arXiv subjects

Andrés Santos

Publications and source records attributed to Andrés Santos.

At least 19 recordsLinked to original sources

arXiv2026

A Unified Rational-Function Approximation for Square-Well, Square-Shoulder, and Nonadditive Hard-Sphere Mixtures

We develop a rational-function approximation for the structural properties of multicomponent fluids with narrow square-well and square-shoulder interactions, together with weakly nonadditive hard-sphere mixtures. The theory is obtained by reformulating the analytical Percus--Yevick solution for additive sticky hard-sphere mixtures so as to account for finite interaction widths, leading to a unified semianalytical framework for these classes of fluids. The approximation satisfies the exact low-density limit and preserves the continuity of the cavity functions; a simple local correction restores the continuity of their first derivatives. Comparison with Monte Carlo simulations for binary mixtures shows that the theory accurately describes both the radial distribution functions and their Fourier transforms for narrow wells and shoulders and for weak nonadditivity. The proposed formulation extends previous sticky-hard-sphere-based approaches while retaining their analytical simplicity.

cond-mat.soft↗

arXiv2026

Thermodynamic and structural behavior of one-dimensional divalent patchy hard rods: Wertheim's first-order thermodynamic perturbation theory vs exact results

We investigate the thermodynamic and structural properties of divalent patchy hard rods confined to a one-dimensional channel by modeling the bonding sites as attractive square-well (SW) patches located at the rod tips. The zero-range sticky limit is recovered by letting the well width vanish while keeping the stickiness parameter finite. While Wertheim's first-order thermodynamic perturbation theory becomes exact in this sticky limit, it fails for finite-range site--site interactions. Because the present model is mathematically equivalent to an exactly solvable one-dimensional nearest-neighbor fluid, we use the exact solution to reformulate the thermodynamics in terms of association-theory variables, including the fraction of unbonded sites and a generalized law of mass action. Finite-range SW sites produce a richer structural behavior than sticky sites, including monotonic and oscillatory asymptotic decay of the pair correlation function, separated by the Fisher--Widom line. In the monotonic regime, the correlation length exhibits an absolute maximum defining the Widom line, while in the oscillatory regime it may display a local maximum and minimum, whose locus defines the ``Extrema of the Correlation length under Oscillatory decay'' line. These features disappear in the sticky limit, where the system remains entirely in the oscillatory regime. We also show that the high-pressure behavior of the correlation length changes from $ξ\sim p^2$ for finite-range SW sites to $ξ\sim p^3$ in the sticky limit.

cond-mat.soft↗

arXiv2026

Exact Rheology of Uniform Shear Flow in a Gas of Inelastic and Rough Maxwell Particles

We investigate the steady uniform shear flow of a granular gas composed of inelastic and rough Maxwell particles. Exploiting the mean-field character of the model, we derive exact expressions for the collisional production rates of the second-degree moments and obtain a closed nonlinear solution for the stress and spin-spin tensors. The rotational-to-translational temperature ratio and the proportionality between the spin-spin and stress tensors are shown to be independent of the coefficient of normal restitution and determined solely by roughness and moment of inertia. The reduced normal stresses, shear stress, and shear rate are obtained explicitly in terms of two effective parameters generalizing the cooling and stress relaxation rates of the smooth model. From these results we derive exact expressions for the non-Newtonian shear viscosity, the first viscometric function, and the friction coefficient. The dependence of the rheological properties on the normal and tangential restitution coefficients is analyzed in detail, revealing strong non-Newtonian behavior and nonmonotonic effects of roughness. The results reduce, in the appropriate limits, to those of the inelastic Maxwell model for smooth particles and to the Pidduck gas in the elastic perfectly rough case.

cond-mat.soft↗

arXiv2026

Algebraic to exponential decay of spatial correlations in one-dimensional and confined hard-core fluids: A Laplace-pole analysis

