From Walking to Tunneling: An Investigation of Generalized Pilot-Wave DynamicsWe investigate the ability of millimetric walking droplets to tunnel between spatially-structured cavities. By synthesizing experimental and theoretical analysis, we provide a comprehensive framework…Akilan Sankaran, Diego Israel Chavez·Dec 23, 2025SaveLearn
Finite time energy cascade for mixed 3- and 4-wave kinetic equationsIn this work we study a kinetic equation whose collision operator comprises three distinct wave interaction mechanisms: one representing a 3-wave process, and two corresponding to 4-wave processes.…Gigliola Staffilani, Minh-Binh Tran·Dec 22, 2025SaveLearn
Evolution of finite temperature Bose-Einstein Condensates: Some rigorous studies on condensate growthIn trapped Bose-Einstein condensates (BECs), condensate growth refers to the process in which an increasing number of quasi-particles are immediately transferred from the non-condensate state…Gigliola Staffilani, Minh-Binh Tran·Dec 22, 2025SaveLearn
Open Quantum Systems as Regular Holonomic D-Modules: The Mixed Hodge Structure of Spectral SingularitiesThe geometric description of open quantum systems via the Quantum Geometric Tensor (QGT) traditionally relies on the assumption that the physical states form a differentiable vector bundle over the…Prasoon Saurabh·Dec 22, 2025SaveLearn
The Semiclassical Limit of the 2D Dirac--Hartree Equation with Periodic PotentialsWe study the semiclassical limit of the two-dimensional Dirac--Hartree equation in the presence of a periodic external potential. The spinor dynamics are formulated using the matrix-valued Wigner…Jinyeop Lee, Kunlun Qi·Dec 22, 2025SaveLearn
Geometry-dependent Ekman layer approximations on curved domains: L∞ convergenceThe Ekman boundary layer is a fundamental concept in fluid dynamics that describes fluid motion near boundaries affected by Earth's rotation. Most theoretical studies have simplified their analysis…Yifei Jia, Yi Du, Lihui Guo·Dec 21, 2025SaveLearn
Localization of the 1D Non-Stationary Anderson ModelThis paper considers the family of Schr\"odinger operators on 2(Z) given by independent but not necessarily identically distributed and possibly unbounded potentials. We assume a…Karl Zieber·Dec 20, 2025SaveLearn
Electromagnetic Modes in Spherical Cavities: Complete Theory of Angular Spectra, Dispersion Relations, and Self-Adjoint ExtensionsWe present a complete theory of electromagnetic modes in spherical cavities, resolving fundamental questions about the nature of angular quantization. The standard result that angular indices…Mustafa Bakr, Tongyu Zhang, Smain Amari·Dec 20, 2025SaveLearn
Uniqueness Theorem: With Normal Components Specified on External Spherical SurfaceA uniqueness theorem for time-harmonic electromagnetic fields which requires the normal components of electromagnetic fields specified on a spherical surface is proposed and proved. The statement of…Rajavardhan Talashila·Dec 20, 2025SaveLearn
A Phase Space Representation of the Metaplectic GroupThe symplectic group Sp(n) acts on phase space while the unitary representation of its double cover, Mp(n), the metaplectic group, acts on functions defined on configuration space. We will construct…Maurice de Gosson·Dec 20, 2025SaveLearn
Lorentz Invariance of the Multidimensional Dirac-Hestenes EquationThis paper investigates the Lorentz invariance of the multidimensional Dirac-Hestenes equation, that is, whether the equation remains form-invariant under pseudo-orthogonal transformations of the…S. V. Rumyantseva, D. S. Shirokov·Dec 20, 2025SaveLearn
From entropic constraints to reinforced processes: a probabilistic origin of multiscale measuresWe investigate multiscale Gibbs measures from a variational and probabilistic viewpoint, focusing on the structural asymmetry among conditional entropies that characterizes their construction. We…Francesco Camilli, Pierluigi Contucci, Emanuele Mingione·Dec 20, 2025SaveLearn
