We investigate the asymptotic behavior of solutions to a kinetic equation describing the evolution of particles subject to the sum of a fixed, confining, Hamiltonian, and a small, time-oscillating, perturbation. The equation also involves an interaction operator which acts as a relaxation in the energy variable. This paper aims at providing a classical counterpart to the derivation of rate equa...

Strong final state interaction (FSI) effects can play a central role in the Standard Model prediction of weak K → 2π matrix elements. Here, I discuss how FSI's affect the direct CP violation parameter ε ′ /ε by solving the Omnès problem for the necessary K → 2π amplitudes. The main results of this analysis have been reported in a previous paper 1 and are further discussed in Refs. 2,3. The resu...

This paper is devoted to the cubic nonlinear Schrödinger equation in a two dimensional waveguide with shrinking cross section of order ε. For a Cauchy data living essentially on the first mode of the transverse Laplacian, we provide a tensorial approximation of the solution ψε in the limit ε → 0, with an estimate of the approximation error, and derive a limiting nonlinear Schrödinger equation i...

It is essential to alter effective electromagnetic parameters of a material to enhance its response. In the present work, we propose a novel Left Hand Metamaterial (LHM) structure comprising double turn spiral resonator (DTSR) and capacitance loaded strips (CLS). This structure is numerically explored to examine the resonance and effective material parameters i.e. permeability and permittivity....

Abstract. In this paper we shall develop a theory of (extended) double shuffle relations of Euler sums which generalizes that of multiple zeta values (see Ihara, Kaneko and Zagier, Derivation and double shuffle relations for multiple zeta values. Compos. Math. 142 (2)(2006), 307–338). After setting up the general framework we provide some numerical evidence for our two main conjectures. At the ...

let a be a unital algebra over a field of characteristic zero. we show that every derivation from( ) n m a into its dual ( ) n m a ∗ is the sum of an inner derivation and a derivation induced by a derivationfrom a into a∗

We discuss a new estimate of ε/ε in the kaon system. The present approach is based on the evaluation of the hadronic matrix elements of the ∆S = 1 effective quark lagrangian by means of the chiral quark model, with the inclusion of meson one-loop renormalization and NLO Wilson coefficients. The estimate here reviewed is fully consistent with the ∆I = 1/2 selection rule in K → ππ decays, which i...

We present a recent analysis of ε′/ε in the 1/Nc expansion. We show that the 1/Nc corrections to the matrix element of Q6 are large and positive, indicating a ∆I = 1/2 enhancement similar to the one of Q1 and Q2 which dominate the CP conserving amplitude. This enhances the CP ratio and can bring the standard model prediction close to the measured value for central values of the parameters. Seve...

providing clear evidence for a non-zero ε/ε value. The theoretical status is instead more debated (see ref. [2] for a brief review). One of the problems that had to be faced during the past years has been that, while CP violation is born at a scale say O(MW ), the observables that enter in the game have to be estimated at a scale of O(MK) (see fig. 1). Changing the order of magnitude of the sca...

“I’ve never touched the hard stuff, only smoked grass a few times with the boys to be polite, and that’s all, though ten is the age when the big guys come around teaching you all sorts to things. But happiness doesn’t mean much to me, I still think life is better. Happiness is a mean son of a bitch and needs to be put in his place. Him and me aren’t on the same team, and I’m cutting him dead. I...