Research Note: A Kinematic Origin for Universal Scaling in Quantum Fluids

Weizhu Bao, Yongyong Cai, Ionut Danaila +1 more

The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers.This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose–Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.

MANFRED L. RISTIG

Hubert MASSAU

This Note 18 establishes the formal mathematical link between wave quantum mechanics and Massau's Symplectic Kinematics. Through a dimensional analysis of the Fabric's areal diffusion Axiom, we demonstrate that Planck's quantum of action (h) corresponds strictly to the product of a particle's mass inertia and the geometric diffusion constant of the medium (h = M . A_m). This equivalence fundamentally redefines mass as the resistance opposing symplectic areal diffusion, thereby geometrically unifying de Broglie's wavelength (lambda . v) with the kinematics of Maxwell fluids. Cette Note 18 établit le lien mathématique formel entre la mécanique quantique ondulatoire et la Cinématique symplectique de Massau. Par une analyse dimensionnelle de l'Axiome de diffusion aréolaire de la Trame, nous démontrons que le quantum d'action de Planck (h) correspond strictement au produit de l'inertie massique d'une particule par la constante de diffusion géométrique du milieu (h = M . A_m). Cette équivalence redéfinit fondamentalement la masse comme la résistance opposée à la diffusion aréolaire symplectique, unifiant ainsi géométriquement la longueur d'onde de de Broglie (lambda . v) avec la cinématique des fluides de Maxwell.

Alberto Bramati, Michele Modugno

Heejeong Jeong, Shengwang Du, Na Young Kim

This publisher’s note corrects the funding section in article [1]. The funding section originally read as follows: Research Grants Council, University Grants Committee (RGC, UGC) (16303417, 16301214); Hong Kong University of Science and Technology (HKUST) (IGN16SC06). The corrected funding section reads as follows: Research Grants Council, University Grants Committee (RGC, UGC) (16303417); Hong Kong University of Science and Technology (HKUST) (IGN16SC06). The article [1] was corrected on 20 February 2019. © 2019 Optical Society of America.