Related papers: Registering Seconds with a Conic Clock
We consider a slow particle with wave function $\psi_t(\vec{x})$, moving freely in some direction. A mirror is briefly switched on around a time $T$ and its position is scanned. It is shown that the measured reflection probability then…
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points.…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
Physical systems are usually assumed to evolve relative to an external time parameter, which is problematic because in quantum theory that parameter is not a physical observable. Page & Wootters (1984) solved this by proposing that the…
Circular orbits of a particle sliding on a frictionless surface of revolution about a vertical axis are unstable below a critical radius if the curvature of the surface satisfies a specified condition. This behavior can be realized in a…
The Conley theory has a tool to guarantee the existence of periodic trajectories in isolating neighborhoods of semi-dynamical systems. We prove that the positive trajectories generated by a piecewise-smooth vector field $Z=(X, Y)$ defined…
We show that a particular noncommutative geometry, sometimes called angular or $\rho$-Minkowski, requires that the spectrum of time be discrete. In this noncommutative space the time variable is not commuting with the angular variable in…
The essence of the gravitomagnetic clock effect is properly defined showing that its origin is in the topology of world lines with closed space projections. It is shown that, in weak field approximation and for a spherically symmetric…
Spatially separated bodies in relative motion through vacuum experience a tiny friction force known as quantum friction. This force has so far eluded experimental detection due to its small magnitude and short range. Quantitative details…
Observation time is the key parameter for improving the precision of measurements of gravitational quantum states of particles levitating above a reflecting surface. We propose a new method of long confinement in such states of atoms,…
Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are…
Millisecond and binary pulsars are the most stable astronomical standards of frequency. They can be applied to solving a number of problems in astronomy and time-keeping metrology including the search for a stochastic gravitational wave…
Atom-like quantum systems in solids have been proposed as a compact alternative for atomic clocks, but realizing the potential of solid-state technology will requires an architecture design which overcomes traditional limitations such as…
We describe a low-cost system designed to monitor wander in digital clocks with a precision of $\le$ 1 ps. With this system we have shown that it is possible to track phase variations at the sub-picosecond level by adding noise to a…
We analyze spin squeezing via Rydberg dressing in optical lattice clocks with random fractional filling. We compare the achievable clock stability in different lattice geometries, including unity-filled tweezer clock arrays and fractionally…
We show that the sensitivity of an atomic clock can be enhanced below the shot-noise level by initially squeezing, and then measuring in output, the population of a single atomic level. This can simplify current experimental protocols which…
The circadian clocks keeping time of day in many living organisms rely on self-sustained biochemical oscillations which can be entrained by external cues, such as light, to the 24-hour cycle induced by Earth rotation. However, environmental…
Resonance capture is studied numerically in the three-body problem for arbitrary inclinations. Massless particles are set to drift from outside the 1:5 resonance with a Jupiter-mass planet thereby encountering the web of the planet's…
The flow of granular material in a rotating cylinder was simulated by molecular dynamics in two dimensions using spherical as well as nonspherical grains. At very low but constant angular velocity we found that the flow varies irregularly…
Time reversal symmetry is studied in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time reversal symmetry breaking in the space. On…