arXiv subjects

Henrique Santos Lima

Publications and source records attributed to Henrique Santos Lima.

15 recordsLinked to original sources

arXiv2026

Heat Transport of the $β$-Fermi--Pasta--Ulam--Tsingou chain in the long-wave limit

Resolving the anomalous conductivity exponent of the symmetric $β$-Fermi--Pasta--Ulam--Tsingou chain by molecular dynamics can require very large systems because of long finite-size crossovers and thermal-contact resistance. Motivated by this computational challenge, we derive a long-wavelength continuum description and investigate whether the kinetic-theory scaling $κ\propto L^{2/5}$ becomes accessible with a moderate number of numerical degrees of freedom. The nonlinear elastic field retains the cubic stress of the microscopic interaction and exchanges heat with Langevin reservoirs. A flux-conservative spatial discretization constructs the force and energy current from the same stress, providing a consistent interior transport estimator. For $L>8$, corresponding to approximately $10^3$ mesh nodes and above at the reference resolution, the fitted exponent is $0.399\pm0.004$. Mesh refinement supports the stability of this exponent between the two finer resolutions, although the conductivity amplitude remains resolution-dependent. The main result is thus an accessible finite-size regime near $2/5$, rather than convergence of the absolute conductivity as the mesh spacing vanishes. This formulation provides a practical route to studying anomalous transport in anharmonic systems and a conservative continuum framework for investigating energy flow in nonlinear elastic media.

cond-mat.stat-mech↗

arXiv2026

Asymptotic hydrographs and anomalous dispersion in mass-conserving storage cascades

Sums of independent exponential random variables lead to the Erlang distribution, providing a direct probabilistic route from exponential waiting times to the integer-shape gamma law. This paper investigates how this classical construction changes when the exponential waiting-time density is replaced by the $q$-exponential density of nonextensive statistics. Our main result is an analytical asymptotic expression for the outflow of a mass-conserving cascade of reservoirs driven by a $q$-exponential waiting-time kernel. In the critical case $q=5/3$, the large-cascade flow rate converges to a stable Lévy density whose time argument is shifted by a Galilean-type transformation. This shifted Lévy law gives the asymptotic hydrograph of the cascade. We also found that for the entire regime $1<q<2$ the macroscopic dynamics are governed by $α$-stable Lévy laws. This proves that anomalous non-Gaussian dispersion can emerge from pure mass-conserving convolutional chains without invoking fractional derivatives.

cond-mat.stat-mech↗

arXiv2026

A spectral model of power-law decay in natural and engineered systems

We present a first-principles spectral mechanism for the emergence of nonextensive $q$-exponential dilution and power-law relaxation in non-ideal transport systems. By modeling an incompletely mixed reactor as a layered diffusion matrix with an absorbing boundary, we demonstrate that macroscopic power-law tails depend on the geometric interaction between the initial tracer placement and the domain's boundary configuration. For a one-dimensional system, an asymmetric, volumetrically distributed initial concentration profile projects onto the low-wavenumber eigenmodes, generating an emergent Gamma distribution of relaxation rates; at an infinitesimal boundary layer thickness ($Δz \to 0$), this profile yields the nonextensive $q$-exponential decay function exactly across the entire temporal domain with $q = 5/3$. Extended to $d$ dimensions under a highly localized, boundary-adjacent singular initial condition, the resulting scaling exponents and corresponding $q$ values depend explicitly on the spatial configuration of the absorbing boundaries. However, in the one-dimensional limit ($d=1$), these distinct initial states and boundary formulations intersect, rendering the $q=5/3$ exponent geometrically invariant. Our approach establishes a clear connection between linear diffusion transport and nonextensive statistical mechanics, showing how heavy-tailed transport can be derived from boundary geometry and spectral dimensionality.

