Symmetries of coupled harmonic oscillators

It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2)

Feynman's Decoherence

Gell-Mann's quarks are coherent particles confined within a hadron at rest, but Feynman's partons are incoherent particles which constitute a hadron moving with a velocity close to that of light. It is widely believed that the quark model and the parton model are two different manifestations of the same covariant entity. If this is the case, the question arises whether the Lorentz boost destroys coherence. It is pointed out that this is not the case, and it is possible to resolve this puzzle without inventing new physics. It is shown that this decoherence is due to the measurement processes which are less than complete.Comment: RevTex 15 pages including 6 figs, presented at the 9th Int'l Conference on Quantum Optics (Raubichi, Belarus, May 2002), to be published in the proceeding

The language of Einstein spoken by optical instruments

Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell's equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics is largely based on two-by-two matrices or $ABCD$ matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincar\'e sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations which correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.Comment: LaTex 8 pages, presented at the 10th International Conference on Quantum Optics (Minsk, Belarus, May-June 2004), to be published in the proceeding

Prediction of vertical bearing capacity of waveform micropile

This study proposes a predictive equation for bearing capacity considering the behaviour characteristics of a waveform micropile that can enhance the bearing capacity of a conventional micropile. The bearing capacity of the waveform micropile was analysed by a three-dimensional numerical model with soil and pile conditions obtained from the field and centrifuge tests. The load-transfer mechanism of the waveform micropile was revealed by the numerical analyses, and a new predictive equation for the bearing capacity was proposed. The bearing capacities of the waveform micropile calculated by the new equation were comparable with those measured from the field and centrifuge tests. This validated a prediction potential of the new equation for bearing capacity of waveform micropiles