Self-similar renormalization for nonlinear problemsA new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory.…V. I. Yukalov, E. P. Yukalova·May 17, 2025SaveLearn
On soliton asymptotics for 2D Maxwell-Lorentz equations with rotating particleWe consider 2D Maxwell-Lorentz equations with extended charged rotating particle. The system admits solitons which are solutions corresponding to a particle moving with a constant velocity and…Elena Kopylova·May 17, 2025SaveLearn
A Framework of Model Reduction with Arbitrary Orders of Accuracy for the Boltzmann EquationThis paper presents a general framework for constructing reduced models that approximate the Boltzmann equation with arbitrary orders of accuracy in terms of the Knudsen number Kn,…Zhenning Cai, Ruo Li, Yixiao Lu et al.·May 16, 2025SaveLearn
Braid twists and HZ factorisation via character expansionThe HOMFLY-PT polynomial of a closed braid admits a character expansion, expressed as a sum of SU(N) characters over Young diagrams. The Harer-Zagier (HZ) transform, which converts the HOMFLY-PT…Andreani Petrou, Shinobu Hikami·May 15, 2025SaveLearn
Finite size corrections in the bulk for circular β ensemblesThe circular β ensemble for β =1,2 and 4 corresponds to circular orthogonal, unitary and symplectic ensemble respectively as introduced by Dyson. The statistical state of the eigenvalues…Peter J. Forrester, Bo-Jian Shen·May 15, 2025SaveLearn
Variational formulations of transport phenomena on combinatorial meshesWe develop primal and mixed variational formulations of transport phenomena on cell complexes with simple polytope connectivity. This framework addresses materials with internal structures comprising…Kiprian Berbatov, Andrey P. Jivkov·May 14, 2025SaveLearn
Localization for heavy-tailed Anderson modelsUsing recent results on uniform large deviation estimates for random matrix products obtained by S. Raman and the author, we prove localization for one dimensional Anderson models with heavy tails.Omar Hurtado·May 14, 2025SaveLearn
The Anti-Unitarity of Time Reversal & Co-representations of Lorentzian Pin GroupsIn the representation theory of Lorentzian orthogonal groups, there are well known arguments as to why the parity inversion operator P and the time reversal operator T, should…Craig McRae·May 14, 2025SaveLearn
Interaction anomalies and one-particle dynamics in very special relativity theoriesIt is well known that relativistic invariance introduce strong constraints in the interactions of classical particles. We generalize the non-interaction theorems for Lorentz violating systems which…Manuel Asorey, Fernando Falceto, Giuseppe Marmo·May 13, 2025SaveLearn
Weak coupling limit for quantum systems with unbounded weakly commuting system operatorsThis work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a…Ilya Lopatin, Alexander Pechen·May 13, 2025SaveLearn
On the Novikov problem for dihedral symmetry potentialsWe consider Novikov's problem of describing level lines of quasiperiodic functions on a plane for two-dimensional potentials of dihedral symmetry. It is shown that quasiperiodic potentials of this…A. Ya. Maltsev·May 12, 2025SaveLearn
Chern-Simons potentials of higher-dimensional Pontryagin densitiesWe develop a novel and systematic approach to computing the (2n-1)-form Chern-Simons potential given the Pontryagin density, i.e. the nth Chern character, in arbitrary even dimensions…Onur Ayberk Çakmak, Özgür Sarıoğlu·May 12, 2025SaveLearn
The weak coupling limit of the Pauli-Fierz modelWe investigate the weak coupling limit of the Pauli- Fierz Hamiltonian within a mathematically rigorous framework. Furthermore, we establish the asymptotic behavior of the effective mass in this…Fumio Hiroshima·May 12, 2025SaveLearn
Structure of Dubrovin-Zhang free energy functions and universal identitiesWe prove a structural theorem relating the higher genera free energy functions of the Dubrovin-Zhang hierarchies to the Witten-Kontsevich free energy function of the Korteweg-de Vries hierarchy. As…Sergey Shadrin, Zhe Wang·May 12, 2025SaveLearn
Ordering of Energy Levels in the Fr\"ohlich ModelConsider a one-dimensional system of \( N \) electrons subject to an external potential \( U \). Let \( E el(S) \) denote the ground state energy of the system with total spin \( S \). The…Fumio Hiroshima, Akihiro Kobayashi, Tadahiro Miyao et al.·May 11, 2025SaveLearn
Polar Duality and the Donoho--Stark Uncertainty PrinciplePolar duality is a fundamental geometric concept that can be interpreted as a form of Fourier transform between convex sets. Meanwhile, the Donoho-Stark uncertainty principle in harmonic analysis…Maurice de Gosson·May 11, 2025SaveLearn
Gagliardo-Nirenberg-Sobolev inequalities and ground states of Fermions in relativistic Hartree-Fock modelThis paper presents a rigorous mathematical analysis of the relativistic Hartree-Fock model for finite Fermi systems. We first establish an optimal Gagliardo-Nirenberg-Sobolev (GNS) inequality with…Yuan-da Wu, Xiaoyu Zeng, Yimin Zhang·May 10, 2025SaveLearn
Unified Structural Embedding of Orbifold Sigma ModelsThis study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional…Francesco D'Agostino·May 9, 2025SaveLearn
Hamiltonian formalism for non-diagonalisable systems of hydrodynamic typeWe study the system of first order PDEs for pseudo-Riemannian metrics governing the Hamiltonian formalism for systems of hydrodynamic type. In the diagonal setting the integrability conditions ensure…Paolo Lorenzoni, Sara Perletti, Karoline van Gemst·May 9, 2025SaveLearn
On removing orders from amplitude equationsIn this paper, we introduce a modified version of the renormalization group (RG) method and test its numerical accuracy. It has been tested on numerous scalar ODEs and systems of ODEs. Our method is…David Juhasz, Per Kristen Jakobsen·May 9, 2025SaveLearn
Madelung Structure of the Dirac EquationWe consider the Dirac equations in polar form proving that they can equivalently be re-configured into a system of equations consisting of derivatives of the velocity density plus the Hamilton-Jacobi…Luca Fabbri·May 9, 2025SaveLearn
A note on quantum Hamiltonian reduction and anomaliesQuantization of field-theoretic models with gauge symmetries is often obstructed by quantum anomalies. It is commonly believed that the origin of these anomalies lies in the infinite number of…Boris M. Elfimov, Alexey A. Sharapov·May 9, 2025SaveLearn
The effective energy of a lattice metamaterialWe study the sense in which the continuum limit of a broad class of discrete materials with periodic structures can be viewed as a nonlinear elastic material. While we are not the first to consider…Xuenan Li, Robert V. Kohn·May 8, 2025SaveLearn
In memoriam: aspects of Santosh Kumar's work on exact results in RMTSantosh Kumar was an active researcher on the topic of exact results in random matrix theory and their various applications, particularly to quantum chaos and information theory. Barely entering his…Peter J. Forrester·May 8, 2025SaveLearn
On the Higher Categorical Structure of Topological Defects in Quantum Field TheoriesWe propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as…Lukas Müller·May 7, 2025SaveLearn