Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles

The EPRB experiment with massive partcles can be formulated if one defines spin in a relativistic way. Two versions are discussed: The one using the spin operator defined via the relativistic center-of-mass operator, and the one using the Pauli-Lubanski vector. Both are shown to lead to the SAME prediction for the EPRB experiment: The degree of violation of the Bell inequality DECREASES with growing velocity of the EPR pair of spin-1/2 particles. The phenomenon can be physically understood as a combined effect of the Lorentz contraction and the Moller shift of the relativistic center of mass. The effect is therefore stronger than standard relativistic phenomena such as the Lorentz contraction or time dilatation. The fact that the Bell inequality is in general less violated than in the nonrelativistic case will have to be taken into account in tests for eavesdropping if massive particles will be used for a key transfer.Comment: Figures added as appeared in PRA, two typos corrected (one important in the formula for eigenvector in Sec. IV); link to the unpublished 1984 paper containing the results (without typos!) of Sec. IV is adde

Refined Factorizations of Solvable Potentials

A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse and Coulomb potentials to obtain a wide set of raising and lowering operators, and to show clearly the connection that link these systems.Comment: 11 pages, LaTeX file, no figure

Superluminal X-shaped beams propagating without distortion along a coaxial guide

In a previous paper [Phys. Rev. E64 (2001) 066603; e-print physics/0001039], we showed that localized Superluminal solutions to the Maxwell equations exist, which propagate down (non-evanescence) regions of a metallic cylindrical waveguide. In this paper we construct analogous non-dispersive waves propagating along coaxial cables. Such new solutions, in general, consist in trains of (undistorted) Superluminal "X-shaped" pulses. Particular attention is paid to the construction of finite total energy solutions. Any results of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics, geophysics, etc.). [PACS nos.: 03.50.De; 41.20;Jb; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs; 46.40.Cd; 52.35.Lv. Keywords: Wave equations; Wave propagation; Localized beams; Superluminal waves; Coaxial cables; Bidirectional decomposition; Bessel beams; X-shaped waves; Maxwell equations; Microwaves; Optics; Special relativity; Coaxial metallic waveguides; Acoustics; Seismology; Mechanical waves; Elastic waves; Guided gravitational waves.]Comment: plain LaTeX file (22 pages), plus 15 figures; in press in Phys. Rev.

Covariant Uniform Acceleration

We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page

Existence of positive representations for complex weights

The necessity of computing integrals with complex weights over manifolds with a large number of dimensions, e.g., in some field theoretical settings, poses a problem for the use of Monte Carlo techniques. Here it is shown that very general complex weight functions P(x) on R^d can be represented by real and positive weights p(z) on C^d, in the sense that for any observable f, _P = _p, f(z) being the analytical extension of f(x). The construction is extended to arbitrary compact Lie groups.Comment: 9 pages, no figures. To appear in J.Phys.

Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians

The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides analytic solutions, or which can be treated with more general spectrum generating algebraic methods. We find dynamical symmetries for which we derive the transfer matrices and dispersion relations. Both compact and non-compact groups are found to play a role.Comment: 4 pages + 2 figs. Revtex/epsf. To appear: Phys Rev Lett, v.83 199

Generation of single-mode SU(1,1) intelligent states and an analytic approach to their quantum statistical properties

We discuss a scheme for generation of single-mode photon states associated with the two-photon realization of the SU(1,1) algebra. This scheme is based on the process of non-degenerate down-conversion with the signal prepared initially in the squeezed vacuum state and with a measurement of the photon number in one of the output modes. We focus on the generation and properties of single-mode SU(1,1) intelligent states which minimize the uncertainty relations for Hermitian generators of the group. Properties of the intelligent states are studied by using a ``weak'' extension of the analytic representation in the unit disk. Then we are able to obtain exact analytical expressions for expectation values describing quantum statistical properties of the SU(1,1) intelligent states. Attention is mainly devoted to the study of photon statistics and linear and quadratic squeezing.Comment: to appear in Quantum Semiclass. Opt., LaTeX, epsf style, 21 pages including 5 Postscript figures. More information on http://www.technion.ac.il/~brif/science.htm

Karakteristik Morfologi dan Distribusi Karbohidrat Netral pada Uterus Kelelawar Buah (Pteropus Vampyrus) Asal Pulau Timor

Timorese fruit bat(Pteropusvampyrus)is the only fly mammalian with its unique behavior which hanging upside down inspite of its pregnancy. This research is aimed to reveal the morphology of the Timorese fruit bats and the distribution of neutral carbohydrate within this organ. Three uterus samples derived from three different Timorese fruit bats were used in the research.Both macroscopical and microscopical examinations using H&E and PAS methods were applied. Macroscopically, Timorese fruit bats showedsoft reddish white duplex uterus. Meanwhile microscopically, endometrium consisted of epithelial layer and lamina propria and was the place where simple tubular glands located. The epithelial layer comprised of simple cylindric secretory cells and ciliated cells. Neutral carbohydrate distribution was seen within this epithelial layer. Myometrium was a thick circular smooth muscle layer which consisted of smooth muscle separated by collagen and elastic fibre. Perimetrium was a visceral layer and consisted of mesothelial cells

Shape Invariance and Its Connection to Potential Algebra

Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority of these potentials have also been shown to possess a potential algebra, and hence are also solvable by group theoretical techniques. In this paper, for a subset of solvable problems, we establish a connection between the two methods and show that they are indeed equivalent.Comment: Latex File, 10 pages, One figure available on request. Appeared in the proceedings of the workshop on "Supersymmetric Quantum Mechanics and Integrable Models" held at University of Illinois, June 12-14, 1997; Ed. H. Aratyn et a

SLˉ(4,R)\bar{SL}(4,R) Embedding for a 3D World Spinor Equation

A generic-curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the $\bar{SL}(n,R)$ group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved by embedding $\bar{SL}(3,R)$ vector operator $X_{\mu}$, that plays a role of Dirac's $\gamma_{\mu}$ matrices, into $\bar{SL}(4,R)$. Decomposition of the unitary irreducible spinorial $\bar{SL}(4,R)$ representations gives rise to an explicit form of the infinite $X_{\mu}$ matrices