Non-adiabatic optomechanical Hamiltonian of a moving dielectric membrane in a cavity

We formulate a non-relativistic Hamiltonian in order to describe the interaction between a moving dielectric membrane and radiation pressure. Such a Hamiltonian is derived without making use of the single-mode adiabatic approximation, and hence it enables us to incorporate multi-mode effects in cavity optomechanics. By performing second quantization, we show how a set of generalized Fock states can be constructed to represent quantum states of the membrane and cavity field. In addition, we discuss examples showing how photon scattering among different cavity modes would modify the interaction strengths and the mechanical frequency of the membrane

Language as a Geometry in Wittgenstein"s Tractatus

In TLP 4.011, while admitting that propositions expressed by the phonetic notation, or the alphabet, just like the written notes of a piece of music, do not seem at first sight to be pictures of what they represent, the Tractatus insists that those "sign-languages" (that is, the phonetic notation and the written musical notes) prove to be pictures of what they represent (that is, our speech and the piece of music, respectively) "even in the ordinary sense". (TLP 4.016 also says that "alphabetic script developed out of [hieroglyphic script] without losing what was essential to depiction".) So, contrary to the view of some commentators (e.g. Pears 1987, 115-121), instead of making an analogy here, the Tractatus holds that a proposition is a picture literally. How can a proposition be a picture literally

Charm Lifetimes and Mixing

A review of the latest results on charm lifetimes and D-mixing is presented. The e+e- collider experiments are now able to measure charm lifetimes quite precisely, however comparisons with the latest results from fixed-target experiments show that possible systematic effects could be evident. The new D-mixing results from the B-factories have changed the picture that is emerging. Although the new world averaged value of y_CP is now consistent with zero, there is still a very interesting and favoured scenario if the strong phase difference between the Doubly-Cabibbo-suppressed and the Cabibbo-flavoured D0 -> Kpi decay is large.Comment: Presented at the 9th International Symposium on Heavy Flavors, Caltech, Pasadena, 10-13 Sept. 2001. To appear in proceeding

A lower bound for the decoder error probability of the linear MDS code

A lower bound for the decoder error probability (P sub E (u)) of a linear maximum distance separable (MDS) code is derived by counting the dominant types of decoding words around code words. It is shown that the lower bound derived is similar in form, and close numerically, to the upper bound derived

On the decoder error probability of linear codes

By using coding and combinatorial techniques, an approximate formula for the weight distribution of decodable words of most linear block codes is evaluated. This formula is then used to give an approximate expression for the decoder error probability P(sub E)(u) of linear block codes, given that an error pattern of weight u has occurred. It is shown that P(sub E)(u) approaches the constant Q as u gets large, where Q is the probability that a completely random error pattern will cause decoder error

A labeling procedure for linear finite-state codes

A method to define the labels of the state diagram of a linear finite-state code is presented and investigated. This method is particularly suitable for simple hardware implementation since it simplifies the encoder structure. The method can also be applied to the labeling of a state diagram that is not completely connected to obtain a linear finite state code with larger free distance

Probing Contact Interactions at High Energy Lepton Colliders

Fermion compositeness and other new physics can be signalled by the presence of a strong four-fermion contact interaction. Here we present a study of $\ell\ell qq$ and $\ell\ell\ell'\ell'$ contact interactions using the reactions: $\ell^+ \ell^- \to \ell'^+\ell'^-,b\bar b, c\bar c$ at future $e^+e^-$ linear colliders with $\sqrt s=0.5-5$ TeV and $\mu^+\mu^-$ colliders with $\sqrt s=0.5,4$ TeV. We find that very large compositeness scales can be probed at these machines and that the use of polarized beams can unravel their underlying helicity structure.Comment: 12 pg, to appear in the {\it Proceedings of the 1996 DPF/DPB Summer Study on New Directions for High Energy Physics - Snowmass96}, Snowmass, CO, 25 June - 12 July, 199

Electron and muon parameters of EAS and the composition of primary cosmic rays in 10(15) to approximately 10(16) eV

Estimation of the relative intensities of protons and heavy nuclei in primary cosmic rays in the energy region 10 to the 15th power approx. 10 to the 17th power eV, was done by a systematic comparison between all available observed data on various parameters of extensive air showers (EAS) and the results of simulation. The interaction model used is an extrapolation of scaling violation indicated by recent pp collider results. A composition consisting of various percentages of Fe in an otherwise pure proton beam was assumed. Greatest overall consistency between the data and the simulation is found when the Fe fraction is in the region of 25%