We derive the asymptotic behavior of the radial distribution function $g(x)$ for one-dimensional (1D) hard-rod systems and related quasi-one-dimensional geometries at high packing fractions using Laplace transform techniques and pole analysis. By identifying the poles and residues of the Laplace transform in the limit of small void fraction, we obtain compact representations of $g(x)$ in terms of the Jacobi elliptic theta function $θ_3$. This formulation naturally captures the two regimes governing the oscillatory decay toward unity: an intermediate algebraic decay and a long-distance exponential decay, consistent with previous results for the Tonks gas. Our approach provides a unified framework that (i) expresses $g(x)$ in a single well-tabulated special function, (ii) links spatial correlations directly to the pole structure in complex Laplace space, offering clear physical insight into decay rates and oscillation frequencies, and (iii) generalizes straightforwardly to 1D binary mixtures and confined hard-disk systems, where direct Gaussian decompositions are cumbersome. The equivalence between the theta-function representation and the Gaussian superposition of Bouzar and Messina [Phys. Rev. E \textbf{112}, L042105 (2025)] is established via the Poisson summation formula, highlighting the versatility and conceptual advantages of the Laplace-pole framework.

cond-mat.soft↗

arXiv2026

Orientational ordering and correlations in a quasi-one-dimensional hard-dumbbell fluid

We study a quasi-one-dimensional fluid of hard dumbbells with continuous orientational degrees of freedom using an exact transfer-matrix formulation. The model allows for a complete analytical characterization of thermodynamic properties, orientational ordering, and correlation functions in terms of the spectral properties of an integral operator. We derive exact expressions for the equation of state, the orientational distribution function, and both partial and total radial distribution functions. Their asymptotic behavior is governed by the complex poles of the Laplace-transformed correlation functions, which determine the positional and orientational correlation lengths. As density increases, the system exhibits a continuous crossover from a weakly ordered regime with a unimodal orientational distribution to a strongly constrained regime characterized by bimodal orientational ordering. This crossover is accompanied by a nonmonotonic behavior of the pressure relative to the Tonks gas and by a qualitative change in the decay of correlation functions from oscillatory to monotonic. In the high-pressure limit, we show that orientational and positional fluctuations contribute equally to the pressure, leading to a universal ratio of twice the Tonks pressure. The theoretical predictions are supported by numerical solutions of the discretized transfer operator and by scaling arguments that elucidate the high-pressure behavior of ordering and correlation lengths.

cond-mat.soft↗

arXiv2026

The Mpemba effect in the Descartes protocol: A time-delayed Newton's law of cooling approach

We investigate the direct and inverse Mpemba effects within the framework of the time-delayed Newton's law of cooling by introducing and analyzing the Descartes protocol, a three-reservoir thermal scheme in which each sample undergoes a single-step quench at different times. This protocol enables a transparent separation of the roles of the delay time $τ$, the waiting time $t_{\text{w}}$, and the normalized warm temperature $ω$, thus providing a flexible setting to characterize anomalous thermal relaxation. For instantaneous quenches, exact conditions for the existence of the Mpemba effect are obtained as bounds on $ω$ for given $τ$ and $t_{\text{w}}$. Within those bounds, the effect becomes maximal at a specific value $ω=\widetildeω(t_{\text{w}})$, and its magnitude is quantified by the extremal value of the temperature-difference function at this optimum. Accurate and compact approximations for both $\widetildeω(t_{\text{w}})$ and the maximal magnitude $\text{Mp}(t_{\text{w}})$ are derived, showing in particular that the absolute maximum at fixed $τ$ is reached for $t_{\text{w}}=τ$. A comparison with a previously studied two-reservoir protocol reveals that, despite its additional control parameter, the Descartes protocol yields a smaller maximal magnitude of the effect. The analysis is extended to finite-rate quenches, where strict equality of bath conditions prevents a genuine Mpemba effect, although an approximate one survives when the bath time scale is sufficiently short. The developed framework offers a unified and analytically tractable approach that can be readily applied to other multi-step thermal protocols.

cond-mat.stat-mech↗

arXiv2026

Predicting random close packing of binary hard-disk mixtures via third-virial-based parameters

