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Ref Arxiv: 1803.09931
DOI: 10.1007/s11005-018-1128-2
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1 Citation
Résumé:

We introduce the notion of $N$-reflection equation which provides a large generalization of the usual classical reflection equation describing integrable boundary conditions. The latter is recovered as a special example of the $N=2$ case. The basic theory is established and illustrated with several examples of solutions of the $N$-reflection equation associated to the rational and trigonometric $r$-matrices. A central result is the construction of a Poisson algebra associated to a non skew-symmetric $r$-matrix whose form is specified by a solution of the $N$-reflection equation. Generating functions of quantities in involution can be identified within this Poisson algebra. As an application, we construct new classical Gaudin-type Hamiltonians, particular cases of which are Gaudin Hamiltonians of $BC_L$-type .

Commentaires: 12 pages. References added. Explicit relation between our non-skew symmetric r-matrices and standard rational r-matrix given in the Gaudin models section

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Ref Arxiv: 1806.07748
DOI: 10.1088/1742-5468/aae2e0
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5 Citations
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Starting from the Bethe ansatz solution for the open Totally Asymmetric Simple Exclusion Process (TASEP), we compute the largest eigenvalue of the deformed Markovian matrix, in exact agreement with results obtained by the matrix ansatz. We also compute the eigenvalues of the higher conserved charges. The key step is to find a simpler equivalent T-Q relation, which is similar to the one for the TASEP with periodic boundary conditions.

Ref HAL: hal-01818216_v1
DOI: 10.1140/epje/i2018-11671-2
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11 Citations
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The physical behavior of glass-forming liquids presents complex features of both dynamic and thermodynamic nature. Some studies indicate the presence of thermodynamic anomalies and of crossovers in the dynamic properties, but their origin and degree of universality is difficult to assess. Moreover, conventional simulations are barely able to cover the range of temperatures at which these crossovers usually occur. To address these issues, we simulate the Kob-Andersen Lennard-Jones mixture using efficient protocols based on multi-CPU and multi-GPU parallel tempering. Our setup enables us to probe the thermodynamics and dynamics of the liquid at equilibrium well below the critical temperature of mode-coupling theory, TMCT=0.435. We find that below T=0.4 the analysis is hampered by partial crystallization of the metastable liquid, which nucleates extended regions populated by large particles arranged in an fcc structure. By filtering out crystalline samples, we reveal that the specific heat grows in a regular manner down to T=0.38. Possible thermodynamic anomalies suggested by previous studies can thus occur only in a region of the phase diagram where the system is highly metastable. Using the equilibrium configurations obtained from the parallel tempering simulations, we perform molecular dynamics and Monte Carlo simulations to probe the equilibrium dynamics down to T=0.4. A temperature-derivative analysis of the relaxation time and diffusion data allows us to assess different dynamic scenarios around TMCT. Hints of a dynamic crossover come from analysis of the four-point dynamic susceptibility. Finally, we discuss possible future numerical strategies to clarify the nature of crossover phenomena in glass-forming liquids.

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Ref Arxiv: 1805.08230
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DOI: 10.1103/PhysRevD.98.083533
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4 Citations
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Assuming a simple form for the growth index γ(z) depending on two parameters γ0≡γ(z=0) and γ1≡γ′(z=0), we show that these parameters can be constrained using background expansion data. We explore systematically the preferred region in this parameter space. Inside general relativity we obtain that models with a quasistatic growth index and γ1≈-0.02 are favored. We find further the lower bounds γ0≳0.53 and γ1≳-0.15 for models inside GR. Models outside GR having the same background expansion as ΛCDM and arbitrary γ(z) with γ0=γ0ΛCDM, satisfy Geff,0>G for γ1>γ1ΛCDM, and Geff,0

Ref HAL: hal-01806569_v1
DOI: 10.1063/1.5023707
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18 Citations
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We propose a new scheme to parameterize effective potentials that can be used to simulate atomic systems such as oxide glasses. As input data for the optimization, we use the radial distribution functions of the liquid and the vibrational density of state of the glass, both obtained from ab initio simulations, as well as experimental data on the pressure dependence of the density of the glass. For the case of silica, we find that this new scheme facilitates finding pair potentials that are significantly more accurate than the previous ones even if the functional form is the same, thus demonstrating that even simple two-body potentials can be superior to more complex three-body potentials. We have tested the new potential by calculating the pressure dependence of the elastic moduli and found a good agreement with the corresponding experimental data.