Related papers: Sur le th\'eor\`eme KAM
In this paper, we present two infinite-dimensional KAM theorems with frequency-preserving for a nonresonant frequency of Diophantine type or even weaker. To be more precise, under a nondegenerate condition for an infinite-dimensional…
Recent NA48 results from detailed studies of $K_{L,S}\to \pi^+ \pi^- e^+ e^-$ and $K_S\to\pi^0 \gamma\gamma$ decay modes are presented. The results are based on the data collected with the NA48 detector at the CERN SPS during the 1998-199 9…
We examine an analytical expression for the survival probability for the time evolution of quantum decay to discuss a regime where quantum decay is nonexponential at all times. We find that the interference between the exponential and…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…
We present a concise review of the recent theoretical progress concerning the standard model calculations of the rare K_L -> pi^0 nu anti-nu, K^+ -> pi^+ nu anti-nu (gamma), anti-B -> X_s gamma, and anti-B -> X_s l^+ l^- decays. The current…
In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.
As a stable analogue of degenerations, we introduce the notion of stable degenerations for Cohen-Macaulay modules over a Gorenstein local algebra. We shall give several necessary and/or sufficient conditions for the stable degeneration.…
We consider one dimensional chains of interacting particles subjected to one dimensional almost-periodic media. We formulate and prove two KAM type theorems corresponding to both short-range and long-range interactions respectively. Both…
We review some new developments in the theoretical description of the processes K ->pi gamma gamma, K_L ->gamma l^+ l^-, K_L ->pi^0 e^+ e^- and K_L ->mu^+ mu^-.
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
In this paper we consider nonlinear Schrodinger systems with periodic boundary condition in high dimension. We establish an abstract infinite dimensional KAM theorem and apply it to the nonlinear Schrodinger equation systems with real…
A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. The explicitly integrable two level system is considered as an example. It is demonstrated that the error…
We find conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate $n$-state atom, where transitions are caused by an…
In this talk I describe work on computing non-leptonic matrix elements consistently with both long and short distance contributions included. On the simpler example of the $\pi^+$-$\pi^0$ mass difference I explain in detail the matching…
This review of CP violation focuses on the status of the subject and its likely future development through experiments in the Kaon system and with B-decays. Although present observations of CP violation are perfectly consistent with the CKM…
The purpose of this note is to prove the celebrated Discrete Renewal Theorem in a common special case. We use only very elementary methods from real analysis, rather than markov chain theory, complex analysis, or generating functions.…
In this paper we prove the existence and linear stability of full dimensional tori with subexponential decay for 1-dimensional nonlinear wave equation with external parameters, which relies on the method of KAM theory and the idea proposed…
In present paper, from the viewpoint of physical intuition we introduce a Hamiltonian system with multiscale rotation, which describes many systems, for example, the forced pendulum with fast rotation, weakly coupled $N$-oscillators with…
In this letter we examine a model recently proposed to produce phase synchronization [K. Wood et al, Phys. Rev. Lett. 96, 145701 (2006)] and we show that the onset to synchronization corresponds to the emergence of an intermittent process…
In this paper, we will prove the existence of full dimensional tori for 1-dimensional nonlinear Schr\"odinger equation \begin{eqnarray}\label{maineq0} \mathbf{i}u_{t}-u_{xx}+V*u+\epsilon f(x)|u|^{4}u=0,\…