Related papers: Higher-order perturbation theory for highly-improv…
We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
We discuss a program for replacing standard perturbative methods with Monte Carlo simulations in short distance lattice gauge theory calculations.
A new method of estimating higher order perturbative coefficients is discussed. It exploits the rapid, asymptotic growth of perturbative coefficients and the information on the singularities in the complex Borel plane. A comparison with…
A theoretical framework is presented to treat hadronic observables within analytic perturbative QCD beyond the leading order of the coupling and for more than one single large momentum scale. The approach generalizes and extends the…
We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with…
The `strong-coupling' perturbation theory over the inverse interaction constant $1/g$ near the nontrivial solution of Lagrange equation is formulated. The ordinary `week-coupling' perturbation theory over $g$ is described also to compare…
We extend the Fermilab formalism for heavy quarks to develop a more improved action. We give results of matching calculations of the improvement couplings at tree level. Finally, we estimate the discretization errors associated with the new…
Conventionally, data driven identification and control problems for higher order dynamical systems are solved by augmenting the system state by the derivatives of the output to formulate first order dynamical systems in higher dimensions.…
First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
Recent years have witnessed the rise of compositional semantics as a foundation for formal verification of complex systems. In particular, interaction trees have emerged as a popular denotational semantics. Interaction trees achieve…
A linear output feedback control scheme is developed for a coupled map lattice system. H-infinity control theory is used to make the scheme local: both the collection of information and the feedback are implemented through an array of…
A first order trace formula is obtained for a higher-order differential operator on a segment in the case where the perturbation is an operator of multiplication by a finite complex-valued measure. For the operators of even order $n\ge4$ a…
The equivalence between integral-chain differentiator and usual high-gain differentiator is given under suitable coordinate transformation. Integral-chain differentiator can restrain noises more thoroughly than usual high-gain linear…
I give a survey of recent progress in our understanding of QCD at high density and temperature. I pay particular attention to color superconductivity, applications of lattice gauge theory at nonzero density as well as high temperature,…
An effective way to design structured coherent wave interference patterns that builds on the theory of coherent lattices, is presented. The technique combines prime number factorization in the complex plane with moir\'e theory to provide a…
Effective Quantum Field Theories and QCD Lattice methods have become more and more complementary and mutually supportive in the study of Hard Probes. I present some of the progress that this alliance already delivered and I discuss future…
As an explicit example of HQET, we construct correlation functions containing a heavy-light axial current, both in the static approximation and in full QCD. This enables us to investigate the size of finite mass effects. As we use the…
Higher structures - infinity algebras and other objects up to homotopy, categorified algebras, `oidified' concepts, operads, higher categories, higher Lie theory, higher gauge theory... - are currently intensively investigated in…