We propose a simple and accurate approach to estimate the random close packing (RCP) fraction of binary hard-disk mixtures. By introducing a parameter based on the mixture's reduced third virial coefficient -- which effectively captures three-body correlations and excluded-area constraints -- we show that the RCP fraction depends nearly linearly on this parameter, leading to a near-universal collapse of simulation data over a wide range of size ratios and compositions. Comparisons with previous models by Brouwers and Zaccone indicate that the present approach provides more accurate and consistent predictions. The method can be naturally extended to polydisperse mixtures with continuous size distributions and is structurally consistent with the surplus equation-of-state formulation, offering a compact framework for understanding the near universality of RCP in hard-disk systems.

cond-mat.soft↗

arXiv2025

On the First Quantum Correction to the Second Virial Coefficient of a Generalized Lennard-Jones Fluid

We derive an explicit analytic expression for the first quantum correction to the second virial coefficient of a $d$-dimensional fluid whose particles interact via the generalized Lennard-Jones $(2n,n)$ potential. By introducing an appropriate change of variable, the correction term is reduced to a single integral that can be evaluated in closed form in terms of parabolic cylinder or generalized Hermite functions. The resulting expression compactly incorporates both dimensionality and stiffness, providing direct access to the low- and high-temperature asymptotic regimes. In the special case of the standard Lennard-Jones fluid ($d=3$, $n=6$), the formula obtained is considerably more compact than previously reported representations based on hypergeometric functions. The knowledge of this correction allows us to determine the first quantum contribution to the Boyle temperature, whose dependence on dimensionality and stiffness is explicitly analyzed, and enables quantitative assessment of quantum effects in noble gases such as helium, neon, and argon. Moreover, the same methodology can be systematically extended to obtain higher-order quantum corrections.

cond-mat.stat-mech↗

arXiv2025

Exact anisotropic properties of hard spheres in narrow cylindrical confinement

We investigate a quasi-one-dimensional (Q1D) system of hard spheres confined within a cylindrical pore so narrow that only nearest-neighbor interactions occur. By mapping this Q1D system onto a one-dimensional polydisperse mixture of nonadditive hard rods, we obtain exact thermodynamic and structural properties, including the radial distribution function, which had remained elusive in previous studies. We derive analytical results for limiting cases, such as small pore diameters, virial expansions, and the high-pressure regime. In particular, we identify a crossover in the anisotropic pressure components: at high densities, the transverse pressure overtakes the longitudinal one when the pore diameter exceeds a critical threshold. We also examine spatial correlations in particle arrangements and radial fluctuations, shedding light on the emergence of ordering in confined systems.

cond-mat.soft↗

arXiv2025

Time-delayed Newton's law of cooling with a finite-rate thermal quench: Impact on the Mpemba and Kovacs effects

The Mpemba and Kovacs effects are two notable memory phenomena observed in nonequilibrium relaxation processes. In a recent study [Phys.~Rev.~E \textbf{109}, 044149 (2024)], these effects were analyzed within the framework of the time-delayed Newton's law of cooling under the assumption of instantaneous temperature quenches. Here, the analysis is extended to incorporate finite-rate quenches, characterized by a nonzero quench duration $σ$. The results indicate that a genuine Mpemba effect is absent under finite-rate quenches if both samples experience the same thermal environment during the quenching process. However, if $σ$ remains sufficiently small, the deviations in the thermal environment stay within an acceptable range, allowing the Mpemba effect to persist with a slightly enhanced magnitude. In contrast, the Kovacs effect is significantly amplified, with the transient hump in the temperature evolution becoming more pronounced as both the waiting time and $σ$ increase. These findings underscore the importance of incorporating finite-time effects in nonequilibrium thermal relaxation models and offer a more realistic perspective for experimental studies.

cond-mat.stat-mech↗

arXiv2025

Revisiting the Laplace transform in quantum mechanics: correcting a flawed approach for the stationary Schrödinger equation

