Orbital motion effects in astrometric microlensing

We investigate lens orbital motion in astrometric microlensing and its detectability. In microlensing events, the light centroid shift in the source trajectory (the astrometric trajectory) falls off much more slowly than the light amplification as the source distance from the lens position increases. As a result, perturbations developed with time such as lens orbital motion can make considerable deviations in astrometric trajectories. The rotation of the source trajectory due to lens orbital motion produces a more detectable astrometric deviation because the astrometric cross-section is much larger than the photometric one. Among binary microlensing events with detectable astrometric trajectories, those with stellar-mass black holes have most likely detectable astrometric signatures of orbital motion. Detecting lens orbital motion in their astrometric trajectories helps to discover further secondary components around the primary even without any photometric binarity signature as well as resolve close/wide degeneracy. For these binary microlensing events, we evaluate the efficiency of detecting orbital motion in astrometric trajectories and photometric light curves by performing Monte Carlo simulation. We conclude that astrometric efficiency is 87.3 per cent whereas the photometric efficiency is 48.2 per cent.Comment: 9 pages, 8 figures, accepted for publication in MNRA

Quantum trajectories for Brownian motion

We present the stochastic Schroedinger equation for the dynamics of a quantum particle coupled to a high temperature environment and apply it the dynamics of a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on the environmental memory time scale, in the mean, our result recovers the solution of the known non-Lindblad quantum Brownian motion master equation. A remarkable feature of our approach is its localization property: individual quantum trajectories remain localized wave packets for all times, even for the classically chaotic system considered here, the localization being stronger the smaller $\hbar$.Comment: 4 pages, 3 eps figure

Two charges on plane in a magnetic field: special trajectories

A classical mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and $(e_2, m_2)$ subject to a constant magnetic field perpendicular to a plane is considered. Special "superintegrable" trajectories (circular and linear) for which the distance between charges remains unchanged are indicated as well as their respectful constants of motion. The number of the independent constants of motion for special trajectories is larger for generic ones. A classification of pairs of charges for which special trajectories occur is given. The special trajectories for three particular cases of two electrons, (electron - positron), (electron - $\alpha$-particle) are described explicitly.Comment: 22 pages, 5 figure

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories are those conceived in a modified de Broglie-Bohm scheme and we note that identical classical and quantum trajectories for coherent states are obtained only in the present approach. The study is extended to Gazeau-Klauder and SUSY quantum mechanics-based coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller (PT) potential by solving for the trajectories numerically. For the coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the PT potential, though classical trajectories are not regained, a periodic motion results as t --> \infty.Comment: More example