PT-Symmetry in 2× 2 Matrix Polynomials Formed by Pauli Matrices2×2 matrix polynomials of the form Pn(z)= nj=0\,σj\,zj, for the cases n=1,2,3 are constructed, and the nature of PT-symmetry is examined across different points…Stalin Abraham, Ameeya A. Bhagwat·Dec 5, 2024SaveLearn
KdV Equation for Theta Functions on Non-commutative ToriIn the fields of non-commutative geometry and string theory, quantum tori appear in different mathematical and physical contexts. Therefore, quantized theta functions defined on quantum tori are also…Wanli Cheng·Dec 5, 2024SaveLearn
Intertwining vectors, and Boltzmann weight matrices, of a Solid-on-Solid model from the 20-vertex modelWe initiate a new study on the correspondence between the 20-vertex model and a SOS (Solid-on-Solid) model. In comparison to two previous works of the author in 2024 which characterized properties of…Pete Rigas·Dec 5, 2024SaveLearn
Energy cascades and condensation via coherent dynamics in Hamiltonian systemsThis work makes analytic progress in the deterministic study of turbulence in Hamiltonian systems by identifying two types of energy cascade solutions and the corresponding large- and small-scale…Anxo Biasi, Patrick Gérard·Dec 4, 2024SaveLearn
Spectral theory of effective transport for discrete uniaxial polycrystalline materialsWe previously demonstrated that the bulk transport coefficients of uniaxial polycrystalline materials, including electrical and thermal conductivity, diffusivity, complex permittivity, and magnetic…N. Benjamin Murphy, Daniel Hallman, Elena Cherkaev et al.·Dec 4, 2024SaveLearn
Minimization of the discrete interaction energy with smooth potentialsWe study the pair interaction on flat tori of functions whose Fourier coefficients are positive and decay sufficiently rapidly. In dimension one we find that the minimizer, up to translation, is the…Yaniv Almog·Dec 4, 2024SaveLearn
Eikonal 2.0: General Solutions for Modified Eikonal EquationsWe find implicit general solutions for modified eikonal equations ua ua=F(ut), where lower indices at dependent variables designate derivatives, a=1,2,..,n, and summation is implied over the…Iryna Yehorchenko·Dec 3, 2024SaveLearn
Eikonal 3.1: General solution for coupled system of eikonal equations, three space dimensionsA general solution for a coupled system of eikonal equations uμ uμ =0, vμ vμ =0, uμ vμ =1 is presented, where lower indices designate derivatives, μ=0,1,2,3, and summation…Iryna Yehorchenko·Dec 3, 2024SaveLearn
Direct Interaction Approximation for generalized stochastic models in the turbulence problemThe purpose of this paper is to consider the application of the direct interaction approximation (DIA) developed by Kraichnan to generalized stochastic models in the turbulence problem. Previous…Bhimsen Shivamoggi, Nicole Tuovila·Dec 3, 2024SaveLearn
Calculation of Spin Group Elements RevisitedIn this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results…D. S. Shirokov·Dec 3, 2024SaveLearn
On Rank of Multivectors in Geometric AlgebrasWe introduce the notion of rank of multivector in Clifford geometric algebras of arbitrary dimension without using the corresponding matrix representations and using only geometric algebra…D. S. Shirokov·Dec 3, 2024SaveLearn
Matrix representation of Picard--Lefschetz--Pham theory near the real plane in C2A matrix formalism is proposed for computations based on Picard--Lefschetz theory in a 2D case. The formalism is essentially equivalent to the computation of the intersection indices necessary for…A. V. Shanin, A. I. Korolkov, N. M. Artemov et al.·Dec 3, 2024SaveLearn
The renormalized Nelson model in the weak coupling limitThe Nelson model describes non-relativistic particles coupled to a relativistic Bose scalar field. In this article, we study the renormalized version of the Nelson model with massless bosons in…Esteban Cárdenas, David Mitrouskas·Dec 2, 2024SaveLearn
Simultaneous symplectic spectral decomposition of positive semidefinite matricesWe establish necessary and sufficient conditions on simultaneous symplectic spectral decomposition of a family of 2n × 2n real positive semidefinite matrices with symplectic kernels. We also…Rudra R. Kamat, Hemant K. Mishra·Dec 2, 2024SaveLearn
Spectral theory of effective transport for continuous uniaxial polycrystalline materialsFollowing seminal work in the early 1980s that established the existence and representations of the homogenized transport coefficients for two phase random media, we develop a mathematical framework…N. Benjamin Murphy, Daniel Hallman, Elena Cherkaev et al.·Dec 2, 2024SaveLearn
On the phase diagram of the multiscale mean-field spin-glassIn this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of…Francesco Camilli, Pierluigi Contucci, Emanuele Mingione et al.·Dec 1, 2024SaveLearn
Continuous Topological Insulators Classification and Bulk Edge CorrespondenceThis paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the…Guillaume Bal·Dec 1, 2024SaveLearn
Classical elliptic integrable systems from the moduli space of instantonsThis paper is intended to serve as a review of a series of papers with Nikita Nekrasov, where we achieved several important results concerning the relation between the moduli space of instantons and…Andrei Grekov·Dec 1, 2024SaveLearn
Superintegrability and geometry: a review of the extended Hamiltonian approachWe review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first…Claudia Maria Chanu, Giovanni Rastelli·Nov 29, 2024SaveLearn
Ruijsenaars spectral transformSpectral decomposition with respect to the wave functions of Ruijsenaars hyperbolic system defines an integral transform, which generalizes classical Fourier integral. For a certain class of…N. Belousov, S. Khoroshkin·Nov 29, 2024SaveLearn
Distribution of the Diagonal Entries of the Resolvent of a Complex Ginibre MatrixThe study of eigenvalue distributions in random matrix theory is often conducted by analyzing the resolvent matrix GMN(z) = (z 1 - M)-1 . The normalized…Pierre Bousseyroux, Jean-Philippe Bouchaud, Marc Potters·Nov 28, 2024SaveLearn
Why a System of Three Bosons on Separate Lines Can Not Exhibit the Confinement Induced Efimov EffectWe study a system of three bosons interacting with short-range potentials which can move along three different lines. Two of these lines are parallel to each other within one plane. The third line is…Dirk Hundertmark, Marvin R. Schulz, Semjon Vugalter·Nov 28, 2024SaveLearn
Enhanced Lieb-Robinson bounds for commuting long-range interactionsRecent works have revealed the intricate effect of long-range interactions on information transport in quantum many-body systems: In D spatial dimensions, interactions decaying as a power-law…Marius Lemm, Tom Wessel·Nov 28, 2024SaveLearn
Optimal control applied to viral competitionThe emergence of mutant lineages within a viral species has become a public health problem, as the existing treatments and drugs are usually more effective on the original lineages than in the mutant…Javier López-Pedrares, Cristiana J. Silva, M. Elena Vázquez-Cendón et al.·Nov 28, 2024SaveLearn
Universality for random matrices with an edge spectrum singularityWe study invariant random matrix ensembles equation* Pn(d M)=Zn-1(-n\,tr(V(M)))\,d M equation* defined on complex Hermitian matrices M of size n× n, where V…Thomas Bothner, Toby Shepherd·Nov 27, 2024SaveLearn