arXiv subjects

Paolo V. Giaquinta

Publications and source records attributed to Paolo V. Giaquinta.

11 recordsLinked to original sources

arXiv2021

Entropy Multiparticle Correlation Expansion for a Crystal

As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded on theoretical arguments, that both entropies are extensive quantities.

cond-mat.stat-mech↗

arXiv2019

Ground state of weakly repulsive soft-core bosons on a sphere

We study a system of penetrable bosons embedded in a spherical surface. Under the assumption of weak interaction between the particles, the ground state of the system is, to a good approximation, a pure condensate. We employ thermodynamic arguments to investigate, within a variational ansatz for the single-particle state, the crossover between distinct finite-size "phases" in the parameter space spanned by the sphere radius and the chemical potential. In particular, for radii up to a few interaction ranges we examine the stability of the fluid phase with respect to a number of crystal-like arrangements having the symmetry of a regular or semi-regular polyhedron. We find that, while quantum fluctuations keep the system fluid at low density, upon compression it eventually becomes inhomogeneous, i.e., particles gather together in clusters. As the radius increases, the nature of the high-density aggregate varies and we observe a sequence of transitions between different cluster phases ("solids"), whose underlying rationale is to maximize the coordination number of clusters, while ensuring at the same time the proper distance between each neighboring pair. We argue that, at least within our mean-field description, every cluster phase is supersolid.

cond-mat.quant-gas↗

arXiv2018

Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, $Δs$, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), $s_\text{ex}$, and the pair-correlation contribution, $s_2$. Thus, the RMPE represents the net contribution to $s_\text{ex}$ due to spatial correlations involving three, four, or more particles. A heuristic `ordering' criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension $1<d<3$ has been proposed [Santos, A.; López de Haro, M. \emph{Phys. Rev. E} \textbf{2016}, \emph{93}, 062126]. The aim of this work is to use this approach to evaluate the RMPE as a function of both $d$ and the packing fraction $ϕ$. It is observed that, for any given dimensionality $d$, the RMPE takes negative values for small densities, reaches a negative minimum $Δs_{\text{min}}$ at a packing fraction $ϕ_{\text{min}}$, and then rapidly increases, becoming positive beyond a certain packing fraction $ϕ_0$. Interestingly, while both $ϕ_{\text{min}}$ and $ϕ_0$ monotonically decrease as dimensionality increases, the value of $Δs_{\text{min}}$ exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality $d\simeq 2.38$. A plot of the scaled RMPE $Δs/|Δs_{\text{min}}|$ shows a quasiuniversal behavior in the region $-0.14\lesssimϕ-ϕ_0\lesssim 0.02$.

cond-mat.soft↗

arXiv2016

Linear Quantum Entropy and Non-Hermitian Hamiltonians

We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly considered.

quant-ph↗

arXiv2013

Fluids in porous media: The case of neutral walls

The bulk phase behavior of a fluid is typically altered when the fluid is brought into confinement by the walls of a random porous medium. Inside the porous medium, phase transition points are shifted, or may disappear altogether. A crucial determinant is how the walls interact with the fluid particles. In this work, we consider the situation whereby the walls are neutral with respect to the liquid and vapor phase. In order to realize the condition of strict neutrality, we use a symmetric binary mixture inside a porous medium that interacts identically with both of the mixture species. Monte Carlo simulations are then used to obtain the phase behavior. Our main finding is that, in the presence of the porous medium, a liquid-vapor type transition still occurs, but with critical exponents that deviate from bulk Ising values. In addition, we observe clear violations of self-averaging. These findings provide further evidence that random confinement by neutral walls induces critical behavior of the random Ising model (i.e. Ising models with dilution type disorder, where the disorder couples to the energy).

cond-mat.stat-mech↗

arXiv2012

Hexatic phase and water-like anomalies in a two-dimensional fluid of particles with a weakly softened core

We study a two-dimensional fluid of particles interacting through a spherically-symmetric and marginally soft two-body repulsion. This model can exist in three different crystal phases, one of them with square symmetry and the other two triangular. We show that, while the triangular solids first melt into a hexatic fluid, the square solid is directly transformed on heating into an isotropic fluid through a first-order transition, with no intermediate tetratic phase. In the low-pressure triangular and square crystals melting is reentrant provided the temperature is not too low, but without the necessity of two competing nearest-neighbor distances over a range of pressures. A whole spectrum of water-like fluid anomalies completes the picture for this model potential.

