Governing dynamics by squeezing in a system of cold trapped ions

We consider a system of laser-cooled ions in a linear harmonic trap and study the phenomenon of squeezing exchange between their internal and motional degrees of freedom. An interesting relation between the quantum noise reduction (squeezing) and the dynamical evolution is found when the internal and motional subsystems are prepared in properly squeezed (intelligent) states. Specifically, the evolution of the system is fully governed by the relative strengths of spectroscopic and motional squeezing, including the phenomenon of total cancellation of the interaction when the initial squeezing parameters are equal.Comment: REVTeX, 5 pages, 2 figures, to appear in Phys. Rev.

Higher Dimensional Taub-NUTs and Taub-Bolts in Einstein-Maxwell Gravity

We present a class of higher dimensional solutions to Einstein-Maxwell equations in d-dimensions. These solutions are asymptotically locally flat, de-Sitter, or anti-de Sitter space-times. The solutions we obtained depend on two extra parameters other than the mass and the nut charge. These two parameters are the electric charge, q and the electric potential at infinity, V, which has a non-trivial contribution. We Analyze the conditions one can impose to obtain Taub-Nut or Taub-Bolt space-times, including the four-dimensional case. We found that in the nut case these conditions coincide with that coming from the regularity of the one-form potential at the horizon. Furthermore, the mass parameter for the higher dimensional solutions depends on the nut charge and the electric charge or the potential at infinity.Comment: 11 pages, LaTe

Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity

We present the exact solution of two-body motion in (1+1) dimensional dilaton gravity by solving the constraint equations in the canonical formalism. The determining equation of the Hamiltonian is derived in a transcendental form and the Hamiltonian is expressed for the system of two identical particles in terms of the Lambert $W$ function. The $W$ function has two real branches which join smoothly onto each other and the Hamiltonian on the principal branch reduces to the Newtonian limit for small coupling constant. On the other branch the Hamiltonian yields a new set of motions which can not be understood as relativistically correcting the Newtonian motion. The explicit trajectory in the phase space $(r, p)$ is illustrated for various values of the energy. The analysis is extended to the case of unequal masses. The full expression of metric tensor is given and the consistency between the solution of the metric and the equations of motion is rigorously proved.Comment: 34 pages, LaTeX, 16 figure

Research and development at ORNL/CESAR towards cooperating robotic systems for hazardous environments

One of the frontiers in intelligent machine research is the understanding of how constructive cooperation among multiple autonomous agents can be effected. The effort at the Center for Engineering Systems Advanced Research (CESAR) at the Oak Ridge National Laboratory (ORNL) focuses on two problem areas: (1) cooperation by multiple mobile robots in dynamic, incompletely known environments; and (2) cooperating robotic manipulators. Particular emphasis is placed on experimental evaluation of research and developments using the CESAR robot system testbeds, including three mobile robots, and a seven-axis, kinematically redundant mobile manipulator. This paper summarizes initial results of research addressing the decoupling of position and force control for two manipulators holding a common object, and the path planning for multiple robots in a common workspace

Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive

Phase space can be constructed for $N$ equal and distinguishable subsystems that could be (probabilistically) either {\it weakly} (or {\it "locally"}) correlated (e.g., independent, i.e., uncorrelated), or {\it strongly} (or {\it globally}) correlated. If they are locally correlated, we expect the Boltzmann-Gibbs entropy $S_{BG} \equiv -k \sum_i p_i \ln p_i$ to be {\it extensive}, i.e., $S_{BG}(N)\propto N$ for $N \to\infty$. In particular, if they are independent, $S_{BG}$ is {\it strictly additive}, i.e., $S_{BG}(N)=N S_{BG}(1), \forall N$. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy $S_q\equiv k [1- \sum_i p_i^q]/(q-1)$ (with $S_1=S_{BG}$) for some special value of $q\ne1$ to be the one which extensive (i.e., $S_q(N)\propto N$ for $N \to\infty$).Comment: 15 pages, including 9 figures and 8 Tables. The new version is considerably enlarged with regard to the previous ones. New examples and new references have been include

Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity

We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation, which leads to the exact Hamiltonian to infinite order of the gravitational coupling constant. In the equal mass case explicit expressions of the trajectories of the particles are given as the functions of the proper time, which show characteristic features of the motion depending on the strength of gravity (mass) and the magnitude and sign of the cosmological constant. As expected, we find that a positive cosmological constant has a repulsive effect on the motion, while a negative one has an attractive effect. However, some surprising features emerge that are absent for vanishing cosmological constant. For a certain range of the negative cosmological constant the motion shows a double maximum behavior as a combined result of an induced momentum-dependent cosmological potential and the gravitational attraction between the particles. For a positive cosmological constant, not only bounded motions but also unbounded ones are realized. The change of the metric along the movement of the particles is also exactly derived.Comment: 37 pages, Latex, 24 figure