On the quantum Guerra-Morato Action FunctionalGiven a smooth potential W:Tn R on the torus, the Quantum Guerra-Morato action functional is given by $ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,…Josue Knorst, Artur O. Lopes·Mar 9, 2024SaveLearn
Generalized Yang Poisson Models on Canonical Phase SpaceWe discuss the generalized Yang Poisson models. We construct generalizations of the Yang Poisson algebra related to o(1,5) algebra discussed by Meljanac and Mignemi (2023). The exact…Tea Martinić Bilać, Stjepan Meljanac, Salvatore Mignemi·Mar 8, 2024SaveLearn
A short proof of a strong Weyl law in dimension 1For the Dirichlet realization of -d2/dx2-λ2V on a bounded interval, with V a positive C2 potential bounded away from 0 and λ>0 a large parameter, we prove an asymptotic law…August Bjerg·Mar 8, 2024SaveLearn
Phase Transitions in Ising models: the Semi-infinite with decaying field and the Random Field Long-rangeIn this thesis, we present results on phase transition for two models: the semi-infinite Ising model with a decaying field, and the long-range Ising model with a random field. We study the…João Maia·Mar 7, 2024SaveLearn
Liouville models of particle-laden flowLangevin (stochastic differential) equations are routinely used to describe particle-laden flows. They predict Gaussian probability density functions (PDFs) of a particle's trajectory and velocity,…Daniel Domínguez-Vázquez, Gustaaf B. Jacobs, Daniel M. Tartakovsky·Mar 7, 2024SaveLearn
Fractional diffusion equations interpolate between damping and wavesThe behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional…Andy Manapany, Sébastien Fumeron, Malte Henkel·Mar 7, 2024SaveLearn
On finite group global and gauged q-form symmetries in TQFTWe describe a method to implement finite group global and gauged q-form symmetries into the axiomatic structure of d-dimensional Topological Quantum Field Theory (TQFT) in terms of bordisms…Manuel Furlan, Pavel Putrov·Mar 7, 2024SaveLearn
Galilean symmetry of the KdV hierarchyBy solving the infinitesimal Galilean symmetry for the KdV hierarchy, we obtain an explicit expression for the corresponding one-parameter Lie group, which we call the Galilean symmetry of the KdV…Jianghao Xu, Di Yang·Mar 7, 2024SaveLearn
Classifying bulk-edge anomalies in the Dirac HamiltonianWe study the Dirac Hamiltonian in dimension two with a mass term and a large momentum regularization, and show that bulk-edge correspondence fails. Despite a well defined bulk topological index --the…Hansueli Jud, Clément Tauber·Mar 7, 2024SaveLearn
On a variational problem related to the Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalitiesWe explicitly solve a variational problem related to upper bounds on the optimal constants in the Cwikel--Lieb--Rozenblum (CLR) and Lieb--Thirring (LT) inequalities, which has recently been derived…Thiago Carvalho Corso, Tobias Ried·Mar 7, 2024SaveLearn
Exponential decay property for eigenfunctions of quantum walksUnder an abstract setting, we show that eigenvectors belong to discrete spectra of unitary operators have exponential decay properties. We apply the main theorem to multi-dimensional quantum walks…Kazuyuki Wada·Mar 7, 2024SaveLearn
B\"ottcher-Wenzel inequality for weighted Frobenius norms and its application to quantum physicsBy employing a weighted Frobenius norm with a positive matrix ω, we introduce natural generalizations of the famous B\"ottcher-Wenzel (BW) inequality. Based on the combination of the weighted…Aina Mayumi, Gen Kimura, Hiromichi Ohno et al.·Mar 7, 2024SaveLearn
Coulomb Green's function and an addition formula for the Whittaker functionsA series of the form Σ=0∞c(,)\,M,+1/2(r0)W,+1/2(r)P((γ)) is evaluated explicitly where c(,) are suitable complex…Pavel Šťovíček·Mar 6, 2024SaveLearn
The Tensor Track VIII: Stochastic AnalysisAssuming some familiarity with quantum field theory and with the tensor track approach that we presented in the previous series Tensor Track I-VII, we provide, as usual, the developments in tensors…V. Rivasseau·Mar 6, 2024SaveLearn
Some solutions to the eigenstate equation for the free quantum field Hamiltonian in the Schr\"odinger representationUsing closed positive extensions of the quadratic form in the potential term we provide alternative solutions to the eigenstate equation for the free quantum field Hamiltonian in the…T. A. Bolokhov·Mar 5, 2024SaveLearn
On Airy solutions of PII and the complex cubic ensemble of random matrices, IIWe describe the pole-free regions of the one-parameter family of special solutions of PII, the second Painlev\'e equation, constructed from the Airy functions. This is achieved by…Ahmad Barhoumi, Pavel Bleher, Alfredo Deaño et al.·Mar 5, 2024SaveLearn
Refining the grading of irreducible Lie colour algebra representationsWe apply the loop module construction of arXiv:1504.05114 in the context of Lie colour algebras. We construct a bijection between the equivalence classes of all finite-dimensional graded irreducible…Mitchell Ryan·Mar 5, 2024SaveLearn
Existence of de Almeida-Thouless-type instability in the transverse field Sherrington-Kirkpatrick modelThe interpolation method for mean field spin glass models developed by Guerra and Talagrand is extended to a quantum mean field spin glass model. This extension enables us to obtain both…C. Itoi, K. Fujiwara, Y. Sakamoto·Mar 5, 2024SaveLearn
Arctic curves of the T-system with Slanted Initial DataWe study the T-system of type A∞, also known as the octahedron recurrence/equation, viewed as a 2+1-dimensional discrete evolution equation. Generalizing the study of [P. Di Francesco and R.…Philippe Di Francesco, Hieu Trung Vu·Mar 4, 2024SaveLearn
Edge states for tight-binding operators with soft wallsWe study one- and two-dimensional periodic tight-binding models under the presence of a potential that grows to infinity in one direction, hence preventing the particles to escape in this direction…Camilo Gómez Araya, David Gontier, Hanne Van Den Bosch·Mar 4, 2024SaveLearn
The spin-statistics theorem for topological quantum field theoriesWe establish the spin-statistics theorem for topological quantum field theories (TQFTs) in the framework of Atiyah. We incorporate spin via spin structures on bordisms, and represent statistics using…Luuk Stehouwer·Mar 4, 2024SaveLearn
An Alexander-like theorem for a particle model with inelastic collisionsWe consider a finite system of hard spheres that collide inelastically according to a particular model, losing a fixed amount of kinetic energy at each collision. We develop the theory of the…Théophile Dolmaire, Juan J. L. Velázquez·Mar 4, 2024SaveLearn
Derivation, characterization, and application of complete orthonormal sequences for representing general three-dimensional states of residual stressResidual stresses are self-equilibrated stresses on unloaded bodies. Owing to their complex origins, it is useful to develop functions that can be linearly combined to represent any sufficiently…Sankalp Tiwari, Eliot Fried·Mar 3, 2024SaveLearn
Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 1. Systems with cylindric symmetryCylindrically symmetric quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion are classified. It is proved that there exist 68 such…A. G. Nikitin·Mar 2, 2024SaveLearn
D'Alamebrt and Hamiltonian principles and classical relativity in Lagrangian mechanicsIn this note we present invariant formulation of the d'Alambert principle and classical time-dependent Lagrangian mechanics with holonomic constraints from the perspective of moving frames.Bozidar Jovanovic·Mar 2, 2024SaveLearn