cond-mat.stat-mech↗

arXiv2026

Purification of a monitored qubit: exact path-integral solution

We investigate the purification dynamics of a single qubit under continuous in time monitoring. By employing a collisional model framework where the system interacts sequentially with ancillary qubits, we describe the conditioned evolution of the density matrix through a stochastic master equation. We show that for initial mixed states, the dynamics reduce to a multiplicative Langevin equation for a single scalar parameter representing the state's purity. This stochastic process is solved exactly using the Onsager-Machlup path integral formalism, allowing us to derive the full probability distribution for the qubit's trajectories. Our analytical results reveal that purification is characterized by a dynamical crossover from a diffusion dominated regime to a measurement dominated regime, visible in the emergence of a bimodal state distribution. The analytical solutions are in strong agreement with numerical simulations, providing a robust theoretical benchmark for the study of information extraction in monitored quantum systems.

quant-ph↗

arXiv2026

Brain criticality through nonadditive entropic analysis of electroencephalograms

On the grounds of nonadditive entropies -- appropriate for complex systems -- we investigate the electroencephalogram amplitudes of typical and ADHD children. The corresponding probability distributions are $q$-Gaussians, i.e., $ρ(x) \propto e_q^{-βx^2} \equiv [1+(q-1) βx^2]^{1/(1-q)}$, where $(q,β)$ are, respectively, the entropic index characterizing complexity and the inverse width. We show that $q$ tends to monotonically vary with $β$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path. We show that $q$ tends to monotonically vary with $β$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path.

cond-mat.stat-mech↗

arXiv2026

Deep brain microelectrode signal: $q$-statistical approach

We characterize the amplitude statistics of intraoperative microelectrode recordings (MERs) obtained during deep brain stimulation (DBS) surgery in 46 patients with Parkinson's disease, using 184 recordings equally balanced between inside and outside the subthalamic nucleus (STN). The probability density of every recording is quantitatively well described by a $q$-Gaussian (grounded on a nonadditive entropic functional), $ρ(x) \propto [1 + β(q-1) x^2]^{-1/(q-1)}$, with $q > 1$ in all cases, reflecting persistent long-range temporal correlations inconsistent with Gaussian dynamics. Within the superstatistics framework, the slowly fluctuating local variance visible in the raw MER signals is a physical mechanism that directly generates the $q > 1$ form. Beyond individual fits, $q$ and $β$ collapse across all 184 recordings onto the single functional constraint $q = 3 - 1.85\,β^{-0.33}$ ($R \approx -0.91$), a reduction to one effective degree of freedom that is the quantitative hallmark of near-critical dynamics, previously identified in scale-free network growth and in acoustic precursors of material fracture. The index $q$ is statistically indistinguishable across the STN boundary ($\langle\bar{q}_\text{out}/\bar{q}_\text{in} \rangle = 1.03$), while the inverse-widthparameter shows a modest systematic difference ($\langle\barβ_\text{out}/\barβ_\text{in} \rangle = 1.18$). Since $q > 1$ is expected for any brain structure exhibiting long-range correlations, healthy or pathological, it is the tight $q(β)$ coupling, not $q > 1$ per se, that constitutes the candidate near-criticality signature of the parkinsonian cortico-basal-ganglia-thalamocortical loop.

physics.med-ph↗

arXiv2025

Neurophysiological correlates to the human brain complexity through $q$-statistical analysis of electroencephalogram

The prospects of assessing neural complexity (NC) by $q$-statistics of the systemic organization of different types and levels of brain activity were studied. In 70 adult subjects, NC was assessed via the parameter $q$ of $q$-statistics, applied to the ongoing and EEG and its spectral power of 20 scalp points (channels). The NC were estimated both globally for all channels (AllCh) and locally (for each single channel) in different Functional States (FSs). The values of $q$ was compared among FSs and single channels, as well they were correlated with the power of $θ$ (4-8Hz), $β_1$ (15-25Hz) and others EEG bands, in each FS. The value of $q$ across all FSs was higher for AllCh than for the single channels FSs. Consistently with previous studies, we found a negative correlation between NC and age. The FSs did not influence the $q$ of the EEG in AllCh, although locally the FS modulated $q$ in a consistent manner (e.g., reducing $q$ in posterior sites with eyes closed). The $q$ was correlated positively with the power of the $θ$ and negatively with that of the $β_1$ band in general. These findings support the idea that, as a first approach, $q$-statistics can describe the human NC. The relationship between $q$ and $θ$ power aligns with greater NC during FSs such as listening music and resting with eyes open, which is consistent with high-order representations rather than low-informative attentional tasks (OddBall).

q-bio.NC↗

arXiv2024

Identifying Attention-Deficit/Hyperactivity Disorder through the electroencephalogram complexity

There are reasons to suggest that a number of mental disorders may be related to alteration in the neural complexity (NC). Thus, quantitative analysis of NC could be helpful in classifying mental and understanding conditions. Here, focusing on a methodological procedure, we have worked with young individuals, typical and with attention-deficit/hyperactivity disorder (ADHD) whose NC was assessed using q-statistics applied to the electroencephalogram (EEG). The EEG was recorded while subjects performed the visual Attention Network Test (ANT) and during a short pretask period of resting state. Time intervals of the EEG amplitudes that passed a threshold were collected from task and pretask signals from each subject. The data were satisfactorily fitted with a stretched $q$-exponential including a power-law prefactor(characterized by the exponent c), thus determining the best $(c, q)$ for each subject, indicative of their individual complexity. We found larger values of $q$ and $c$ in ADHD subjects as compared with the typical subjects both at task and pretask periods, the task values for both groups being larger than at rest. The $c$ parameter was highly specific in relation to DSM diagnosis for inattention, where well-defined clusters were observed. The parameter values were organized in four well-defined clusters in $(c, q)$-space. As expected, the tasks apparently induced greater complexity in neural functional states with likely greater amount of internal information processing. The results suggest that complexity is higher in ADHD subjects than in typical pairs. The distribution of values in the $(c, q)$-space derived from $q$-statistics seems to be a promising biomarker for ADHD diagnosis.

q-bio.NC↗

arXiv2024

Fourier's law breakdown for the planar-rotor chain with long-range coupling

The thermal conductivity, $κ$, of a homogeneous chain of generically-ranged interacting planar rotors, more precisely the inertial $α-XY$ model, is numerically studied with the coupling constant decaying as $r^{-α}$. The conductance ($σ\equiv κ/L$) is calculated for typical values of $α$, temperature $T$ and lattice size $L$. For large $L$, the results can be collapsed into an universal $q$-stretched exponential form, namely $L^{δ_α} σ\propto e_{q_α}^{-B_α(L^{γ_α}T)^{η_α}}$, where $e_q^z\equiv [1+ (1-q)z]^{1/(1-q)}$. The parameters $(γ_α,δ_α,B_α, η_α)$ are $α$-dependent, and $q_α$ is the index of the $q$-stretched exponential. This form is achievable due to the ratio $η_α/(q-1)$ being almost constant with respect to the lattice size $L$. Two distinct regimes are identified: for $0 \le α< 2$, the Fourier law is violated, whereas for $α\ge 2$, it is satisfied. These findings provide significant insights into heat conduction mechanisms in systems with long-range interactions.

cond-mat.stat-mech↗

arXiv2023

de Broglie-Bohm analysis of a nonlinear membrane: From quantum to classical chaos

Within the de Broglie-Bohm theory, we numerically study a generic two-dimensional anharmonic oscillator including cubic and quartic interactions. Our analysis of the quantum velocity fields and trajectories reveals the emergence of dynamical vortices. In their vicinity, fingerprints of chaotic behavior such as unpredictability and sensitivity to initial conditions are detected. The simultaneous presence of off-diagonal and nonlinear terms leads to robust quantum chaos very analogous to its classical version.

quant-ph↗

arXiv2023

First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model

The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size $L$ is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, $T_{h}$ and $T_{l}$ ($T_{h}>T_{l}$), respectively. These particles at extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators ($i=2, \cdots , L-1$) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier's law for the heat flux is verified numerically with the thermal conductivity becoming independent of the lattice size in the limit $L \to \infty$, scaling with the temperature as $κ(T) \sim T^{-2.25}$, where $T=(T_{h}+T_{l})/2$. Moreover, the thermal conductance, $σ(L,T)=κ(T)/L$, is well-fitted by a function, typical of nonextensive statistical mechanics, according to $σ(L,T)=A \exp_{q}(-B x^η)$, where $A$ and $B$ are constants, $x=L^{0.475}T$, $q=2.28 \pm 0.04$, and $η=2.88 \pm 0.04$.

