respectively. Using a semi-analytical treatment relying on a power series of the density matrix as a function of time, we find that the crossover occurs in a characteristic time that scales as the inverse of the Hilbert space dimension. The RMT results are contrasted with a paradigmatic model of many-body localization in the chaotic regime, where the GUE statistics is reached at large times, while for short times the statistics strongly depends on the peculiarity of the considered subspace.

We study the phenomena of Anderson localization and quantum transport in disordered media with \alpha-stable distributions, both in distances between scatterers and/or in the on-site energies of 1D discrete chains. We observe that using this kind of disorder leads to novel results on quantum transport, where results from DMPK and Single Parameter Scaling (SPS) do not apply as usually stated, instead we obtain numerically a more general relation between the first two cumulants of the probability distribution of the logarithm of the transmission coefficient, <−ln(T )>, in therms of the stability parameter, \alpha. Moreover, letting a wave-package evolve on the center of the disordered chain, confirms the recently proposed Anomalous Anderson Localization (AAL), where localization takes place as the wave-function decays exponentially with the stability parameter \alpha as |\Phi(x)|^2~ exp(-x^\alpha), we relate this decay with the \alpha-stable distributions and the density of scatterers on the media.

The phenomenon of localization in solids refers to the occurrence of quantum states in which electrons remain confined to a region of space. In 1958, P.W. Anderson introduced the first model that successfully explained the phenomenon of localization of a particle as a result of structural disorder in a lattice. To date, understanding the influence of disorder and interactions on electronic transport remains an open question, as the mobility of electrons is a determining factor in the thermodynamic and electromagnetic properties of materials. Another important factor in the transport phenomenon is the dimensionality and size of the lattice. In Anderson's model, it is found that arbitrarily small disorder values lead to localization of all states of a particle in one and two dimensions, whereas in three dimensions, a threshold disorder value is required to have extended and localized states. In 1980, a new model was proposed to study the effects of structural disorder, called the Aubry-André model, which consists of the Hamiltonian of a particle in a quasiperiodic lattice with nearest-neighbor tunneling. The main result of this model is the existence of localization in one dimension above a certain threshold. An open question is how the results of the Aubry-André model are modified when long-range tunneling is considered. This model is referred to as extended in the sense that it considers all possible hopping terms in the entire lattice. While the analysis of the transport phenomenon is multifactorial given the involvement of dimensionality, short- and long-range interactions, structural disorder of the lattice, and its size, a valid question in the context of recent experiments with Rydberg atoms moving in networks is the analysis of localization phenomenon in disordered networks with power-law tunneling. This work aims to study the transport phenomenon of a particle moving in a one-dimensional quasiperiodic lattice. In addition, it aims to integrate a factor representing tunneling between lattice sites, considering amplitudes of short and long range. Previous literature exists on the Aubry-André model, without considering long-range tunneling, i.e., only considering nearest-neighbor tunneling. To carry out the analysis of the transport phenomenon, both the stationary and time-dependent versions of the Schrödinger equation for the particle confined in the quasiperiodic lattice will be studied in this work. Specifically, various quantities will be studied to characterize the localization phenomenon as a function of the parameters defining the model Hamiltonian. Beyond a theoretical model, it also presents itself as a proposal for experimental development, as this theoretical model depends on physical factors that are easily experimentally accessible, with the insertion of optical potentials generated by lasers that mimic the natural environment of the lattice and allow for control of disorder.

Nonlinear quantum transformations play an important role in quantum state distillation, aiding quantum communication schemes. Provided we have multiple copies of a qubits in the same quantum state, we can design a protocol consisting of a joint unitary operation on all of them and a subsequent measurement on all but one of the outputs.  Accepting only certain measurement outcomes, we arrive, in general, at a nonlinear quantum transformation on the remaining system (see Fig. 1). The simplest of these involve quadratic rational maps for qubits, higher order versions have not been explored in detail. We studied a special class of higher order iterated nonlinear maps and showed the presence of a universal phase transition.

To characterize the global properties of these protocols, we determine the fixed points  and relevant fixed cycles. We show that a repelling mixed fixed point exists for all orders, marking a phase transition related to the disappearance of the fractalness of borders of different basins of attraction (see Fig. 2). The transition point is marked by a repelling fixed point, which has an increasing purity, tending to 1 as we increase the order n of the map. The generalized Julia set, defined as the set of border points between the basins of attraction for fixed purity initial states, has a constant fractal dimension as a function of the purity, above a critical value. Remarkably, we found that this fractal dimension is universal in this family, it is independent of the order n of the map.

[1] M. Malachov, I. Jex, O. K ́alm ́an, and T. Kiss, Chaos, 29 033107 (2019)
[2] A. Portik, O. K ́alm ́an, I. Jex, and T. Kiss, Phys. Lett. A, 431 127999 (2022)
[3] A. Portik, O. K ́alm ́an, I. Jex, and T. Kiss, Phys. Rev. A, 109 042410 (2024)

In the present work, a formal and rigorous description of the complex scaling method was developed that stands out in the framework of scattering theory. The complex scaling method was studied in terms of two separate scattering models described by a double short-range smooth potential well and a Dirac delta in front of a potential wall. Obtaining a result consistent with the theory of the dispersion matrix and a significant equivalence is shown for the potential involving a Dirac delta.

In one dimension, there is a subset of time-dependent Hamiltonian systems for which integrability holds. In such cases, the energy is no longer conserved and there exists another conserved quantity that usually takes up this role: the action. This quantity is usually obtained by perturbation techniques, for instance, using the adiabatic formalism. In this work, we study the frequency time-dependent harmonic oscillator for which an exact invariant exists, the so-called Ermakov invariant. First, we show how to obtain the exact invariant via an algebraic approach. Next, we analyze how to obtain the invariant perturbatively, using the adiabatic formalism and the Kruskal perturbative technique, both up to first order in the perturbation parameter ε. For a specific form of the time-dependent frequency, we compare the exact and perturbative solution, as well as their trajectories in phase space and on the first order adiabatic invariant. Finally, we show how to obtain the same Ermakov invariant for the quantized version of the system, using a coherent state as an ansatz for the Schrödinger equation.

In this work, we investigate the Jaynes-Cummings model in the atomic bare state description, through the framework of the characteristic functions (the Fourier transform of the Wigner functions). Analyzing these functions and their dynamical equations, we identify the lie point symmetries and construct the corresponding invariant solutions. In addition, we calculate and investigate the conservation laws associated to the model.

It is known that there are algorithms in quantum computing implemented for search problems, which are more efficient than most of stochastic algorithms. In the present work, we construct a quantum extension to create a quantum version corresponding to the classical algorithm. We study Ising-spin system, where each spin has 4 random neighbors with random ferromagnetic/antiferromagnetic interaction, We only worked with disordered systems without local minimal energy configurations. Studying this system as an open quantum system. We found that the quantum process can find minimum energy configurations in less time than the classical process. Finally, it is found that the half-time in the classical and quantum processes satisfies a power law as a function of the system size, where the quantum exponent is smaller than the classical one. As a result, the advantage of the quantum process over the classical one increases with the size of the system.

We study general ’normally’ (Gaussian) distributed random unitary transformations. These distributions can be defined in terms of a diffusive random walk in the respective group manifold.   On the one hand, a Gaussian distribution induces a unital quantum channel, which we will call  ’normal’. On the other hand, the diffusive random walk defines a unital quantum process, generated by a Lindblad master equation. In the single qubit case, we show different distributions may induce the same quantum channel. In the case of two qubits, we study normal quantum channels, induced by Gaussian distributions in SU(2)⊗SU(2). They provide an appropriate framework for modeling quantum errors with classical correlations. In contrast to correlated Pauli errors, for instance, they conserve their Markovianity, and they lead to very different results in  error correcting codes. This is illustrated with an application to entanglement distillation.  Taken from the similarly titled paper: Alejandro Contreras Reynoso and Thomas Gorin 2024 J. 

Phys. A: Math. Theor. 57 225301.

The Lindblad master equation is important for the study of temporal evolution in open quantum systems, so that analyzing the expansion beyond weak coupling could provide relevant information. In this work, we show the mathematical development for the fourth and sixth order of expansion, where we can see that our obtained master equations have the Lindblad form and thus the completely positive (CP) is satisfied. These are fundamental physical properƟes for the density operator. We compare our results with the Lindblad master equations for two different systems (spontaneous emission and two-level system), where we esƟmate corrections in the traditional Lindblad equation that can be verified with experimental results.

