A Note on the Binding Energy for Bosons in the Mean-field LimitWe consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose-Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from…Lea Boßmann, Nikolai Leopold, David Mitrouskas et al.·Jul 24, 2023SaveLearn
Geometric properties for a class of deformed trace functionsWe investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of…Frank Hansen·Jul 24, 2023SaveLearn
Effective Mass of the Fr\"ohlich Polaron and the Landau-Pekar-Spohn ConjectureWe prove that there is a constant C∈ (0,∞) such that the effective mass m(α) of the Fr\"ohlich Polaron satisfies m(α) ≥ C α4, which is sharp…Rodrigo Bazaes, Chiranjib Mukherjee, Mark Sellke et al.·Jul 24, 2023SaveLearn
Hierarchical physically based machine learning in material science: the case study of spider silkMultiscale phenomena exhibit complex structure-function relationships, and predicting their macroscopic behavior requires deducing differential equations at different scales. The complexity of these…Vincenzo Fazio, Nicola Maria Pugno, Orazio Giustolisi et al.·Jul 24, 2023SaveLearn
Causal Localizations of the Massive Scalar BosonThe positive operator valued localizations (POL) of a massive scalar boson are constructed and a characterization and structural analyses of their kernels are obtained. In the focus of this article…Domenico P. L. Castrigiano·Jul 24, 2023SaveLearn
Violation of Ferromagnetic Ordering of Energy Levels in Spin Rings for the SingletWe demonstrate a violation of the ``ferromagnetic ordering of energy levels'' conjecture (FOEL) for even length spin rings. The FOEL conjecture was a guess made by Nachtergaele, Spitzer and an author…David Heson, Shannon Starr, Jacob Thornton·Jul 24, 2023SaveLearn
Operator Norm Bounds on the Correlation Matrix of the SK Model at High TemperatureWe prove that the two point correlation matrix M= ( σi ; σj)1≤ i,j≤ N ∈ RN× N of the Sherrington-Kirkpatrick model has the property…Christian Brennecke, Changji Xu, Horng-Tzer Yau·Jul 24, 2023SaveLearn
Algebraic entropy for systems of quad equationsIn this work I discuss briefly the calculation of the algebraic entropy for systems of quad equations. In particular, I observe that since systems of multilinear equations can have algebraic…Giorgio Gubbiotti·Jul 23, 2023SaveLearn
Euler-Poisson equations of a dancing spinning top, integrability and examples of analytical solutionsEquations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson…Alexei A. Deriglazov·Jul 23, 2023SaveLearn
Noether symmetries and conservation laws of a reduced gauged bilayer graphene modelA canonical Hamiltonian is found for a reduced version of the Jackiw-Pi model for bilayer graphene. From the corresponding Lagrangian, the Noether point symmetries and conserved quantities are…Fernando Haas·Jul 21, 2023SaveLearn
Exact hydrodynamics and onset of phase separation for an active exclusion processWe consider a lattice model of active matter with exclusion and derive its hydrodynamic description exactly. The hydrodynamic limit leads to an integro-differential equation for the density of…James Mason, Clement Erignoux, Robert Jack et al.·Jul 21, 2023SaveLearn
Vanishing cycles and analysis of singularities of Feynman diagramsIn this work, we analyze vanishing cycles of Feynman loop integrals by means of the Mayer-Vietoris spectral sequence. A complete classification of possible vanishing geometries are obtained. We…Stanislav Srednyak, Vladimir Khachatryan·Jul 21, 2023SaveLearn
Finite temperature properties of an integrable zigzag ladder chainWe consider the interaction-round-a-face version of the six-vertex model for arbitrary anisotropy parameter, which allow us to derive an integrable one-dimensional quantum Hamiltonian with three-spin…T. S. Tavares, G. A. P. Ribeiro·Jul 21, 2023SaveLearn
Exponential decay of the number of excitations in the weakly interacting Bose gasWe consider N trapped bosons in the mean-field limit with coupling constant λN=1 / (N-1). The ground state of such systems exhibits Bose--Einstein condensation. We prove that the…David Mitrouskas, Peter Pickl·Jul 20, 2023SaveLearn
Exactness of the first Born approximation in electromagnetic scatteringFor the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of…Farhang Loran, Ali Mostafazadeh·Jul 20, 2023SaveLearn
High-temperature cluster expansion for classical and quantum spin lattice systems with multi-body interactionsWe develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the use of ``decoupling…Nguyen Tong Xuan, Roberto Fernandez·Jul 20, 2023SaveLearn
Exponential bounds of the condensation for dilute Bose gasesWe consider N bosons on the unit torus = [0,1]3 in the Gross-Pitaevski regime where the interaction potential scales as N2 V (N(x -y)). We prove that the thermal equilibrium at low…Phan Thành Nam, Simone Rademacher·Jul 20, 2023SaveLearn
The vacuum energy with non-ideal boundary conditions via an approximate functional equationWe discuss the vacuum energy of a quantized scalar field in the presence of classical surfaces, defining bounded domains ⊂ Rd, where the field satisfies ideal or…E. Arias, G. O. Heymans, H. T. Lopes et al.·Jul 19, 2023SaveLearn
On the behaviour of a periodically forced and thermostatted harmonic chainWe consider a chain consisting of n+1 pinned harmonic oscillators subjected on the right to a time dependent periodic force (t) while Langevin thermostats are attached at both endpoints of the…Pedro Garrido, Tomasz Komorowski, Joel L. Lebowitz et al.·Jul 18, 2023SaveLearn
Critical points of the discretized Hartree-Fock functional of connected molecules preserving structures of molecular fragmentsIn this paper a method to obtain a critical point of the discretized Hartree-Fock functional from an approximate critical point is given. The method is based on Newton's method on the Grassmann…Sohei Ashida·Jul 18, 2023SaveLearn
Nonlinear feedback, double bracket dissipation and port control of Lie-Poisson systemsMethods from controlled Lagrangians, double bracket dissipation and interconnection and damping assignment -- passivity based control (IDA-PBC) are used to construct nonlinear feedback controls which…Simon Hochgerner·Jul 18, 2023SaveLearn
Simple and high-order N-solitons of the nonlocal generalized Sasa-Satsuma equation via an improved Riemann-Hilbert methodIn this paper, we investigate the nonlocal generalized Sasa-Satsuma (ngSS) equation based on an improved Riemann-Hilbert method (RHM). Different from the traditional RHM, the t-part of the Lax pair…Guixian Wang, Xiu-Bin Wang, Haie Long et al.·Jul 18, 2023SaveLearn
Continuum limit for Laplace and Elliptic operators on latticesContinuum limits of Laplace operators on general lattices are considered, and it is shown that these operators converge to elliptic operators on the Euclidean space in the sense of the generalized…Keita Mikami, Shu Nakamura, Yukihide Tadano·Jul 17, 2023SaveLearn
On the algebraic area of cubic lattice walksWe obtain an explicit formula to enumerate closed random walks on a cubic lattice with a specified length and 3D algebraic area. The 3D algebraic area is defined as the sum of algebraic areas…Li Gan·Jul 17, 2023SaveLearn
Weakly interacting Fermions: mean-field and semiclassical regimesThe derivation of effective macroscopic theories approximating microscopic systems of interacting particles is a major question in non-equilibrium statistical mechanics. In these notes we present an…Chiara Saffirio·Jul 15, 2023SaveLearn