Entropy evaluation sheds light on ecosystem complexity

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem on a lattice in which two species struggle for survival. The method quantitatively reproduces the scale-free law of the prey shoals size, where the simpler mean-field approach fails: the direct near neighbor correlations are found to be the fundamental ingredient describing the system self-organized behavior. Furthermore, entropy allows the measurement of structural ordering, that is found to be a key ingredient in characterizing two different coexistence behaviors, one where predators form localized patches in a sea of preys and another where species display more complex patterns. The general nature of the introduced method paves the way for its application in many other systems of interest.Comment: 13 pages, 5 figure

Pressure and stress tensor of complex anharmonic crystals within the stochastic self-consistent harmonic approximation

The self-consisted harmonic approximation (SCHA) allows the computation of free energy of anharmonic crystals considering both quantum and thermal fluctuations. Recently, a stochastic implementation of the SCHA has been developed, tailored for applications that use total energy and forces computed from first principles. In this work, we extend the applicability of the stochastic SCHA to complex crystals with many degrees of freedom, with the optimisation of both the lattice vectors and the atomic positions. To this goal, we provide an expression for the evaluation of the pressure and stress tensor within the stochastic SCHA formalism. Moreover, we develop a more robust free energy minimisation algorithm, which allows us to perform the SCHA variational minimisation very efficiently in systems having a broad spectrum of phonon frequencies and many degrees of freedom. We test and illustrate the new approach with an application to the phase XI of water ice using density-functional theory. We find that the SCHA reproduces extremely well the experimental thermal expansion of ice in the whole temperature range between 0 K and 270 K, in contrast with the results obtained within the quasi-harmonic approximation, that underestimates the effect by about 25 %.Comment: 20 pages, 8 figure

Quantum effects in muon spin spectroscopy within the stochastic self-consistent harmonic approximation

In muon spin rotation experiments the positive implanted muon vibrates with large zero point amplitude by virtue of its light mass. Quantum mechanical calculations of the host material usually treat the muon as a point impurity, ignoring this large vibrational amplitude. As a first order correction, the muon zero point motion is usually described within the harmonic approximation, despite the large anharmonicity of the crystal potential. Here we apply the stochastic self-consistent harmonic approximation, a quantum variational method devised to include strong anharmonic effects in total energy and vibrational frequency calculations, in order to overcome these limitations and provide an accurate ab initio description of the quantum nature of the muon. We applied this full quantum treatment to the calculation of the muon contact hyperfine field in textbook-case metallic systems, such as Fe, Ni, Co including MnSi and MnGe, significantly improving agreement with experiments. Our results show that muon vibrational frequencies are strongly renormalized by anharmonicity. Finally, in contrast to the harmonic approximation, we show that including quantum anharmonic fluctuations, the muon stabilizes at the octahedral site in bcc Fe.Comment: 10 page

Black metal hydrogen above 360 GPa driven by proton quantum fluctuations

Hydrogen metallization under stable conditions is a major quest for realizing the first room temperature su- perconductor. Recent low-temperature experiments report different metallization pressures, varying from 360GPa to 490GPa. In this work, we simulate structural properties, vibrational Raman, IR and optical spectra of hydrogen phase III accounting for proton quantum effects. We demonstrate that nuclear quantum fluctuations downshift the vibron frequencies by 25%, introduce a broad line-shape in the Raman spectra, and reduce the optical gap by 3eV. We show that hydrogen metallization occurs at 380GPa in phase III due to band overlap, in good agreement with transport data. Our simulations predict this state is a black metal - transparent in the IR - so that the shiny metal observed at 490GPa is not phase III. We predict the conductivity onset and the optical gap will substantially increase if hydrogen is replaced by deuterium, underlining that metallization is driven by quantum fluctuations and is thus isotope dependent. We show how hydrogen acquires conductivity and brightness at different pressures, explaining the apparent contradictions in existing experimental scenarios.European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement No. 802533

Quantum Enhancement of Charge Density Wave in NbS₂ in the Two-Dimensional Limit

At ambient pressure, bulk 2H-NbS₂ displays no charge density wave instability, which is at odds with the isostructural and isoelectronic compounds 2H-NbSe₂, 2H-TaS₂, and 2H-TaSe₂, and in disagreement with harmonic calculations. Contradictory experimental results have been reported in supported single layers, as 1H-NbS₂ on Au(111) does not display a charge density wave, whereas 1H-NbS₂ on 6H-SiC(0001) endures a 3 × 3 reconstruction. Here, by carrying out quantum anharmonic calculations from first-principles, we evaluate the temperature dependence of phonon spectra in NbS₂ bulk and single layer as a function of pressure/strain. For bulk 2H-NbS₂, we find excellent agreement with inelastic X-ray spectra and demonstrate the removal of charge ordering due to anharmonicity. In the two-dimensional limit, we find an enhanced tendency toward charge density wave order. Freestanding 1H-NbS₂ undergoes a 3 × 3 reconstruction, in agreement with data on 6H-SiC(0001) supported samples. Moreover, as strains smaller than 0.5% in the lattice parameter are enough to completely remove the 3 × 3 superstructure, deposition of 1H-NbS₂ on flexible substrates or a small charge transfer via field-effect could lead to devices with dynamical switching on/off of charge order