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[hal-01768084] On the Schrodinger-Poisson--Vlasov-Poisson correspondence  (23/04/18)  
The Schr\"odinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As $\hbar/m\to 0$, $m$ being the boson mass, the equations have been postulated to approximate the collisionless Vlasov-Poisson equations also known as the collisionless Boltzmann-Poisson equations. The latter describe collisionless matter with a 6D classical distribution function. We investigate the nature of this correspondence with a suite of numerical test problems in 1D, 2D, and 3D along with analytic treatments when possible. We demonstrate that, while the density field of the superfluid always shows order unity oscillations as $\hbar/m\to 0$ due to interference and the uncertainty principle, the potential field converges to the classical answer as $(\hbar/m)^{2}$. Thus, any dynamics coupled to the superfluid potential is expected to recover the classical collisionless limit as $\hbar/m\to 0$. The quantum superfluid is able to capture rich phenomena such as multiple phase-sheets, shell-crossings, and warm distributions. Additionally, the quantum pressure tensor acts as a regularizer of caustics and singularities in classical solutions. This suggests the exciting prospect of using the Schr\"odinger-Poisson equations as a low-memory method for approximating the high-dimensional evolution of the Vlasov-Poisson equations. As a particular example we consider dark matter composed of ultra-light axions, which in the classical limit ($\hbar/m\to 0$) is expected to manifest itself as collisionless cold dark matter.

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[hal-01619361] Large deviations of surface height in the 1+1-dimensional Kardar-Parisi-Zhang equation: exact long-time results for λH < 0  (11/01/18)  

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Game theory Dynamical friction Coarsening Diffusion Baseball Statistical Mechanics Théorème du viriel Self-gravitating systems Chemotaxis Colloids Statistical mechanics Evaporation Classical phase transitions theory Brownian Dynamics 0510Gg AQUEOUS-SOLUTION Mouvement brownien Colliqionless stellar-systems Polytrope Violent relaxation Bethe ansatz Smoluchowski equation Dissipationless galaxy formation Catastrophe Keller-Segel Asymptotic expansion Collapse Long-range interactions DNA Chemotactic aggregation Bose Einstein condensation Dwarf galaxies ADN DYNAMICS SIMULATIONS AQUEOUS-SOLUTIONS Smoluchowski-Poisson Phase transition Dark matter Persistence AIR/WATER INTERFACE Bending Critical exponent Black hole Cyclodextrin COMPOSITE POLYAMIDE RO Adsorption COATING LAYER Collective behaviour Axion Disordered systems Interacting agents Chemotaxie Glass transition Brownian motion Absorption Collisionless stellar-systems Ions close to interfaces Dark matter halo Drag forces Membrane transport Effondrement gravitationnel Euler-Maclaurin Nanofiltration Competition Transition vitreuse Gravitational collapse Scalar field CARBON NANOTUBE MEMBRANES Fokker-Planck Barotropic stars Physique statistique Crossings Dipole Angle-action variables Marcheur aléatoire Thermodynamics Processus stochastique COMPUTER-SIMULATION Generalized thermodynamics Random walker Atmosphere TASEP 7722Ej Turbulence Random tilings Dynamical scaling Entropy Current fluctuations Virial theorem Dynamic transition Metastable states Automatic Keywords BEHAVIOR Denaturation Brisure de symétrie Catastrophe theory Density Brisure de symétrie des répliques Random process Computational modelling