M\"obius invariant Y-systems (cluster structures) for Miquel dynamicsMiquel dynamics is a discrete time dynamics for circle patterns, which relies on Miquel's six circle theorem. Previous work shows that the evolution of the circle centers satisfy the dSKP equation on…Niklas Christoph Affolter·Dec 12, 2023SaveLearn
Solution of the v-representability problem on a one-dimensional torusWe provide a solution to the v-representability problem for a non-relativistic quantum many-particle system on a ring domain in terms of Sobolev spaces and their duals. Any one-particle density that…Sarina M. Sutter, Markus Penz, Michael Ruggenthaler et al.·Dec 12, 2023SaveLearn
The energy-stepping Monte Carlo method: an exactly symmetry-preserving, a Hamiltonian Monte Carlo method with a 100% acceptance ratioWe introduce the energy-stepping Monte Carlo (ESMC) method, a Markov chain Monte Carlo (MCMC) algorithm based on the conventional dynamical interpretation of the proposal stage but employing an…Ignacio Romero, Michael Ortiz·Dec 12, 2023SaveLearn
The role of the branch cut of the logarithm in the definition of the spectral determinant for non-selfadjoint operatorsThe spectral determinant is usually defined using the spectral zeta function that is meromorphically continued to zero. In this definition, the complex logarithms of the eigenvalues appear. Hence the…Jiří Lipovský, Tomáš Macháček·Dec 12, 2023SaveLearn
Families of KP solutions associated with tropical curves having nontrivial weightsIn order to generalize a program by Agostini and others producing new KP solutions, we construct families of quasi-periodic KP solutions which are derived from degenerating Riemann surfaces…Takashi Ichikawa·Dec 12, 2023SaveLearn
Ground States of Fermionic Nonlinear Schr\"odinger Systems with Coulomb Potential II: The L2-Critical CaseAs a continuation of me, we consider ground states of the N coupled fermionic nonlinear Schr\"odinger system with a parameter a and the Coulomb potential V(x) in the L2-critical…Bin Chen, Yujin Guo, Shu Zhang·Dec 12, 2023SaveLearn
Alterfold Topological Quantum Field TheoryWe introduce the 3-alterfold topological quantum field theory (TQFT) by extending the quantum invariant of 3-alterfolds. The bases of the TQFT are explicitly characterized and the Levin-Wen model is…Zhengwei Liu, Shuang Ming, Yilong Wang et al.·Dec 11, 2023SaveLearn
Coupled Free Fermion Conformal Field Theory and RepresentationsConformal field theory (CFT) has become an active area of research beyond its origins in statistical physics and attracted much attention due to its intrinsic mathematical interest, which reveals…Bolin Han·Dec 11, 2023SaveLearn
Shuffle algebras, lattice paths and Macdonald functionsWe consider partition functions on the N× N square lattice with the local Boltzmann weights given by the R-matrix of the Ut(sl(n+1|m)) quantum algebra. We identify boundary…Alexandr Garbali, Ajeeth Gunna·Dec 11, 2023SaveLearn
On the relativistic quantum mechanics of a photon between two electrons in 1+1 dimensionsA Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac…Lawrence Frolov, Samuel E. Leigh, A. Shadi Tahvildar-Zadeh·Dec 10, 2023SaveLearn
Poisson structures of some heavenly type dynamical systemsThe paper investigates the Poisson structures associated with dynamical systems of the heavenly type, focusing on the Mikhalev-Pavlov and Pleba\'nski equation. The dynamical system is represented as…Yarema Prykarpatskyy·Dec 9, 2023SaveLearn
Poincar\'e Duality and SupergravityWe study relative differential and integral forms on families of supermanifolds and their cohomology. We prove a relative Poincar\'e--Verdier duality and show that it relates the cohomology of…Konstantin Eder, John Huerta, Simone Noja·Dec 8, 2023SaveLearn
Reflection Maps Associated with Involutions and Factorization Problems, and Their Poisson GeometryThe study of the set-theoretic solutions of the reflection equation, also known as reflection maps, is closely related to that of the Yang-Baxter maps. In this work, we construct reflection maps on…Luen-Chau Li, Vincent Caudrelier·Dec 8, 2023SaveLearn
