Probing the electron-phonon coupling in ozone-doped graphene by Raman spectroscopy

We have investigated the effects of ozone treatment on graphene by Raman scattering. Sequential ozone short-exposure cycles resulted in increasing the $p$ doping levels as inferred from the blue shift of the 2$D$ and $G$ peak frequencies, without introducing significant disorder. The two-phonon 2$D$ and 2$D'$ Raman peak intensities show a significant decrease, while, on the contrary, the one-phonon G Raman peak intensity remains constant for the whole exposure process. The former reflects the dynamics of the photoexcited electrons (holes) and, specifically, the increase of the electron-electron scattering rate with doping. From the ratio of 2$D$ to 2$D$ intensities, which remains constant with doping, we could extract the ratio of electron-phonon coupling parameters. This ratio is found independent on the number of layers up to ten layers. Moreover, the rate of decrease of 2$D$ and 2$D'$ intensities with doping was found to slowdown inversely proportional to the number of graphene layers, revealing the increase of the electron-electron collision probability

From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is shown that if the perturbed harmonic oscillators with a homogeneous-{\it cubic} polynomial potential and with a homogeneous-{\it quartic} polynomial potentials admit the same BG-normalization up to degree-4 then both oscillators satisfy the Bertrand-Darboux integrability condition.Comment: 23 pages, LaTeX (iop.sty), typos and Appendix adde

New Universality of Lyapunov Spectra in Hamiltonian Systems

A new universality of Lyapunov spectra {\lambda_i} is shown for Hamiltonian systems. The universality appears in middle energy regime and is different from another universality which can be reproduced by random matrices in the following two points. One is that the new universality appears in a limited range of large i/N rather than the whole range, where N is degrees of freedom. The other is Lyapunov spectra do not behave linearly while random matrices give linear behavior even on 3D lattice. Quadratic terms with smaller nonlinear terms of potential functions play an intrinsic role in the new universality.Comment: 19 pages, 16 Encapsulated Postscript figures, LaTeX (100 kb

Mechanism of confinement in low-dimensional organic conductors

Confinement-deconfinement transition in quarter-filled two-coupled chains comprising dimerization, repulsive interactions and interchain hopping has been demonstrated by applying the renormalization group method to the bosonized Hamiltonian. The confinement given by the irrelevant interchain hopping occurs with increasing umklapp scattering which is induced by the dimerization leading to effectively half-filling. It is shown that the transition originates in a competition between a charge gap and the renormalized interchain hopping.Comment: 5 pages, 7 figures, Proc. CREST Int. Workshop, Nagoya 2000, submitted to J. Phys. Chem. Solid

Additional Constants of Motion for a Discretization of the Calogero--Moser Model

The maximal super-integrability of a discretization of the Calogero--Moser model introduced by Nijhoff and Pang is presented. An explicit formula for the additional constants of motion is given.Comment: 7 pages, no figure

Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property

We give an explicit formula for the solution to the initial value problem of the full symmetric Toda hierarchy. The formula is obtained by the orthogonalization procedure of Szeg\"{o}, and is also interpreted as a consequence of the QR factorization method of Symes \cite{symes}. The sorting property of the dynamics is also proved for the case of a generic symmetric matrix in the sense described in the text, and generalizations of tridiagonal formulae are given for the case of matrices with $2M+1$ nonzero diagonals.Comment: 13 pages, Latex

Phase decorrelation, streamwise vortices and acoustic radiation in mixing layers

Several direct numerical simulations were performed and analyzed to study various aspects of the early development of mixing layers. Included are the phase jitter of the large-scale eddies, which was studied using a 2-D spatially-evolving mixing layer simulation; the response of a time developing mixing layer to various spanwise disturbances; and the sound radiation from a 2-D compressible time developing mixing layer

On the Orbit Structure of the Logarithmic Potential

We investigate the dynamics in the logarithmic galactic potential with an analytical approach. The phase-space structure of the real system is approximated with resonant detuned normal forms constructed with the method based on the Lie transform. Attention is focused on the properties of the axial periodic orbits and of low order `boxlets' that play an important role in galactic models. Using energy and ellipticity as parameters, we find analytical expressions of several useful indicators, such as stability-instability thresholds, bifurcations and phase-space fractions of some orbit families and compare them with numerical results available in the literature.Comment: To appear on the Astrophysical Journa