cond-mat.stat-mech↗

arXiv2023

Numerical validation of Ehrenfest theorem in a Bohmian perspective for non-conservative systems

In this work we make a high precision numerical study of the Ehrenfest theorem using the Bohmian approach, where we obtain classical solutions from the quantum trajectories performing the Bohmian averages. We analyse the one-dimensional quantum harmonic and Duffing oscillator cases, finding numerical solutions of the time-dependent Schrödinger equation and the guidance equation for different sets of initial conditions and connects these results with the corresponding classical solutions. We also investigate the effect of introducing external forces of three types: a simple constant force, a fast-acting Gaussian impulse, and an oscillatory force with different frequencies. In the last case the resonance in the quantum trajectories was observed.

quant-ph↗

arXiv2023

Ising chain: Thermal conductivity and first-principle validation of Fourier law

The thermal conductivity of a $d=1$ lattice of ferromagnetically coupled planar rotators is studied through molecular dynamics. Two different types of anisotropies (local and in the coupling) are assumed in the inertial XY model. In the limit of extreme anisotropy, both models approach the Ising model and its thermal conductivity $κ$, which, at high temperatures, scales like $κ\sim T^{-3}$. This behavior reinforces the result obtained in various $d$-dimensional models, namely $κ\propto L\, e_{q}^{-B(L^γT)^η}$ where $e_q^z \equiv[1+(1-q)z]^{\frac{1}{1-q}}\;(e_1^z=e^z)$, $L$ being the linear size of the $d$-dimensional macroscopic lattice. The scaling law $\frac{η\,γ}{q-1}=1$ guarantees the validity of Fourier's law, $\forall d$.

cond-mat.stat-mech↗

arXiv2023

Neural complexity -- Statistical-mechanical approach of human electroencephalograms

The brain is a complex system whose understanding enables potentially deeper approaches to mental phenomena. Dynamics of wide classes of complex systems have been satisfactorily described within $q$-statistics, a current generalization of Boltzmann-Gibbs (BG) statistics. Here, we study human electroencephalograms of typical human adults (EEG), very specifically their inter-occurrence times across an arbitrarily chosen threshold of the signal (observed, for instance, at the midparietal location in scalp). The distributions of these inter-occurrence times differ from those usually emerging within BG statistical mechanics. They are instead well approached within the $q$-statistical theory, based on non-additive entropies characterized by the index $q$. The present method points towards a suitable tool for quantitatively accessing brain complexity, thus potentially opening useful studies of the properties of both typical and altered brain physiology.

q-bio.NC↗

arXiv2023

First-principle validation of Fourier's law in d=1,2,3 classical systems

We numerically study the thermal transport in the classical inertial nearest-neighbor XY ferromagnet in $d=1,2,3$, the total number of sites being given by $N=L^d$, where $L$ is the linear size of the system. For the thermal conductance $σ$, we obtain $σ(T,L)\, L^{δ(d)} = A(d)\, e_{q(d)}^{- B(d)\,[L^{γ(d)}T]^{η(d)}}$ (with $e_q^z \equiv [1+(1-q)z]^{1/(1-q)};\,e_1^z=e^z;\,A(d)>0;\,B(d)>0;\,q(d)>1;\,η(d)>2;\,δ\ge 0; \,γ(d)>0)$, for all values of $L^{γ(d)}T$ for $d=1,2,3$. In the $L\to\infty$ limit, we have $σ\propto 1/L^{ρ_σ(d)}$ with $ρ_σ(d)= δ(d)+ γ(d) η(d)/[q(d)-1]$. The material conductivity is given by $κ=σL^d \propto 1/L^{ρ_κ(d)}$ ($L\to\infty$) with $ρ_κ(d)=ρ_σ(d)-d$. Our numerical results are consistent with 'conspiratory' $d$-dependences of $(q,η,δ,γ)$, which comply with normal thermal conductivity (Fourier law) for all dimensions.

cond-mat.stat-mech↗