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[hal-01529359] The quasilinear theory in the approach of long-range systems to quasi-stationary states (5/31/17)

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[hal-01510488] Cosmological evolution of a complex scalar field with repulsive or attractive self-interaction (4/20/17)

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[hal-01490216] Ground state energy of the δ-Bose and Fermi gas at weak coupling from double extrapolation (3/22/17)

We consider the ground state energy of the Lieb-Liniger gas with $\delta$ interaction in the weak coupling regime $\gamma\to0$. For bosons with repulsive interaction, previous studies gave the expansion $e_{\text{B}}(\gamma)\simeq\gamma-4\gamma^{3/2}/3\pi+(1/6-1/\pi^{2})\gamma^{2}$. Using a numerical solution of the Lieb-Liniger integral equation discretized with $M$ points and finite strength $\gamma$ of the interaction, we obtain very accurate numerics for the next orders after extrapolation on $M$ and $\gamma$. The coefficient of $\gamma^{5/2}$ in the expansion is found approximately equal to $-0.00158769986550594498929$, accurate within all digits shown. This value is supported by a numerical solution of the Bethe equations with $N$ particles followed by extrapolation on $N$ and $\gamma$. It was identified as $(3\zeta(3)/8-1/2)/\pi^{3}$ by G. Lang. The next two coefficients are also guessed from numerics. For balanced spin $1/2$ fermions with attractive interaction, the best result so far for the ground state energy was $e_{\text{F}}(\gamma)\simeq\pi^{2}/12-\gamma/2+\gamma^{2}/6$. An analogue double extrapolation scheme leads to the value $-\zeta(3)/\pi^{4}$ for the coefficient of $\gamma^{3}$.

[hal-01413008] Extrapolation methods and Bethe ansatz for the asymmetric exclusion process (12/12/16)

The one-dimensional asymmetric simple exclusion process (ASEP), where N hard-core particles hop forward with rate 1 and backward with rate q<1, is considered on a periodic lattice of L site. Using KPZ universality and previous results for the totally asymmetric model q=0, precise conjectures are formulated for asymptotics at finite density ρ=N/L of ASEP eigenstates close to the stationary state. The conjectures are checked with high precision using extrapolation methods on finite size Bethe ansatz numerics. For weak asymmetry 1−q∼1/sqrt(L), double extrapolation combined with an integer relation algorithm gives an exact expression for the spectral gap up to 10-th order in the asymmetry.

[hal-01401579] Collapse of a self-gravitating Bose-Einstein condensate with attractive self-interaction (11/24/16)

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[hal-01380598] Secular diffusion in discrete self-gravitating tepid discs I. Analytic solution in the tightly wound limit (10/14/16)

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[hal-01379504] Partially relativistic self-gravitating Bose-Einstein condensates with a stiff equation of state (10/12/16)

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[cea-01366736] Collective response to perturbations in a data-driven fish school model (2/18/17)

Fish schools are able to display a rich variety of collective states and behav-ioural responses when they are confronted by threats. However, a school's response to perturbations may be different depending on the nature of its collective state. Here we use a previously developed data-driven fish school model to investigate how the school responds to perturbations depending on its different collective states, we measure its susceptibility to such perturbations, and exploit its relation with the intrinsic fluctuations in the school. In particular, we study how a single or a small number of perturbing individuals whose attraction and alignment parameters are different from those of the main population affect the long-term behaviour of a school. We find that the responsiveness of the school to the perturbations is maximum near the transition region between milling and schooling states where the school exhibits multistability and regularly shifts between these two states. It is also in this region that the susceptibility, and hence the fluctuations, of the polarization order parameter is maximal. We also find that a significant school's response to a perturbation only happens below a certain threshold of the noise to social interactions ratio.

[hal-01360415] A variational approach to the liquid-vapor phase transition for hardcore ions in the bulk and in nanopores. (10/18/16)

We employ a field-theoretical variational approach to study the behavior of ionic solutions in the grand canonical ensemble. To describe properly the hardcore interactions between ions, we use a cutoff in Fourier space for the electrostatic contribution of the grand potential and the Carnahan-Starling equation of state with a modified chemical potential for the pressure one. We first calibrate our method by comparing its predictions at room temperature with Monte Carlo results for excess chemical potential and energy. We then validate our approach in the bulk phase by describing the classical “ionic liquid-vapor” phase transition induced by ionic correlations at low temperature, before applying it to electrolytes at room temperature confined to nanopores embedded in a low dielectric medium and coupled to an external reservoir of ions. The ionic concentration in the nanopore is then correctly described from very low bulk concentrations, where dielectric exclusion shifts the transition up to room temperature for sufficiently tight nanopores, to high concentrations where hardcore interactions dominate which, as expected, modify only slightly this ionic “capillary evaporation.”

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