An Analogue of the Classical Yang-Baxter Equation for General Algebraic Structures.
An analysis of the effect of ghost force oscillation on quasicontinuum error
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a one-dimensional quasicontinuum energy around a uniform strain that the effect of the ghost forces on the displacement nearly cancels and has a small effect on the error away from the interface. We give optimal order error estimates that show that the quasicontinuum displacement converges to the atomistic...
An analytic formula for the Jack polynomials.
An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material
An atomic MV-effect algebra with non-atomic center
Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.
An axiomatic approach to Quantum Gauge Field Theory
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge transformations. That is, we propose a new set of Osterwalder Schrader like axioms for the characteristic functional of a measure on the space of generalized connections modulo gauge transformations rather than for the associated Schwinger distributions. We show non-triviality...
An electrostatic inequality with applications to the constitution of matter
An elementary construction on nonlinear coherent states associated to generalized Bargmann spaces.
An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics
This paper gives an error analysis of the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of multi-particle time-dependent Schrödinger equations. The MCTDH method approximates the multivariate wave function by a linear combination of products of univariate functions and replaces the high-dimensional linear Schrödinger equation by a coupled system of ordinary differential equations and low-dimensional nonlinear partial differential equations. The main result of this...
An exactly solvable spin chain related to Hahn polynomials.
An explicit formula for symmetric polynomials related to the eigenfunctions of Calogero-Sutherland models.
An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups
We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schrödinger operators obtained in this...
An extension of a result by Dinaburg and Sinai on quasi-periodic potentials.
An idempotent for a Jordanian quantum complex sphere
A new Jordanian quantum complex 4-sphere together with an instanton-type idempotent is obtained as a suspension of the Jordanian quantum group .
An improved formulation of axioms for quantum mechanics
An infinite level atom coupled to a heat bath.
An infinite torus braid yields a categorified Jones-Wenzl projector
A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.
An interpretation of the Vakulenko-Kapitanskiĭ estimate.
An introduction to algebraic K-theory
This paper gives an exposition of algebraic K-theory, which studies functors , an integer. Classically introduced by Bass in the mid 60’s (based on ideas of Grothendieck and others) and introduced by Milnor [Introduction to algebraic K-theory, Annals of Math. Studies, 72, Princeton University Press, 1971: Zbl 0237.18005]. These functors are defined and applications to topological K-theory (Swan), number theory, topology and geometry (the Wall finiteness obstruction to a CW-complex being finite,...
An introduction to quantum annealing
Quantum annealing, or quantum stochastic optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by quantum annealing....