Inverse Power Law Potential Research Articles

Simulations of classical three-body thermalization in one dimension.

One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of pointlike particles, typically the dominant process for reaching thermal equilibrium in higher-dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential V_{ij}∝1/|x_{i}-x_{j}|^{n} or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equationto evolve a perturbed thermal state with temperature T toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low-density limit. For the inverse power-law potential, the rate of thermalization is proportional to ρ^{2}T^{1/2-1/n}, where ρ is the number density. The corresponding proportionality constant decreases with increasing n.

Quantum gravity effects on the tachyon inflation from thermodynamic perspective

By considering the Friedmann equations emerging from the entropy-area law of black hole thermodynamics in the context of the generalized uncertainty principle, we study tachyon inflation in the early universe. The presence of a minimal length modifies the Friedmann equations and hence the slow-roll and perturbation parameters in the tachyon model. These modifications, though small, affect the viability of the tachyon inflation in confrontation with observational data. We compare the numerical results of the model with Planck2018 TT, TE, EE +lowE+lensing+BAO+BK14(18) data and Planck2018 TT, TE,EE +lowE+lensing+BK14(18) +BAO+LIGO & Virgo2016 data at 68% and 95% CL. We show that while the tachyon inflation with power-law, inverse power-law and inverse exponential potentials is not observationally viable in comparison with the 1σ and 2σ confidence levels of the new joint data, in the presence of the minimal length the model becomes observationally viable.

Stringlet excitation model of the boson peak.

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

The Inflationary with Inverse Power-Law Potential in Tsallis Entropy

The Inflationary with Inverse Power-Law Potential in Tsallis Entropy

Phase-space analysis in non-minimal symmetric-teleparallel dark energy

We modify the symmetric-teleparallel dark energy through the addition of a further Yukawa-like term, in which the non-metricity scalar, Q, is non-minimally coupled to a scalar field Lagrangian where the phion acts as quintessence, describing dark energy. We investigate regions of stability and find late-time attractors. To do so, we conduct a stability analysis for different types of physical potentials describing dark energy, namely the power-law, inverse power-law, and exponential potentials. Within these choices, we furthermore single out particular limiting cases, such as the constant, linear and inverse potentials. For all the considered scenarios, regions of stability are calculated in terms of the signs of the coupling constant and the exponent, revealing a clear degeneracy among coefficients necessary to ensure stability. We find that a generic power-law potential with α>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha > 0$$\\end{document} is not suitable as a non-minimal quintessence potential and we put severe limits on the use of inverse potential, as well. In addition, the equations of state of each potential have been also computed. We find the constant potential seems to be favored than other treatments, since the critical point appears independent of the non-minimal coupling.

Low-frequency hybridized excess vibrations of two-dimensional glasses

One hallmark of glasses is the existence of excess vibrational modes at low frequencies ω beyond Debye’s prediction. Numerous studies suggest that understanding low-frequency excess vibrations could help gain insight into the anomalous mechanical and thermodynamic properties of glasses. However, there is still intensive debate as to the frequency dependence of the population of low-frequency excess vibrations. In particular, excess modes could hybridize with phonon-like modes and the density of hybridized excess modes has been reported to follow D exc(ω) ∼ ω 2 in 2D glasses with an inverse power law potential. Yet, the universality of the quadratic scaling remains unknown, since recent work suggested that interaction potentials could influence the scaling of the vibrational spectrum. Here, we extend the universality of the quadratic scaling for hybridized excess modes in 2D to glasses with potentials ranging from the purely repulsive soft-core interaction to the hard-core one with both repulsion and attraction as well as to glasses with significant differences in density or interparticle repulsion. Moreover, we observe that the number of hybridized excess modes exhibits a decrease in glasses with higher density or steeper interparticle repulsion, which is accompanied by a suppression of the strength of the sound attenuation. Our results indicate that the density bears some resemblance to the repulsive steepness of the interaction in influencing low-frequency properties.

Avoiding parameter fine-tuning in mass varying neutrino models of DE?