The Laplace transform is a valuable tool in physics, particularly in solving differential equations with initial or boundary conditions. A 2014 study by Tsaur and Wang (2014 \emph{Eur.~J.~Phys.} \textbf{35} 015006) introduced a Laplace-transform-based method to solve the stationary Schrödinger equation for various potentials. However, their approach contains critical methodological flaws: the authors disregard essential boundary conditions and apply the residue theorem incorrectly in the inverse transformation process. These errors ultimately cancel out, leading to correct results despite a flawed derivation. In this paper, we revisit the use of the Laplace transform for the one-dimensional Schrödinger equation, clarifying correct practices in handling boundary conditions and singularities. This analysis offers a sound and consistent framework for the application of Laplace transforms in stationary quantum mechanics, underscoring their educational utility in quantum mechanics coursework.

quant-ph↗

arXiv2025

Discontinuous Structural Transitions in Fluids with Competing Interactions

This paper explores how competing interactions in the intermolecular potential of fluids affect their structural transitions. This study employs a versatile potential model with a hard core followed by two constant steps, representing wells or shoulders, analyzed in both one-dimensional (1D) and three-dimensional (3D) systems. Comparing these dimensionalities highlights the effect of confinement on structural transitions. Exact results are derived for 1D systems, while the rational function approximation is used for unconfined 3D fluids. Both scenarios confirm that when the steps are repulsive, the wavelength of the oscillatory decay of the total correlation function evolves with temperature either continuously or discontinuously. In the latter case, a discontinuous oscillation crossover line emerges in the temperature--density plane. For an attractive first step and a repulsive second step, a Fisher--Widom line appears. Although the 1D and 3D results share common features, dimensionality introduces differences: these behaviors occur in distinct temperature ranges, require deeper wells, or become attenuated in 3D. Certain features observed in 1D may vanish in 3D. We conclude that fluids with competing interactions exhibit a rich and intricate pattern of structural transitions, demonstrating the significant influence of dimensionality and interaction features.

cond-mat.soft↗

arXiv2024

Exact equilibrium properties of square-well and square-shoulder disks in single-file confinement

This study investigates the (longitudinal) thermodynamic and structural characteristics of single-file confined square-well and square-shoulder disks by employing a mapping technique that transforms the original system into a one-dimensional polydisperse mixture of nonadditive rods. Leveraging standard statistical-mechanical techniques, exact results are derived for key properties, including the equation of state, internal energy, radial distribution function, and structure factor. The asymptotic behavior of the radial distribution function is explored, revealing structural changes in the spatial correlations. Additionally, exact analytical expressions for the second virial coefficient are presented. The theoretical results for the thermodynamic and structural properties are validated by our Monte Carlo simulations.

cond-mat.soft↗

arXiv2024

Exploring anisotropic pressure and spatial correlations in strongly confined hard-disk fluids. Exact results

This study examines the transverse and longitudinal properties of hard disks confined in narrow channels. Employing an exact mapping of the system onto a one-dimensional polydisperse, nonadditive mixture of hard rods with equal chemical potentials, we compute various thermodynamic properties, including the transverse and longitudinal equations of state, along with their behaviors at both low and high densities. Structural properties are analyzed using the two-body correlation function and the radial distribution function, tailored for the highly anisotropic geometry of this system. The results are corroborated by computer simulations.

cond-mat.soft↗

arXiv2024

Exact transport coefficients from the inelastic rough Maxwell model of a granular gas

Granular gases demand models capable of capturing their distinct characteristics. The widely employed inelastic hard-sphere model (IHSM) introduces complexities that are compounded when incorporating realistic features like surface roughness and rotational degrees of freedom, resulting in the more intricate inelastic rough hard-sphere model (IRHSM). This paper focuses on the inelastic rough Maxwell model (IRMM), presenting a more tractable alternative to the IRHSM and enabling exact solutions. Building on the foundation of the inelastic Maxwell model (IMM) applied to granular gases, the IRMM extends the mathematical representation to encompass surface roughness and rotational degrees of freedom. The primary objective is to provide exact expressions for the Navier--Stokes--Fourier transport coefficients within the IRMM, including the shear and bulk viscosities, the thermal and diffusive heat conductivities, and the cooling-rate transport coefficient. In contrast to earlier approximations in the IRHSM, our study unveils inherent couplings, such as shear viscosity to spin viscosity and heat conductivities to counterparts associated with a torque-vorticity vector. These exact findings provide valuable insights into refining the Sonine approximation applied to the IRHSM, contributing to a deeper understanding of the transport properties in granular gases with realistic features.

