118489944
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).
1673726
Symmetries Shared by the Poincaré Group and the Poincaré Sphere
Henri Poincare formulated the mathematics of Lorentz transformations, known as the Poincare group. He also formulated the Poincare sphere for polarization optics. It is shown that these two mathematical instruments can be derived from the two-by-two representations of the Lorentz group. Wigner’s little groups for internal space-time symmetries are studied in detail. While the particle mass is a Lorentz-invariant quantity, it is shown to be possible to address its variations in terms of the decoherence mechanism in polarization optics.
14939249
Coupled Harmonic Oscillators and Feynman's Rest of the Universe
According to Feynman, the universe consists of two parts - the system in which we are interested and the rest of the universe which our measurement process does not reach. Feynman then formulates the density matrix in terms of the observable world and the rest of the universe. It is shown that coupled harmonic oscillators can serve as an illustrative example for Feynman's ``rest of the universe.'' It is pointed out that this simple example has far-reaching consequences in many branches of physics, including statistical mechanics, measurement theory, information theory, thermo-field dynamics, quantum optics, and relativistic quantum mechanics. It is shown that our ignorance of the rest of the universe increases the uncertainty and entropy in the system in which we are interested.
668406
Quantization of electromagnetic fields in a circular cylindrical cavity
We present a quantization procedure for the electromagnetic field in a circular cylindrical cavity with perfectly conducting walls, which is based on the decomposition of the field. A new decomposition procedure is proposed; all vector mode functions satisfying the boundary conditions are obtained with the help of this decomposition. After expanding the quantized field in terms of the vector mode functions, it is possible to derive the Hamiltonian for this quantized system.
1320799
Wigner rotations and Iwasawa decompositions in polarization optics.
Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions. This is possible because the combined effects of rotation, phase-shift, and attenuation filters lead to transformation matrices of the six-parameter Lorentz group applicable to Jones vectors and Stokes parameters for polarized light waves. The symmetry transformations in special relativity lead to a set of experiments which can be performed in optics laboratories.
73571003
Time separation as a hidden variable to the Copenhagen school of quantum mechanics
The Bohr radius is a space‐like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time‐like separation linearly mixed with the Bohr radius. Indeed, the time‐separation is one of the essential variables in high‐energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman’s rest of the universe. It is noted first that Feynman’s Lorentz‐invariant differential equation for the bound‐state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two‐mode squeezed states in quantum optics, where both photons are observable,...
120238308
Subshell branching ratios of partial photoionization cross sections
119447142
Renormalization group analysis ofρ-meson properties at finite density
We calculate the density dependence of the $\rho$-meson mass and coupling constant($g_{\rho NN}$) for $\rho$-nucleon-nucleon vertex at one loop using the lagrangian where the $\rho$-meson is included as a dynamical gauge boson of a hidden local symmetry. From the condition that thermodynamic potential should not depend on the arbitrary energy scale, renormalization scale, one can construct a renormalization group equation for the thermodynamic potential and argue that the various renormalization group coefficients are functions of the density or temperature. We calculate the $\beta$-function for $\rho$-nucleon-nucleon coupling constant ($g_{\rho NN}$) and $\gamma$-function for $\rho$-meson mass ($\gamma_{m_\rho}$). We found that the $\rho$-meson mass and the coupling constant for $g_{\rho NN}$ drop as density increases in the low energy limit.
9733106
Microlensing Detections of Planets in Binary Stellar Systems
We demonstrate that microlensing can be used for detecting planets in binary stellar systems. This is possible because in the geometry of planetary binary systems, in which the planet orbits one of the binary components and the other binary star is located at a large distance, both planet and secondary companion produce perturbations in a common region around the planet-hosting binary star, and thus the signatures of both planet and binary companion can be detected in the light curves of high-magnification lensing events. We find that identifying planets in binary systems is optimized when the secondary is located within a certain range that depends on the type of the planet. The proposed method can detect planets with masses down to one-tenth of the Jupiter mass in binaries with separations 100 AU. These ranges of planet masses and binary separations are not covered by other methods, and thus microlensing would be able to make the planetary binary sample richer.
55217395
DESIGN OF INJECTION AND EXTRACTION BEAMLINES FOR THE ALPHA PROJECT
The ALPHA facility consists of an electron linac and an electron storage ring to provide uniform intense beams for radiation test, and it has a potential to be a future X-Ray source. The ring uses four dipoles from the Cooler Injection Synchrotron (CIS) [1], which was constructed for proton acceleration from 7 MeV to 240 MeV. The circumference of the ALPHA storage ring is 20 m, and its lattice has an adjustible momentum compaction factor by changing the field strength of a pair of gradient damping wigglers [2]. For the proof of working principles, we use a refurbished 20 MeV CLINAC as the injector. The CLINAC will be upgraded to a 50 MeV linac by the end of 2011. Two operation modes (debunching and accumulation modes) [3] are currently planned for the ALPHA facility. For the debunching mode, two magnetic kickers are located at symmetric positions with respect to the Lambertson magnet. When the magnetic kickers are turned at 24 mrad, the closed orbit of the storage ring passes through the Lambertson magnet, and thus the injected beam is extracted in a single pass. In this case, the storage ring can be considered as a big α– magnet for debunching. For the beam accumulation mode, the magnetic kicker’s power supply is designed to have 500 ns decay time (beam revolution time in ring is 66 ns). The closed orbit is gradually moved back to designed orbit during injection so that multi-turn accumulation can be achieved in this way. In this paper, we describe the design concepts of the injection and extraction beamlines to maximize beam transport and to satisfy desired beam properties.
119962841
Photoelectron angular distributions from the subshells of high-Z elements
Numerical predictions are obtained, within a relativistic multipole central-field approximation calculation, for the radial matrix elements and resulting angular distributions of photoelectrons ejected from inner through outer subshells of uranium and for photoelectron energies from near threshold (1 eV) to 100 keV. Some data are also presented for outer subshells of mercury. We confirm that for inner shells higher-multipole effects persist to low energies, while we find that for outer shells such effects become small. For uranium inner ns subshells the asymmetry parameter ..beta../sub n/s differs from its nonrelativistic value 2, but not more than 30% (for n .. epsilonp/sub 1/2/ and ns ..-->.. epsilonp/sub 3/2/ transitions for these inner shells are similar). For outer s subshells relativistic spin-orbit splittings cause large deviations from the nonrelativistic predictions which can be understood from the magnitudes, zeros, and splittings of the two radial matrix elements. For U 6p/sub 1/2/ and 6p/sub 3/2/, ..beta../sub 6p/ has the same qualitative features found in nonrelativistic calculations for outer p shells of other high-Z elements, but the angular distributions from the two states do differ in detail. Such differences in angular distributions of themore » photoelectrons from the two j substates of given l become smaller for inner p shells. For outer d and f subshells the asymmetry parameter oscillates with photoelectron energy in a manner similar to that found by Manson in nonrelativistic dipole d-subshell calculations, and no qualitatively important relativistic effects have been identified; this is due to the decrease of the fine-structure-splitting interval with increasing angular momentum.« less