Coupled models of quintessence are usually introduced for avoiding or mitigating the parameter fine-tuning problem. At the same time, the coupled models should avoid the fine-tuning problem related to the initial conditions as quintessence models do. One more attractive feature of coupled models might be the explanation of the timescale at which the coincidence of DE and matter energy densities occur and the understanding of reason why after this the DE takes over. And finally, all these nice features should be unaffected by the quantum corrections of the potential. Having in mind these remarks, we shall focus our discussion on mass varying neutrino model of DE with inverse power-law potential to see how naturally does it work.

Global well-posedness of the quantum Boltzmann equation for bosons interacting via inverse power law potentials

We consider the spatially inhomogeneous quantum Boltzmann equation for bosons with a singular collision kernel, the weak-coupling limit of a large system of Bose-Einstein particles interacting through inverse power law. Global well-posedness of the corresponding Cauchy problem is proved in a periodic box near equilibrium for initial data satisfying high temperature condition.

Sound velocities in liquids near freezing: Dependence on the interaction potential and correlations with thermal conductivity

We present systematic investigation of sound velocities in various fluids at the fluid–solid phase transition. First, theoretical estimates indicating that quasi-universal values of sound velocities at freezing can be expected are presented. Then, this prediction is verified on three model systems with quite different interactions (inverse power law, screened Coulomb, and Lennard-Jones pairwise potentials) and 15 real atomic and molecular liquids. It is documented that the ratio of the sound velocity to the thermal velocity tends to a quasi-universal value (cs/vT∼10) in many systems considered, but exceptions also exist. In particular, extremely soft interactions can result in indefinitely large ratios cs/vT. Complex hydrocarbon liquids also demonstrate high ratios cs/vT. On the other hand, liquids composed of light elements, such as hydrogen and neon, demonstrate lower ratios cs/vT. For model systems, we discuss relations between the thermodynamic sound velocity and instantaneous longitudinal, transverse, and bulk sound velocities. It is found that these relations are greatly affected by the potential softness. Finally, correlations between the thermal conductivity coefficient and the sound velocity are briefly discussed in the context of Bridgman's formula.

Wormhole inducing inflation with Einstein–Gauss–Bonnet dilaton interaction

A few Euclidean wormhole configurations are presented using both the analytic and numerical solutions of the field equations in four-dimensional Robertson–Walker Euclidean background with Einstein–Gauss–Bonnet dilaton interaction. In one analytic solution we present transition from a wormhole to an exponential expansion with Lorentzian time [Formula: see text] using [Formula: see text] after passing through an era of oscillating Euclidean wormhole. The numerical solutions of the scale factor [Formula: see text] show multiple local maxima and minima about a global minimum for inverse power law potentials, while for exponential potential the wormholes have a single minimum. An inflationary cosmic scenario away from the throat of the wormhole can be obtained from the Hubble parameter and deceleration parameter obtained by curve fit of [Formula: see text] of the numerical solution invoking analytic continuation by [Formula: see text]. The potential is also observed to decay sharply.

Observational constraints and predictions of the interacting dark sector with field-fluid mapping

We consider an interacting field theory model that describes the interaction between dark energy-dark matter interaction. Only for a specific interaction term, this interacting field theory description has an equivalent interacting fluid description. For inverse power law potentials and linear interaction function, we show that the interacting dark sector model with field-fluid mapping is consistent with four cosmological data sets — Hubble parameter measurements (Hz), Baryonic Acoustic Oscillation data (BAO), Supernova Type Ia data (SN), and High redshift HII galaxy measurements (HIIG). More specifically, these data sets prefer a negative value of interaction strength in the dark sector and lead to consistent best-fit values of Hubble constant and other cosmological parameters. Having established that this interacting field theory model is consistent with cosmological observations, we obtain quantifying tools to distinguish between the interacting and non-interacting dark sector scenarios. We focus on the variation of the scalar metric perturbed quantities as a function of redshift related to structure formation, weak gravitational lensing, and the integrated Sachs-Wolfe effect. We show that the difference in the evolution becomes significant for z < 20, for all length scales, and the difference peaks at smaller redshift values z < 5. We then discuss the implications of our results for the upcoming missions.

