Système isolé

Résumé

vignette|Propriétés des systèmes isolés, fermés et ouverts dans l'échange d'énergie et de matière. Un système isolé, par opposition à un système ouvert, est un système physique qui n'interagit pas avec ses environnements. On dit d’un système qu’il est isolé s’il n'échange ni matière, ni chaleur, ni travail avec l'extérieur (paroi adiabatique et indéformable) – un système fermé peut échanger de la chaleur ou du travail avec l'extérieur, mais pas de la matière. Ce système obéit à un certain nombre de lois de conservation : le total de son énergie et sa masse (en physique classique) reste constant au cours du temps. S'il ne peut y avoir d'interactions avec l'extérieur, il peut y avoir des réorganisations internes à énergie et masse constante. L'univers dans son ensemble est considéré pour l'instant comme un système isolé, ce qui reste un postulat à démontrer. Des systèmes véritablement isolés n'existent pas dans la réalité physique. Il y a toujours des interactions avec l'environnemen

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https://fr.wikipedia.org/wiki/Syst%C3%A8me_isol%C3%A9

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The simulation of condensed matter in first principles Molecular Dynamics (FPMD) heavily relies on Kohn-Sham Density Functional Theory (KS-DFT) calculations. The accuracy of such simulations is governed by the reliability of the underlying potential energy surface (PES) and the accessible time scale; both factors are crucially influenced by the choice of exchange-correlation (xc) functional. Hybrid xc functionals, which include a fraction of exact exchange, are among the most accurate xc approximations available. However, in particular in combination with the plane wave basis commonly used in FPMD, the computational overhead due to the evaluation of exchange integrals significantly limits the time scale of the simulation, thus hampering convergence of observables. This work aims at improving the availability of hybrid xc functionals in a plane wave basis while reducing their computational overhead. Part I provides an introduction to the field of FPMD. Starting from the quantum mechanical partition function, we show the simplifications behind the single-state Born-Oppenheimer approximation, followed by a discussion of the theoretical foundations of KS-DFT, an overview of practical approximations, and their implementation in a plane wave/pseudopotential formalism. In Part II, we outline the implementation and performance of two popular families of xc functionals. We first derive the plane wave expressions for the Coulomb-Attenuation Method (CAM) and compare its performance in a plane wave basis to common atom-centred basis sets. A new xc functional, CAM-O3LYP, is reported, which outperforms the commonly employed CAM-B3LYP in some notorious cases. We then present the implementation of the M05 to M11 families of Minnesota functionals in a plane wave basis. A detailed convergence analysis suggests that a fine enough integration mesh has to be provided in order to obtain accurate energy differences, and a comparison of reaction enthalpies obtained in plane waves and atom-centred bases reveals an unusual sensitivity of certain Minnesota functionals to the choice of basis. We provide a rationale for the observed differences by comparing electron densities between different functionals and basis sets demonstrating that plane waves make it possible to conveniently obtain values for basis set limits for functionals that can be difficult to converge in atom-centred bases. Part III introduces a coordinate-scaling scheme for the calculation of exact exchange integrals for isolated systems in a plane wave basis. By applying the scaling relations of the exact exchange functional to the Hartree-Fock term, we show that it is possible to effectively reduce the cost of the Fast Fourier Transforms (FFT) that constitute the bottleneck of the calculation while retaining good accuracy. We then present the practical implementation and parallelisation of the method in the CPMD code and show that speedups can reach values of up to one order of magnitude, thereby considerably improving the computational footprint of hybrid functionals. In Part IV, we offer a perspective on further work by discussing recent additions to the library of dispersion-corrected atom-centred potentials (DCACP) and by introducing a method for structural refinement based on electron density difference maps, density-difference driven molecular dynamics (d3MD). We conclude by providing a brief overview of the results obtained in this work and by discussing future perspectives.

EPFL2018

Chargement

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays

Hugo Pierre Alexandre Flayac, Eduardo Carlo Mascarenhas Moraes, Vincenzo Savona

We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization-group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method brings considerable advantage when compared to the integration of the time-dependent problem via Trotter decomposition, as it can address arbitrarily long-ranged couplings. Additionally, it ensures numerical stability in the case of weakly dissipative systems thanks to a slow tuning of the dissipation rates along the sweeps. We have tested the method on a driven-dissipative spin chain, under various assumptions for the Hamiltonian, drive, and dissipation parameters, and compared the results to those obtained both by Trotter dynamics and Monte Carlo wave function methods. Accurate and numerically stable convergence was always achieved when applying the method to systems with a gapped Liouvillian and a nondegenerate steady state.

American Physical Society2015

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Do the majority of stars form as gravitationally unbound?

Richard Irving Anderson

Context. Some of the youngest stars (age less than or similar to 10 Myr) are clustered, while many others are observed scattered throughout star forming regions or in complete isolation. It has been intensively debated whether such scattered or isolated stars originate in star clusters or whether they form in truly isolated conditions. Exploring these scenarios could help set constraints on the conditions in which massive stars are formed. Aims. We adopted the assumption that all stars form in gravitationally bound star clusters embedded in molecular cloud cores (Gamma-1 model), which expel their natal gas early after their formation. Then we compared the proportion (fraction) of stars found in clusters with observational data. Methods. The star clusters are modelled by the code NBODY6, which includes binary stars, stellar and circumbinary evolution, gas expulsion, and the external gravitational field of their host galaxy. Results. We find that small changes in the assumptions in the current theoretical model estimating the fraction, Gamma, of stars forming in embedded clusters have a large influence on the results, and we present a counterexample as an illustration. This calls into question theoretical arguments about Gamma in embedded clusters and it suggests that there is no firm theoretical ground for low Gamma in galaxies with lower star formation rates (SFRs). Instead, the assumption that all stars form in embedded clusters is in agreement with observational data for the youngest stars (age less than or similar to 10 Myr). In the Gamma-1 scenario, the observed fraction of the youngest stars in clusters increases with the SFR only weakly; the increase is caused by the presence of more massive clusters in galaxies with higher SFRs, which release fewer stars to the field in proportion to their mass. The Gamma-1 model yields a higher fraction of stars in clusters for older stars (ages between 10 Myr and 300 Myr) than what is observed. This discrepancy can be caused by initially less compact clusters or a slightly lower star-formation efficiency than originally assumed in the Gamma-1 model, or by interactions of the post-gas-expulsion revirialised open clusters with molecular clouds.

2022

Chargement

EPFL2018

Do the majority of stars form as gravitationally unbound?

Richard Irving Anderson

2022