cond-mat.soft↗

arXiv2012

Ab initio molecular dynamics study of dissociation of water under an electric field

The behavior of liquid water under an electric field is a crucial phenomenon in science and engineering. However, its detailed description at a microscopic level is difficult to achieve experimentally. Here we report on the first ab initio molecular-dynamics study on water under an electric field. We observe that the hydrogen-bond length and the molecular orientation are significantly modified at low-to-moderate field intensities. Fields beyond a threshold of about 0.35 V/Åare able to dissociate molecules and sustain an ionic current via a series of correlated proton jumps. Upon applying even more intense fields (1.0 V/Å), a 15-20% fraction of molecules are instantaneously dissociated and the resulting ionic flow yields a conductance of about 7.8 $Ω^{-1}cm^{-1}$, in good agreement with experimental values. This result paves the way to quantum-accurate microscopic studies of the effect of electric fields on aqueous solutions and, thus, to massive applications of ab initio molecular dynamics in neurobiology, electrochemistry and hydrogen economy.

cond-mat.soft↗

arXiv2012

Thermodynamic and structural anomalies of the Gaussian-core model in one dimension

We investigated the equilibrium properties of a one-dimensional system of classical particles which interact in pairs through a bounded repulsive potential with a Gaussian shape. Notwithstanding the absence of a proper fluid-solid phase transition, we found that the system exhibits a complex behaviour, with "anomalies" in the density and in the thermodynamic response functions which closely recall those observed in bulk and confined liquid water. We also discuss the emergence in the cold fluid under compression of an unusual structural regime, characterized by density correlations reminiscent of the ordered arrangements found in clustered crystals.

cond-mat.soft↗

arXiv2007

On the Geometry and Entropy of Non-Hamiltonian Phase Space

We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation and phase space measure are clarified. In particular, we emphasize that a phase space measure should be defined by means of the Jacobian of the transformation between different types of coordinates since such a determinant is different from zero in the non-canonical case even if the phase space compressibility is null. Instead, the Jacobian determinant associated with phase space flows is unity whenever non-canonical coordinates lead to a vanishing compressibility, so that its use in order to define a measure may not be always correct. To better illustrate this point, we derive a mathematical condition for defining non-Hamiltonian phase space flows with zero compressibility. The Jacobian determinant associated with time evolution in phase space is altogether useful for analyzing time translation invariance. The proper definition of a phase space measure is particularly important when defining the entropy functional in the canonical, non-canonical, and non-Hamiltonian cases. We show how the use of relative entropies can circumvent some subtle problems that are encountered when dealing with continuous probability distributions and phase space measures. Finally, a maximum (relative) entropy principle is formulated for non-canonical and non-Hamiltonian phase space flows.

cond-mat.stat-mech↗

arXiv2006

Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles

We test the validity of some widely used phenomenological criteria for the localization of the fluid-solid transition thresholds against the phase diagrams of particles interacting through the exp-6, inverse-power-law, and Gaussian potentials. We find that one-phase rules give, on the whole, reliable estimates of freezing/melting points. The agreement is ordinarily better for a face-centered-cubic solid than for a body-centered-cubic crystal, even more so in the presence of a pressure-driven re-entrant transition of the solid into a denser fluid phase, as found in the Gaussian-core model.

cond-mat.soft↗

arXiv2006

Entropy-based measure of structural order in water

We analyze the nature of the structural order established in liquid TIP4P water in the framework provided by the multi-particle correlation expansion of the statistical entropy. Different regimes are mapped onto the phase diagram of the model upon resolving the pair entropy into its translational and orientational components. These parameters are used to quantify the relative amounts of positional and angular order in a given thermodynamic state, thus allowing a structurally unbiased definition of low-density and high-density water. As a result, the structurally anomalous region within which both types of order are simultaneously disrupted by an increase of pressure at constant temperature is clearly identified through extensive molecular-dynamics simulations.

cond-mat.mtrl-sci↗