Related papers: Sur le th\'eor\`eme KAM
The quantum-mechanical consideration of a passage of fast dimesoatoms through matter is given. A set of quantum-kinetic equations for the density matrix elements describing their internal state evolution is derived. It is shown that…
The lack of information obtained from informationally incomplete quantum measurements can prevent the detection of quantum resources, such as optical nonclassicality. We develop a technique that overcomes this limitation for single-mode…
Let M be a CR manifold of hypersurface type, which is Levi degenerate but also satisfying a k-nondegeneracy condition at all points. This might be only if dim M is greater than or equal to 5 and if dim M = 5, then k= 2 at all points. We…
This letter is the first report of the KL -> pi+- e-+ nu e+ e- decay. Based on 19208+-144 events, we determine the branching fraction, B(KL -> pi+- e-+ nu e+ e-; Mee > 5 MeV/c^2, E*ee > 30 MeV) = (1.285+-0.041)x10^-5, and Gamma(Ke3ee; Mee…
This version corrects a number of mistakes that appeared in the previous draft. In particular, the (EU-LREM) condition is sufficient for existence and uniqueness but not necessary, as we had claimed. We are grateful to P. C. B. Phillips and…
We develop an abstract KAM theorem for systems of infinitely many interacting particles with decaying masses and all-to-all interactions. Using this framework, we construct full-dimensional KAM tori for infinite-dimensional mechanical…
We show that radiation damage to unstained biological specimens is not an intractable problem in electron microscopy. When a structural hypothesis of a specimen is available, quantum mechanical principles allow us to verify the hypothesis…
Conditions for Bayesian posterior robustness have been examined in recent literature. However, many of the proofs seem to be long and complicated. In this paper, we first summarize some basic lemmas that have been applied implicitly or…
Recent results in and future prospects for the study of rare kaon decays are reviewed.
In this work, we show that the quantum coherence among non-degenerate energy subspaces (CANES) is essential for the energy flow in any quantum system. CANES satisfies almost all of the requirements as a coherence measure, except that the…
In the present paper, we will discuss the following non-degenerate Hamiltonian system \begin{equation*} H(\theta,t,I)=\frac{H_0(I)}{\varepsilon^{a}}+\frac{P(\theta,t,I)}{\varepsilon^{b}}, \end{equation*} where…
In this paper, we generalize weak KAM theorem from positive Lagrangian systems to "proper" Hamilton-Jacobi equations. We introduce an implicitly defined solution semigroup of evolutionary Hamilton-Jacobi equations. By exploring the…
In this talk I give the mini-review on recent development in the non-linear QCD (at low $x$).
$CP$ violation experiments, new measurements of the parameters of the neutral \K\ system and searches for rare decays are summarized. Perspectives for the near future are presented.
For Hamiltonian systems with degeneracy of any higher order, we study the persistence of resonant invariant tori, which as some lower-dimensional invariant tori might be elliptic, hyperbolic or of mixed types. Hence we prove a quasiperiodic…
The paper presents a counterexample to the Hodge conjecture.
The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: indeed, the decay is initially quadratic, while at very large times…
I design a simple way of distinguishing non-orthogonal quantum states with perfect reliability using only quantum control-not gates in one condition. In this way, we can implement pure quantum communication in directly sending classical…
In a previous work of ours, the most general family of Kerr deformations -- admitting a Carter constant -- has been presented. This time a simple, necessary and sufficient condition in order for the aforementioned family to have a separable…
We define and describe the class of Quasi-T\"oplitz functions. We then prove an abstract KAM theorem where the perturbation is in this class. We apply this theorem to a Non-Linear-Scr\"odinger equation on the torus $T^d$, thus proving…