Related papers: Sur le th\'eor\`eme KAM
That decoherence can take place in the presence of energy conservation seems to be a poorly known fact. That lack of knowledge has for example bedevilled the discussion of the "black hole information" problem. I present a simple model which…
This paper is concerned with the long time stability of KAM tori for a class of derivative nonlinear Schr\"odinger equations subjected to periodic boundary condition.
The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say,…
A detailed discussion based on exact calculations, possible in the non relativistic quark model, is given to show that there is no 1/m_Q term in the heavy quark expansion of totally integrated semileptonic decay rates. More generally, it is…
Using the q,p-deformed oscillators as basic generating system, we obtain diverse classes (which form distinct sectors of functional continua) of novel versions of q-deformed oscillators, all of which share the property of "accidental"…
Quantum annealing is an innovative idea and method for avoiding the increase of the calculation cost of the combinatorial optimization problem. Since the combinatorial optimization problems are ubiquitous, quantum annealing machine with…
This article explores minimum of an extremal in the variational problem with delay under the degeneracy of the Weierstrass condition. Here for study the minimality of extremal, variations of the Weierstrass type are used in two forms: in…
We, the KAMI (Kaons at the Main Injector) collaboration, express our interest to continue the experimental program of rare kaon decay physics at Fermilab using the Main Injector. KAMI's primary physics goals shall be: 1. The first detection…
Phases of elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, as obtained using decays of $B$ mesons to $\pi^+ \pi^-$, $\pi^\pm K^\mp$, and $\pi^+ K^0$ or $\pi^- \overline{K}^0$, are shown to have a class of discrete ambiguities. In…
A short overview of theoretical predictions for various kaon decays is presented. Particular attention is devoted to pure and radiative nonleptonic decays in the framework of Chiral Perturbation Theory. The relevance of KLOE's future…
We review some recent theoretical results on rare kaon decays. Particular attention is devoted to find Standard Model tests. This is theoretically easy in $K\to \pi \nu \bar{\nu}$, while a careful study of the long distance contributions is…
Invariant manifolds are of fundamental importance to the qualitative understanding of dynamical systems. In this work, we explore and extend MacKay's converse KAM condition to obtain a sufficient condition for the nonexistence of invariant…
We show how an initially prepared quantum state of a radiation mode in a cavity can be preserved for a long time using a feedback scheme based on the injection of appropriately prepared atoms. We present a feedback scheme both for optical…
The current status of the study of rare kaon decays is reviewed. Future prospects are discussed.
Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…
We prove reducibility of a class of quasi-periodically forced linear equations of the form \[ \partial_tu-\partial_x\circ (1+a(\omega t, x))u+\mathcal{Q}(\omega t)u=0,\quad x\in\mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z}, \] where $u=u(t,x)$, $a$…
We consider a conservative system with small periodic perturbations under the assumption that the divergence of the perturbed system is negative. The main theorems provide universal sufficient conditions for the existence and asymptotic…
We prove an abstract infinite dimensional KAM theorem, which could be applied to prove the existence and linear stability of small-amplitude quasi-periodic solutions for one dimensional forced Kirchhoff equations with periodic boundary…
This paper continues the discussion started in [CK19] concerning Arnold's legacy on classical KAM theory and (some of) its modern developments. We prove a detailed and explicit `global' Arnold's KAM Theorem, which yields, in particular, the…
Mirrorless lasing has been a topic of particular interest for about a decade due to promising new horizons for quantum science and applications. In this work, we review first-principles theory that describes this phenomenon, and discuss…