Dynamical stability of the k -essence field interacting nonminimally with a perfect fluid

We study models of non-minimally coupled relativistic fluid and $k$-essence scalar field in the background of a flat Friedmann-Lemaitre-Robertson-Walker universe. The non-minimal coupling term is introduced in the Lagrangian level. We employ the variational approach with respect to independent variables that produce modified $k-$essence field equations and the Friedmann equations. We have analyzed the coupled field-fluid framework explicitly using the dynamical system technique considering two different models based on inverse power-law potential. After examining these models it is seen that both models are capable of producing accelerating attractor solutions satisfying adiabatic sound speed conditions.

The investigation of stability of brane induced gravity model in the ‎presence of a scalar field with various kinds of potential‎

In this manuscript we consider the normal branch of DGP brane cosmological model in the presence of a ‎scalar field on the brane as the dark energy component. Using dynamical system approach we investigate ‎the stability properties of the system. We will see that one of the defined new variables lambda, that ‎depends on the potential function of the scalar field has a significant role in the evolution of the universe. ‎Therefore, we divide our discussion into two parts, the constant and the varying lambda. With a good ‎approximation we consider all the obtained critical points in the case of the constant lambda, as the ‎instantaneous critical points for the case of a varying lambda. We investigate two special scalar field ‎potential function: a double exponential potential and an inverse power law potential. In both of the cases we ‎study the evolution of the system and discuss the fate of the universe. We find that the inverse power law ‎potential function is in a good agreement with the current universe, but the double exponential potential ‎function can predict different future for the universe.‎

Thermodynamic geometry of the Gaussian core model fluid

The three-dimensional Gaussian core model (GCM) for soft-matter systems has repulsive interparticle interaction potential ϕ(r)=εexp[−(r/σ)2], with r the distance between a pair of atoms, and the positive constants ε and σ setting the energy and length scales, respectively. ϕ(r) is mostly soft in character, without the typical hard core present in fluid models. We work out the thermodynamic Ricci curvature scalar R for the GCM, with particular attention to the sign of R, which, based on previous results, is expected to be positive/negative for microscopic interactions repulsive/attractive. Over most of the thermodynamic phase space, R is found to be positive, with values of the order of σ3. However, for low densities and temperatures, the GCM potential takes on the character of a hard-sphere repulsive system, and R is found to have an anomalous negative sign. Such a sign was also found earlier in inverse power law potentials in the hard-sphere limit, and seems to be a persistent feature of hard-sphere models.

A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels

We introduce a fast Fourier spectral method for the spatially homogeneous Boltzmann equation with non-cutoff collision kernels. Such kernels contain non-integrable singularity in the deviation angle which arise in a wide range of interaction potentials (e.g., the inverse power law potentials). Albeit more physical, the non-cutoff kernels bring a lot of difficulties in both analysis and numerics, hence are often cut off in most studies (the well-known Grad's angular cutoff assumption). We demonstrate that the general framework of the fast Fourier spectral method developed in [9,14] can be extended to handle the non-cutoff kernels, achieving the accuracy/efficiency comparable to the cutoff case. We also show through several numerical examples that the solution to the non-cutoff Boltzmann equation enjoys the smoothing effect, a striking property absent in the cutoff case.

