Related papers: Sur le th\'eor\`eme KAM
In quantum mechanics, accidental degeneracy refers to energy degeneracy that occurs coincidentally, without any protection by symmetry. Here, we prove a theorem stating that any two-fold degeneracy (accidental or not) in a quantum system is…
Quantum marking and quantum erasure are discussed for the neutral kaon system. Contrary to other two-level systems, strangeness and lifetime of a neutral kaon state can be alternatively measured via an "active" or a "passive" procedure.…
The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.
Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical…
In [G. Garcia-Calderon, J. L. Mateos, and M. Moshinsky, Phys. Rev. Lett. 74, 337 (1995)], the time evolution of the quantum decay of a state initially located within an interaction region of finite range was investigated. In particular, it…
In this paper we consider the nonlinear wave equation on the circle:\begin{equation} \nonumberu\_{tt} - u\_{xx} + m u = g(x,u), \quad t \in \mathbb{R},\: x \in \mathbb{S}^1,\end{equation}where $m \in [1,2]$ is a mass and $g(x,u)=4u^3+…
A brief review of current results on rare kaon decays, particularly the charged and neutral K-> pi nu nubar channels, is presented along with prospects for future measurements.
In this paper, we prove the existence of full dimensional invariant tori for a non-autonomous, almost-periodically forced nonlinear beam equation with a periodic boundary condition via KAM theory.
The decays $K \to \pi l^{+} l^{-}$, $K \to \pi \gamma \gamma $ and $K \to \pi \nu {\bar \nu}$ are investigated using the higher order terms of the chiral perturbation theory. The counterterms induced by strong, weak and electromagnetic…
This is a Comment on the Article ``Aging, phase ordering and conformal invariance'' by M.Henkel, M.Pleimling, C.Godr\`eche and J.M.Luck [Phys.Rev.Lett. 87, 265701 (2001)].
We solve a long-standing problem by enumerating the number of non-degenerate Desargues configurations. We extend the result to the more difficult case involving Desargues blockline structures in Section 8. A transparent proof of Desargues…
To make the illposedness argument more transparent the argument is rewritten to reduce the equation to the constant dispersion case. Minor errors are corrected. Accepted to the Proceedings of the AMS.
We present an experimental and numerical study of the effects of decoherence on a quantum system whose classical analogue has Kolmogorov-Arnol'd-Moser (KAM) tori in its phase space. Atoms are prepared in a caesium magneto-optical trap at…
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
A phase reference has been a standard requirement in continuous-variable quantum sensing and communication protocols. However, maintaining a phase reference is challenging due to environmental fluctuations, preventing quantum phenomena such…
Tensors are often studied by introducing preorders such as restriction and degeneration: the former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local…
We discuss quantum evolution of a decaying state in relation to a recent experiment of Katz et al. Based on exact analytical and numerical solutions of a simple model, we identify a regime where qubit retains coherence over a finite time…
Light scalar mesons are found to fit rather well a diquark-antidiquark description. The resulting nonet obeys mass formulae which respect, to a good extent, the OZI rule. OZI allowed strong decays are reasonably reproduced by a single…
We study several classical like properties of q-deformed nonlinear coherent states as well as nonclassical behaviours of q-deformed version of the Schrodinger cat states in noncommutative space. Coherent states in q-deformed space are found…
We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly…