On the characterisation of fragmented Bose-Einstein condensation and its emergent effective evolutionFragmented Bose-Einstein condensates are large systems of identical bosons displaying multiple macroscopic occupations of one-body states, in a suitable sense. The quest for an effective…Jinyeop Lee, Alessandro Michelangeli·Nov 14, 2022SaveLearn
Wilson Area Law formula on R4Let g be the Lie Algebra of a compact semi-simple gauge group. For a g-valued 1-form A, consider the Yang-Mills action equation S YM(A) =…Adrian P. C. Lim·Nov 14, 2022SaveLearn
Computation of partition functions of free fermionic solvable lattice models via permutation graphsIn this paper, we introduce a novel and general method for computing partition functions of solvable lattice models with free fermionic Boltzmann weights. The method is based on the ``permutation…Chenyang Zhong·Nov 13, 2022SaveLearn
Two-dimensional Hydrogen-like Atom in a Constant Magnetic FieldThe two-dimensional hydrogen-like atom in a constant magnetic field is considered. It is found that this is actually two separate problems. One for which the magnetic field causes an effective…M. G. Naber·Nov 13, 2022SaveLearn
On the Homology of Unions of Certain Non-Degenerate Quadrics in General PositionMotivated by problems arising in the complex analysis of perturbative quantum field theory, we investigate the homology of finite unions of certain non-degenerate quadratic affine hypersurfaces of…Maximilian Mühlbauer·Nov 12, 2022SaveLearn
Energetic Variational Approaches for inviscid multiphase flow systems with surface flow and tensionWe consider the governing equations for the motion of the inviscid fluids in two moving domains and an evolving surface from an energetic point of view. We employ our energetic variational approaches…Hajime Koba·Nov 12, 2022SaveLearn
Quantum Statistical Mechanics via Boundary Conditions. A Groupoid Approach to Quantum Spin SystemsWe use a groupoid model for the spin algebra to introduce boundary conditions on quantum spin systems via a Poisson point process representation. We can describe KMS states of quantum systems by…Lucas Affonso, Rodrigo Bissacot, Marcelo Laca·Nov 12, 2022SaveLearn
On the partition function of the Sp(2n) integrable vertex modelWe study the partition function per site of the integrable Sp(2n) vertex model on the square lattice. We establish a set of transfer matrix fusion relations for this model. The solution of these…G. A. P. Ribeiro·Nov 11, 2022SaveLearn
Weaving paper strips for designing of general curved surface with geometrical elasticityThis study proposes 'amigami' as a new method of creating a general curved surface. It conducts the shape optimization of weaving paper strips based on the theory of nonlinear elasticity on…Yuto Horikawa, Ryuichi Tarumi·Nov 11, 2022SaveLearn
Hamilton-Jacobi theory for nonholonomic and forced hybrid mechanical systemsA hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical…Leonardo Colombo, Manuel de León, María Emma Eyrea Irazú et al.·Nov 11, 2022SaveLearn
Calogero model revisited, commuting Hamiltonians, Hurwitz numbersThe generalized Mironov-Morozov-Natanson (MMN) equation includes a set of commuting operators, which can be considered as Hamiltonians for the quantum Calogero-Sutherland problem with a special value…A. Yu. Orlov·Nov 10, 2022SaveLearn
Integrability and BRST invariance from BF topological theoryWe consider the BRST invariant effective action of the non-abelian BF topological theory in 1+1 dimensions with gauge group Sl(2,R). By considering different gauge fixing conditions, the…A. Restuccia, A. Sotomayor·Nov 10, 2022SaveLearn
The Zeta Function for the Triangular PotentialThe zeta functions for the Schr\"odinger equation with a triangular potential are investigated. Values of the zeta functions are computed using both the Weierstrass factorization theorem and analytic…M. G. Naber·Nov 10, 2022SaveLearn
The Bessel zeta functionTwo representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully…M. G. Naber, B. M. Bruck, S. E. Costello·Nov 10, 2022SaveLearn
Quantum generalized Calogero-Moser systems from free Hamiltonian reductionThe one-dimensional system of particles with a 1/x2 repulsive potential is known as the Calogero-Moser system. Its classical version can be generalised by substituting the coupling constants with…Katarzyna Kowalczyk-Murynka, Marek Kuś·Nov 10, 2022SaveLearn
Stability of the gapless pure point spectrum of self-adjoint operatorsWe consider a self-adjoint operator T on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of T…Paolo Facchi, Marilena Ligabò·Nov 10, 2022SaveLearn
Elementary excitations in an integrable twisted J1-J2 spin chain in the thermodynamic limitThe exact elementary excitations in a typical U(1) symmetry broken quantum integrable system, that is the twisted J1-J2 spin chain with nearest-neighbor, next nearest neighbor and chiral three spin…Wei Wang, Yi Qiao, Rong-Hua Liu et al.·Nov 10, 2022SaveLearn
On Relative Bounds for Interacting Fermion OperatorsWe consider a Hubbard model with nearest neighbor interaction on a discrete d-dimensional torus of length L around its Hartree-Fock ground state and derive relative bounds of the effective…Volker Bach, Robert Rauch·Nov 9, 2022SaveLearn
Reduced transfer operators for singular difference equationsFor tridiagonal block Jacobi operators, the standard transfer operator techniques only work if the off-diagonal entries are invertible. Under suitable assumptions on the range and kernel of these…Hermann Schulz-Baldes·Nov 9, 2022SaveLearn
Levinson theorem for discrete Schr\"odinger operators on the line with matrix potentials having a first momentThis paper proves new results on spectral and scattering theory for matrix-valued Schr\"odinger operators on the discrete line with non-compactly supported perturbations whose first moments are…Miguel Ballesteros, Gerardo Franco Córdova, Ivan Naumkin et al.·Nov 9, 2022SaveLearn
Nonexistence of wave operators via strong propagation estimates for Schr\"odinger operators with sub-quadratic repulsive potentialsSub-quadratic repulsive potentials accelerate quantum particles and can relax the decay rate in the x of the external potentials V that guarantee the existence of the quantum wave operators. In…Atsuhide Ishida, Masaki Kawamoto·Nov 9, 2022SaveLearn
Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebrasStarting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians and the constants of…Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette et al.·Nov 9, 2022SaveLearn
Theory and Application of Augmented Dimensional AnalysisWe present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant…Dan Jonsson·Nov 8, 2022SaveLearn
Vertex operator for generalised Kac--Moody algebras associated to the two-sphere and the two-torusWe pursue our study of generalised Kac-Moody and Virasoro algebras defined on compact homogeneous manifolds. Extending the well-known Vertex operator in the case of the two-torus or the two-sphere,…Rutwig Campoamor-Stursberg, Michel Rausch de Traubenberg·Nov 8, 2022SaveLearn
Fermion realisations of generalised Kac--Moody and Virasoro algebras associated to the two-sphere and the two-torusUsing the notion of extension of Kac-Moody algebras for higher dimensional compact manifolds recently introduced in [1], we show that for the two-torus S1 × S1 and the…Rutwig Campoamor-Stursberg, Michel Rausch de Traubenberg·Nov 8, 2022SaveLearn