Symplectic reduction and lagrangian submanifolds in Gr(1, n)
In the paper we construct new examples of lagrangian submanifolds in the complex Grassmannian Gr(1, n), equipped with the standard Kahler form by the Plucker embedding. The construction scheme is based on two facts: first, we use the natural correspondence between lagrangian submanifolds in the symplectic manifold which is given by the symplectic reduction procedure and lagrangian submanifolds of the original symplectic manifold with the Hamiltonian group action which one factorize with respect to this action; second, we show that under a particular choice of the generators of the k - dimensional torus T action when k = 2, ..., n-1 on Gr(1, n) and appropriate values of the moment maps one has an isomorphism between the symplectic reduction result Gr(1, n)//T and the total space of the bundle over Gr(1, n-k) with the fibers formed by the direct products of k copies of the projectivized of the tautological bundle over Gr(1, n-k). Combining these facts we get a lower bound on the number of topologically different smooth lagrangian submanifolds in our original Grassmannian Gr(1, n).
N. A. Tyurin, Sb. Math., 2024, 215:10, pp. 167 – 182.
https://doi.org/10.4213/sm10053
Candidate Toroidal Electric Dipole Mode in the Spherical Nucleus 58Ni
Dipole toroidal modes appear in many fields of physics. In nuclei, such a mode was predicted more than 50 years ago, but clear experimental evidence was lacking so far. Using a combination of high-resolution inelastic scattering experiments with photons, electrons, and protons, we identify for the first time candidates for toroidal dipole excitations in the nucleus 58Ni and demonstrate that transverse electron scattering form factors represent a relevant experimental observable to prove their nature.
P. von Neumann-Cosel, V.O. Nesterenko, I. Brandherm, P.I. Vishnevskiy, P.-G. Reinhard, J. Kvasil, H. Matsubara, A. Repko, A. Richter, M. Scheck, and A. Tamii. Phys. Rev. Lett. 133, 232502 (2024).
https://doi.org/10.1103/PhysRevLett.133.232502
Particle fluctuations in systems with Bose-Einstein condensate
Particle fluctuations in systems, exhibiting Bose-Einstein condensation, are reviewed in order to clarify the basic points that attract high interest and often confront misunderstanding. It is explained that the so-called “grand canonical catastrophe”, claiming the occurrence of catastrophic particle fluctuations in the condensed phase, treated by grand canonical ensemble, does not exist. What exists is the incorrect use of the grand canonical ensemble, where gauge symmetry is not broken, while the correct description of the condensed phase necessarily requires gauge symmetry breaking. As soon as gauge symmetry is broken, not only there are no catastrophic condensate fluctuations, but moreover there are no condensate fluctuations at all. Canonical ensemble and grand canonical ensemble with broken gauge symmetry are equivalent with respect to the number of particle scaling.
V. I. Yukalov, Laser Phys. 34 (2024) 113001.
https://iopscience.iop.org/article/10.1088/1555-6611/ad8221
Transverse momentum dependence of the T-even hadronic structure functions in the Drell-Yan process
We present detailed analysis of the T-even lepton angular distribution in the Drell-Yan process including γ/Z0 gauge boson exchange and using perturbative QCD based on the collinear factorization scheme at leading order in the αs expansion. We focus on the study of the transverse momentum QT dependence of the corresponding hadronic structure functions and angular coefficients up to next-to-next-to-leading order in the QT2/Q2 expansion. We analyze QT dependence numerically and compare T-even angular coefficients integrated over rapidity with available data of the ATLAS Collaboration at LHC. Additionally, we present our results for the forward-backward asymmetry and compare it with data.
V. E. Lyubovitskij, A. S. Zhevlakov and I. A. Anikin, Phys. Rev. D 110 (2024), 074028
https://doi.org/10.1103/PhysRevD.110.074028