SO(2,n)-compatible embeddings of conformally flat n-dimensional submanifolds in Rn+2We describe embeddings of n-dimensional Lorentzian manifolds, including Friedmann-Lema\itre-Robertson-Walker spaces, in Rn+2 such that the metrics of the submanifolds are inherited…E. Huguet, J. Queva, J. Renaud·Dec 8, 2023SaveLearn
Absence of embedded eigenvalues of Pauli and Dirac operatorsWe consider eigenvalues of the Pauli operator in R3 embedded in the continuous spectrum. In our main result we prove the absence of such eigenvalues above a threshold which depends on the…Dirk Hundertmark, Hynek Kovarik·Dec 8, 2023SaveLearn
Joint moments of derivatives of characteristic polynomials of random symplectic and orthogonal matricesWe investigate the joint moments of derivatives of characteristic polynomials over the unitary symplectic group Sp(2N) and the orthogonal ensembles SO(2N) and O-(2N). We prove asymptotic…Julio C. Andrade, Christopher G. Best·Dec 8, 2023SaveLearn
Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type and trigonometric GL(N|M) solution of associative Yang-Baxter equationWe propose commuting sets of matrix-valued difference operators in terms of trigonometric GL(N|M)-valued R-matrices thus providing quantum supersymmetric (and possibly anisotropic) spin…M. Matushko, A. Zotov·Dec 7, 2023SaveLearn
Ergodic theorems for continuous-time quantum walks on crystal lattices and the torusWe give several quantum dynamical analogs of the classical Kronecker-Weyl theorem, which says that the trajectory of free motion on the torus along almost every direction tends to equidistribute. As…Anne Boutet de Monvel, Mostafa Sabri·Dec 7, 2023SaveLearn
Non-commutative probability insights into the double-scaling limit SYK Model with constant perturbations: moments cumulants and q-independenceExtending our previous results, we study the double-scaling limit SYK (DSSYK) model with an additional diagonal matrix with a fixed number c of nonzero constant entries θ. This constant…Shuang Wu·Dec 7, 2023SaveLearn
Para-spaces, their differential analysis and an application to Green's quantisationWe introduce a class of non-commutative geometries, loosely referred to as para-spaces, which are manifolds equipped with sheaves of non-commutative algebras called para-algebras. A differential…Ruibin Zhang·Dec 7, 2023SaveLearn
Spectral properties of the Bloch-Torrey operator in three dimensionsWe consider the Bloch-Torrey operator, - + igx, that governs the time evolution of the transverse magnetization in diffusion magnetic resonance imaging (dMRI). Using the matrix formalism, we…Denis S. Grebenkov·Dec 7, 2023SaveLearn
Off-diagonal approach to the exact solution of quantum integrable systemsWe investigate the t-W scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of transfer matrix.…Yi Qiao, Junpeng Cao, Wen-Li Yang et al.·Dec 7, 2023SaveLearn
One-dimensional hydrogenic ions with screened nuclear Coulomb fieldWe study the spectrum of the Dirac hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus…Suchindram Dasgupta, Chirag Khurana, A. Shadi Tahvildar-Zadeh·Dec 7, 2023SaveLearn
Norm convergence of confined fermionic systems at zero temperatureThe semi-classical limit of ground states of large systems of fermions was studied by Fournais, Lewin and Solovej in (Calc. Var. Partial Differ. Equ., 2018). In particular, the authors prove weak…Esteban Cárdenas·Dec 6, 2023SaveLearn
The discrete nonlinear Schr\"odinger equation with linear gain and nonlinear loss: the infinite lattice with nonzero boundary conditions and its finite dimensional approximationsThe study of nonlinear Schr\"odinger-type equations with nonzero boundary conditions define challenging problems both for the continuous (partial differential equation) or the discrete (lattice)…Georgios Fotopoulos, Nikos I. Karachalios, Vassilis Koukouloyannis et al.·Dec 6, 2023SaveLearn