Quantum chaos is the study of quantum systems whose classical counterpart is chaotic. The conjecture of quantum chaos states that the same universal properties characterize those systems as the Gaussian random matrices [1]. Many experimental works give validity to this conjecture [2-3]. Quantum graphs are systems that, due to their simplicity, are useful for studying quantum chaos [4-6]. Their use dates back to Linus Pauling in 1930, but they became relevant when Kottos and Smilansky introduced quantum graphs as a powerful tool for studying quantum chaos. They also showed that connecting semi-infinite wires to their vertices becomes a system with dispersion. One of the key tools we employ in our study is scattering fidelity, or SF, which measures the sensitivity of the scattering matrix to a perturbation [7]. Unlike fidelity, SF can be measured experimentally when the coupling is weak; scattering fidelity aligns with the fidelity. It's important to note that scattering fidelity is a potent tool in studying the nature and strength of a perturbation. In the case of quantum graphs, we are still exploring the type of perturbation that occurs when the length of some (or all) bounds are altered. This work studies the dynamical stability in quantum graphs (with and without time-reversal symmetry GOE and GUE) through fidelity and scattering fidelity; mainly, we study the type and strength of perturbation introduced by bond length shift. We present analytical and numerical results for fidelity in the perturbative regime to obtain strength and type of perturbation. Compared with fidelity in a random-matrix framework, we can extend our result for perturbation beyond the perturbative regime.

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[2] M. V. Berry. Semiclassical theory of spectral rigidity. Proc. R. Soc. Lond. A, 400:229–251, 1985.

[3] S. Müller, S. Heusler, A. Altland, P. Braun, and F. Haake. Periodic- orbit theory of universal level correlations in quantum chaos. New J. of Phys., 11(10):103025, 2009.

[4] T. Kottos and U. Smilansky. Quantum chaos on graphs. Phys. Rev. Lett., 79:4794–4797, Dec 1997.

[5] T. Kottos and U. Smilansky. Periodic orbit theory and spectral statistics for quantum graphs. Ann. Phys., 274(1):76 – 124, 1999.

[6] T. Kottos and U. Smilansky. Quantum graphs: a simple model for chaotic scattering. J. Phys. A: Math. Gen., 36(12):3501–3524, 2003.

[7] R. Schäfer, T. Gorin, H.-J. Stöckmann, and T. H. Seligman. Fidelity amplitude of the scattering matrix in microwave cavities. New J. Phys., 7:152:1–14, 2005.

[8] Thomas Gorin and Thomas H. Seligman. signatures of the correlation hole in total and partial cross sections. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 65:026214:1–18, February 2002. Warsaw, Poland, May 19-22 (2005).

[9] T. Gorin and P. C. Lopez Vazquez. Scattering approach to fidelity decay in closed systems and parametric level correlations. Phys. Rev. E, 88:012906, Jul 2013.

The focus of this project is to compare quantum and classical simulated annealing using the N-Queens Problem with Excluded Diagonals. The classical solver was implemented with FORTRAN and quantum annealing was performed using D-Waves quantum computers. The efficiency of these solvers was compared through an analysis of the times required to find solutions and the scalability of each method. Quantum annealing was limiting because the number of qubits required grew quickly with larger boards. However, excluding diagonals allowed a reduction in the number of qubits needed, which enabled the solution of larger boards. Additionally, hybrid solvers were also analyzed. They implement decomposition methods to break the problem in independent subproblems to perform quantum annealing in smaller sections. This method was able to solve much larger problems. Nevertheless, classical simulated annealing was found to be the most efficient and scalable solver over the current quantum and hybrid solvers.

We characterize the metal-insulator transition in the one-dimensional Aubry Andre model by using the squared module of the Fourier transform of spacings between adjacent energy levels, that is through so-called power spectrum. Also we compute different quantities for this model that presents a phase transition in 1-dimension. Alternatively, we repeat the analysis with the power spectrum of ratios between consecutive spacings and energy eigenstates.

In this research, we introduce the non-Hermitian diluted banded random matrix (nHd-BRM) ensemble as the set of N × N real non-symmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if |i − j| < b and zero otherwise, moreover off-diagonal matrix elements within the bandwidth b are randomly set to zero such that the sparsity α is defined as the fraction of the N(b − 1) / 2 independent non-vanishing off-diagonal matrix elements. By means of a detailed numerical study we demonstrate that the eigenfunction and spectral properties of the nHd-BRM ensemble scale with the parameter x = γ[ (bα) ^ 2 /N ] ^ δ, where γ, δ ∼ 1. Moreover, the normalized localization length β of the eigenfunctions follows a simple scaling law: β = x / (1 + x).

Our work is developed in the context of the theory of random matrices. This theory has proven to be very useful in the study of spectral correlations of many-body quantum systems. It is possible to diagnose these correlations through the study of certain quantities such as spectral form factor, which detects correlations of both short and long range. This quantity exhibits a typical structure as a trough before saturation (also known as a correlation hole) when the system is ergodic. In this work we discuss how this structure could be detected through the dynamics of two physical quantities accessible to experimental quantum many-body systems: the survival probability and the spin autocorrelation function. When the system is small, the correlation hole reaches large enough values in short enough times to be detected with current experimental platforms and commercially available quantum computers.