Thermal transpiration in molecular gas

The thermal transpiration of molecular gas is investigated based on the model of Wu et al. [“A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases,” J. Fluid Mech. 763, 24–50 (2015)], which is solved by a synthetic iterative scheme efficiently and accurately. A detailed investigation of the thermal slip coefficient, Knudsen layer function, and mass flow rate for molecular gas interacting with the inverse power-law potential is performed. It is found that (i) the thermal slip coefficient and Knudsen layer function increase with the viscosity index determined by the intermolecular potential. Therefore, at small Knudsen number, gas with a larger viscosity index has a larger mass flow rate; however, at late transition and free molecular flow regimes, this is reversed. (ii) The thermal slip coefficient is a linear function of the accommodation coefficient in Maxwell’s diffuse–specular boundary condition, while its variation with the tangential momentum accommodation coefficient is complicated in Cercignani–Lampis’s boundary condition. (iii) The ratio of the thermal slip coefficients between monatomic and molecular gases is roughly the ratio of their translational Eucken factors, and thus, molecular gas always has a lower normalized mass flow rate than monatomic gas. (iv) In the transition flow regime, the translational Eucken factor continues to affect the mass flow rate of thermal transpiration, but in the free molecular flow regime, the mass flow rate converges to that of monatomic gas. Based on these results, accommodation coefficients were extracted from thermal transpiration experiments of air and carbon dioxide, which are found to be 0.9 and 0.85, respectively, rather than unity used in the literature. The methodology and data presented in this paper are useful, e.g., in the pressure correction of capacitance diaphragm gauge when measuring low gas pressures.

Attraction Tames Two-Dimensional Melting: From Continuous to Discontinuous Transitions.

Two-dimensional systems may admit a hexatic phase and hexatic-liquid transitions of different natures. The determination of their phase diagrams proved challenging, and indeed, those of hard disks, hard regular polygons, and inverse power-law potentials have only recently been clarified. In this context, the role of attractive forces is currently speculative, despite their prevalence at both the molecular and colloidal scale. Here, we demonstrate, via numerical simulations, that attraction promotes a discontinuous melting scenario with no hexatic phase. At high-temperature, Lennard-Jones particles and attractive polygons follow the shape-dominated melting scenario observed in hard disks and hard polygons, respectively. Conversely, all systems melt via a first-order transition with no hexatic phase at low temperature, where attractive forces dominate. The intermediate temperature melting scenario is shape dependent. Our results suggest that, in colloidal experiments, the tunability of the strength of the attractive forces allows for the observation of different melting scenarios in the same system.

Effective hardness of interaction from thermodynamics and viscosity in dilute gases.

The hardness of the effective inverse power law (IPL) potential, which can be obtained from thermodynamics or collision integrals, can be used to demonstrate similarities between thermodynamic and transport properties. This link is investigated for systems of increasing complexity (i.e., the EXP, square-well, Lennard-Jones, and Stockmayer potentials; ab initio results for small molecules; and rigid linear chains of Lennard-Jones sites). These results show that while the two approaches do not yield precisely the same values of effective IPL exponent, their qualitative behavior is intriguingly similar, offering a new way of understanding the effective interactions between molecules, especially at high temperatures. In both approaches, the effective hardness is obtained from a double-logarithmic temperature derivative of an effective area.

Several exact solutions for three dimensional Schrodinger equation involving inverse square and power law potentials

Several exact solutions for three dimensional Schrodinger equation involving inverse square and power law potentials

Influence of Softness on the Stability of Binary Colloidal Crystals.

Mixtures of two types of nanoparticles can self-assemble into a wide variety of binary colloidal crystals (also called binary nanoparticle superlattices), which are interesting for their structural diversity and potential applications. Although so-called packing models-which usually treat the particles as "hard" with only excluded volume interactions-seem to explain many reported dense crystalline phases, these models often fail to predict the right structure. Here, we examine the role of soft repulsive interparticle interactions on binary colloidal crystals comprising two sizes of spherical particles; such "softness" can arise due to ligand shells or screened electrostatics. We determine the ground state phase diagram of binary systems of particles interacting with an additive inverse power law potential using a basin hopping algorithm to calculate the enthalpy of an extremely large pool of candidate structures. We find that a surprisingly small amount of softness can destabilize dense packings in favor of less densely packed structures, which provides further evidence that considerations beyond packing are necessary for describing many of the observed phases of binary colloidal crystals. Importantly, we find that several of the phases stabilized by softness, which are characterized by relatively few interparticle contacts and a tendency for local icosahedral order, are more likely to be observed experimentally than those predicted by packing models. We also report a previously unknown dense AB4 phase and conduct free energy calculations to examine how the stability of several crystals will vary with temperature. Our results further our understanding of why particular binary colloidal crystals form and will be useful as a reference for experimentalists working with softly repulsive colloids.