cond-mat.soft↗

arXiv2024

On a conjecture concerning the Fisher--Widom line and the line of vanishing excess isothermal compressibility in simple fluids

In the statistical mechanics approach to liquid-state theory, understanding the role of the intermolecular potential in determining thermodynamic and structural properties is crucial. The Fisher--Widom (FW) line, which separates regions in the temperature vs density plane where the decay of the total correlation function is monotonic or oscillatory, provides insights into the dominance of the attractive or repulsive part of the interactions. Stopper et al. have recently conjectured [J. Chem. Phys. \textbf{151}, 014501 (2019)] that the line of vanishing excess isothermal compressibility approximates the FW line in simple fluids. Here, we investigate this conjecture using the Jagla potential and also explore the line of vanishing excess pressure. We employ theoretical approximations and Monte Carlo simulations to study one-dimensional and three-dimensional systems. While exact results for the one-dimensional case do not support the conjecture, our Monte Carlo simulations for the three-dimensional fluid validate it. Our findings not only contribute to the understanding of the relationship between the three transition lines but also provide valuable insights into the thermodynamic and structural behaviour of simple fluids.

cond-mat.soft↗

arXiv2024

Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law

Despite extensive research, the fundamental physical mechanisms underlying the Mpemba effect, a phenomenon where a substance cools faster after initially being heated, remain elusive. Although historically linked with water, the Mpemba effect manifests across diverse systems, sparking heightened interest in Mpemba-like phenomena. Concurrently, the Kovacs effect, a memory phenomenon observed in materials like polymers, involves rapid quenching and subsequent temperature changes, resulting in nonmonotonic relaxation behavior. This paper probes the intricacies of the Mpemba and Kovacs effects within the framework of the time-delayed Newton's law of cooling, recognized as a simplistic yet effective phenomenological model accommodating memory phenomena. This law allows for a nuanced comprehension of temperature variations, introducing a time delay ($τ$) and incorporating specific protocols for the thermal bath temperature, contingent on a defined waiting time ($t_{\text{w}}$). Remarkably, the relevant parameter space is two-dimensional ($τ$ and $t_{\text{w}}$), with bath temperatures exerting no influence on the presence or absence of the Mpemba effect or the relative strength of the Kovacs effect. The findings enhance our understanding of these memory phenomena, providing valuable insights applicable to researchers across diverse fields, ranging from physics to materials science.

cond-mat.soft↗

arXiv2023

Ordering properties of anisotropic hard bodies in one-dimensional channels

The phase behavior and structural properties of hard anisotropic particles (prisms and dumbbells) are examined in one-dimensional channels using the Parsons--Lee (PL) theory, and the transfer-matrix and neighbor-distribution methods. The particles are allowed to move freely along the channel, while their orientations are constrained such that one particle can occupy only two or three different lengths along the channel. In this confinement setting, hard prisms behave as an additive mixture, while hard dumbbells behave as a non-additive one. We prove that all methods provide exact results for the phase properties of hard prisms, while only the neighbor-distribution and transfer-matrix methods are exact for hard dumbbells. This shows that non-additive effects are incorrectly included into the PL theory, which is a successful theory of the isotropic-nematic phase transition of rod-like particles in higher dimensions. In the one-dimensional channel, the orientational ordering develops continuously with increasing density, i.e., the system is isotropic only at zero density, while it becomes perfectly ordered at the close-packing density. We show that there is no orientational correlation in the hard prism system, while the hard dumbbells are orientationally correlated with diverging correlation length at close packing. On the other hand, positional correlations are present for all the systems, the associated correlation length diverging at close packing.

cond-mat.soft↗