Pair Space in Classical Mechanics III. Some Four-Body Central ConfigurationsWe study central configurations in the four body problem, i.e., configurations in which the forces on all the bodies point to a fixed, single point in space. The newly formulated pair-space formalism…Alon Drory·Dec 19, 2025SaveLearn
Perturbative Chern-Simons invariants from non-acyclic flat connectionsWe give a short review of our construction of a higher-loop perturbative invariant of framed 3-manifolds, generalizing the perturbative Chern-Simons invariant of Witten-Axelrod-Singer, associated to…Pavel Mnev, Konstantin Wernli·Dec 19, 2025SaveLearn
On surface polariton resonance and its curvature concentration effects from 3D elastic nanorodsThis paper investigates surface polariton resonance (SPR) in three-dimensional elastic metamaterials with nanorod geometry. The primary motivation is to surpass the physical limitations imposed by…Youjun Deng, Hongyu Liu, Wanjing Tang et al.·Dec 19, 2025SaveLearn
Variational Dissipative Mechanics on Lie AlgebroidsWe formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional scalar variable z.…Alexandre Anahory Simoes, Leonardo Colombo·Dec 19, 2025SaveLearn
Estimates, asymptotics and trace formulas for periodic vector NLS equations, IIWe consider a first order operator with a smooth periodic 3x3 matrix potential on the real line. It is the Lax operator for the periodic vector NLS equation. Its spectrum covers the real line and it…Evgeny Korotyaev·Dec 19, 2025SaveLearn
Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective spaceWe prove the rigidity of isotropic harmonic maps from a 2-torus to a complex projective space, when they are constructed from holomorphic embeddings associated to complete linear systems. We also…Yoshinori Hashimoto, Bruno Mera, Tomoki Ozawa·Dec 19, 2025SaveLearn
An Asymptotic Approach for Modeling Multiscale Complex Fluids at the Fast Relaxation LimitWe present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in…Xuenan Li, Chun Liu, Di Qi·Dec 19, 2025SaveLearn
The Vicsek-Kuramoto model in collective dynamics: macroscopic equations and pattern formationIn this work, we investigate an individual-based model (IBM) for self-propelled agents interacting locally on a plane. Agents are characterized by their position, the angle determining their…Sara Merino-Aceituno, Carmela Moschella·Dec 18, 2025SaveLearn
Granger Causality Maps for Langevin SystemsWahl et al. (2016, 2017) introduced the idea of Granger causality (GC) maps for Langevin systems: dynamics are localised linearly at each point in phase space as vector Ornstein-Uhlenbeck (VOU)…Lionel Barnett, Benjamin Wahl, Nadine Spychala et al.·Dec 18, 2025SaveLearn
An equivalence in random matrix and tensor models via a dually weighted intermediate field representationWe present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field…Juan Abranches, Alicia Castro, Reiko Toriumi·Dec 18, 2025SaveLearn
Ground states for the Hartree energy functional in the critical caseWe consider the problem of finding a minimizer u in H1(R3) for the Hartree energy functional with convolution potential w in L∞(R3)+L3/2,∞(R3)…Tommaso Pistillo·Dec 18, 2025SaveLearn
Rationally-extended radial harmonic oscillator in a position-dependent mass backgroundWe show that the radial harmonic oscillator problem in the position-dependent mass background of the type m(α;r) = (1+α r2)-2, α>0, can be solved by using a point canonical…Christiane Quesne·Dec 18, 2025SaveLearn
Lie symmetry classification and exact solutions of a diffusive Lotka-Volterra system with convectionA mathematical model for description of the viscous fingering induced by a chemical reaction is under study. This complicated five-component model is reduced to a three-component diffusive…Roman Cherniha, Vasyl' Davydovych·Dec 18, 2025SaveLearn