Effective operators and their variational principles for discrete electrical network problemsUsing a Hilbert space framework inspired by the methods of orthogonal projections and Hodge decompositions, we study a general class of problems (called Z-problems) that arise in effective media…Kenneth Beard, Anthony Stefan, Robert Viator et al.·Oct 11, 2022SaveLearn
A Magnetic Pseudodifferential Calculus for Operator-Valued and Equivariant Operator-Valued SymbolsIn this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful…Giuseppe De Nittis, Max Lein, Marcello Seri·Oct 11, 2022SaveLearn
From point processes to quantum optics and backSome fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. Her initial motivation was to provide models for the set of detection times in…Rémi Bardenet, Alexandre Feller, Jérémie Bouttier et al.·Oct 11, 2022SaveLearn
Axiomatic field theory and Hida-Colombeau algebrasAn axiomatic quantum field theory applied to the self-interacting boson field is realised in terms of generalised operators that allows us to form products and take derivatives of the fields in…Alexei Filinkov, Ian G. Fuss·Oct 11, 2022SaveLearn
Topology vs localization in synthetic dimensionsMotivated by recent developments in quantum simulation of synthetic dimensions, e.g. in optical lattices of ultracold atoms, we discuss here d-dimensional periodic, gapped quantum systems for $d…Domenico Monaco, Thaddeus Roussigné·Oct 10, 2022SaveLearn
Generalised model of wear in contact problems: the case of oscillatory loadIn this short paper, we consider a sliding punch problem under recently proposed model of wear which is based on the Riemann-Liouville fractional integral relation between pressure and worn volume,…Dmitry Ponomarev·Oct 10, 2022SaveLearn
BCS Theory in the Weak Magnetic Field Regime for Systems with Nonzero Flux and Exponential Estimates on the Adiabatic Theorem in Extended Quantum Lattice SystemsIn the main part of this PhD thesis, we consider a periodically realized microscopic superconductor described by BCS theory, which is subject to external electromagnetic fields. We show that the…Marcel Maier·Oct 10, 2022SaveLearn
On one-dimensional Bose gases with two- and (critical) attractive three-body interactionsWe consider a one-dimensional, trapped, focusing Bose gas where N bosons interact with each other via both a two-body interaction potential of the form a Nα-1 U(Nα(x-y)) and an…Dinh-Thi Nguyen, Julien Ricaud·Oct 10, 2022SaveLearn
Periodic rhomboidal cells for symmetry-preserving homogenization and isotropic metamaterialsIn the design and analysis of composite materials based on periodic arrangements of sub-units it is of paramount importance to control the emergent material symmetry in relation to the elastic…Giulio G. Giusteri, Raimondo Penta·Oct 10, 2022SaveLearn
Fluctuations and localization length for random band GOE matrixWe prove that GOE random band matrix localization length is C( W)3 W2, where W is the width of the band and C is an absolute constant. Our method consists of Green function…Michael Goldstein·Oct 9, 2022SaveLearn
Determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentialsWe consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point…Sung-Soo Byun, Meng Yang·Oct 8, 2022SaveLearn
Yang-Baxter algebra, higher rank partition functions and K-theoretic Gysin map for partial flag bundlesWe investigate the K-theoretic Gysin map for type A partial flag bundles from the viewpoint of integrability. We introduce several types of partition functions for one version of q=0…Kohei Motegi·Oct 8, 2022SaveLearn
A Concrete Example of Fractional Chern InsulatorWe present a concrete example of fractional Chern insulator whose fermion Hamiltonian consists of hopping and Coulomb repulsive interaction terms. Both of them are of finite range on the square…Tohru Koma·Oct 8, 2022SaveLearn
Interpretation of generalized Langevin equationsMany real-world systems exhibit ``noisy'' evolution in time; interpreting their finitely-sampled behavior as arising from continuous-time processes (in the It\o or Stratonovich sense) has led to…David Sabin-Miller, Daniel M. Abrams·Oct 7, 2022SaveLearn
The thermodynamic limit of an ideal Bose gas by asymptotic expansions and spectral ζ-functionsWe analyze the thermodynamic limit - modeled as the open-trap limit of an isotropic harmonic potential - of an ideal, non-relativistic Bose gas with a special emphasis on the phenomenon of…Daniel Alexander Weiss·Oct 7, 2022SaveLearn
Particle Trajectories for Quantum MapsWe study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system…Yonah Borns-Weil, Izak Oltman·Oct 6, 2022SaveLearn
Commutativity equations and their trigonometric solutionsWe consider commutativity equations Fi Fj =Fj Fi for a function F(x1, …, xN), where Fi is a matrix of the third order derivatives Fikl. We show that under certain non-degeneracy…Maali Alkadhem, Misha Feigin·Oct 6, 2022SaveLearn
Non-Archimedean Quantum Mechanics via Quantum GroupsWe present a new non-Archimedean realization of the Fock representation of the q-oscillator algebras where the creation and annihilation operators act on complex-valued functions, which are defined…W. A. Zúñiga-Galindo·Oct 6, 2022SaveLearn
On Quantum Sobolev InequalitiesWe investigate the quantum analogue of the classical Sobolev inequalities in the phase space, with the quantum Sobolev norms defined in terms of Schatten norms of commutators. These inequalities…Laurent Lafleche·Oct 6, 2022SaveLearn
Perturbative BV-BFV formalism with homotopic renormalization: a case studyWe report a rigorous quantization of topological quantum mechanics on R≥slant 0 and I= [0, 1] in perturbative BV-BFV formalism. Costello's homotopic renormalization is…Minghao Wang, Gongwang Yan·Oct 6, 2022SaveLearn
Integrating curved Yang-Mills gauge theoriesWe construct a gauge theory based on principal bundles P equipped with a right G-action, where G is a Lie group bundle instead of a Lie group. Due to the fact that…Simon-Raphael Fischer·Oct 6, 2022SaveLearn
Quantum pseudo-integrable Hamiltonian impact systemsQuantization of a toy model of a pseudointegrable Hamiltonian impact system is introduced, including EBK quantization conditions, a verification of Weyl's law, the study of their wavefunctions and a…Omer Yaniv, Vered Rom-Kedar·Oct 6, 2022SaveLearn
Scattering theory and an index theorem on the radial part of SL(2,R)We present the spectral and scattering theory of the Casimir operator acting on the radial part of SL(2,R). After a suitable decomposition, these investigations consist in studying a family of…H. Inoue, S. Richard·Oct 5, 2022SaveLearn
On higher-dimensional superintegrable systems: A new family of classical and quantum Hamiltonian modelsWe introduce a family of n-dimensional Hamiltonian systems which, contain, as special reductions, several superintegrable systems as the Tremblay-Turbiner-Winternitz system, a generalized Kepler…Miguel A. Rodriguez, Piergiulio Tempesta·Oct 5, 2022SaveLearn
Hyperuniformity and non-hyperuniformity of quasicrystalsWe develop a general framework to study hyperuniformity of various mathematical models of quasicrystals. Using this framework we provide examples of non-hyperuniform quasicrystals which unlike…Michael Björklund, Tobias Hartnick·Oct 5, 2022SaveLearn