We give an example of a geometry in which two metallic objects in vacuum experience a repulsive Casimir force. The geometry consists of an elongated metal particle centered above a metal plate with a hole. We prove that this geometry has a repulsive regime using a symmetry argument and confirm it with numerical calculations for both perfect and realistic metals. The system does not support stable levitation, as the particle is unstable to displacements away from the symmetry axis.

We present a method to compute Casimir forces in arbitrary geometries and for arbitrary materials based on the finite-difference time-domain ͑FDTD͒ scheme. The method involves the time evolution of electric and magnetic fields in response to a set of current sources, in a modified medium with frequency-independent conductivity. The advantage of this approach is that it allows one to exploit existing FDTD software, without modification, to compute Casimir forces. In this paper, we focus on the derivation, implementation choices, and essential properties of the time-domain algorithm, both considered analytically and illustrated in the simplest parallel-plate geometry.

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Quantum fluctuations give rise to van der Waals and Casimir forces that dominate the interaction between electrically neutral objects at sub-micron separations. Under the trend of miniaturization, such quantum electrodynamical effects are expected to play an important role in micro-and nano-mechanical devices. Nevertheless, utilization of Casimir forces on the chip level remains a major challenge because all experiments so far require an external object to be manually positioned close to the mechanical element. Here by integrating a forcesensing micromechanical beam and an electrostatic actuator on a single chip, we demonstrate the Casimir effect between two micromachined silicon components on the same substrate. A high degree of parallelism between the two near-planar interacting surfaces can be achieved because they are defined in a single lithographic step. Apart from providing a compact platform for Casimir force measurements, this scheme also opens the possibility of tailoring the Casimir force using lithographically defined components of non-conventional shapes.

We present a scheme for obtaining stable Casimir suspension of dielectric nontouching objects immersed in a fluid, validated here in various geometries consisting of ethanol-separated dielectric spheres and semi-infinite slabs. Stability is induced by the dispersion properties of real dielectric (monolithic) materials. A consequence of this effect is the possibility of stable configurations (clusters) of compact objects, which we illustrate via a "molecular" two-sphere dicluster geometry consiting of two bound spheres levitated above a gold slab. Our calculations also reveal a strong interplay between material and geometric dispersion, and this is exemplified by the qualitatively different stability behavior observed in planar versus spherical geometries.

Citation McCauley, Alexander P. et al. "Casimir forces in the time domain: Applications." Physical Review A 81.1 (2010): 012119.Our previous article [Phys. Rev. A 80, 012115 (2009)] introduced a method to compute Casimir forces in arbitrary geometries and for arbitrary materials that was based on a finite-difference time-domain (FDTD) scheme. In this article, we focus on the efficient implementation of our method for geometries of practical interest and extend our previous proof-of-concept algorithm in one dimension to problems in two and three dimensions, introducing a number of new optimizations. We consider Casimir pistonlike problems with nonmonotonic and monotonic force dependence on sidewall separation, both for previously solved geometries to validate our method and also for new geometries involving magnetic sidewalls and/or cylindrical pistons. We include realistic dielectric materials to calculate the force between suspended silicon waveguides or on a suspended membrane with periodic grooves, also demonstrating the application of perfectly matched layer (PML) absorbing boundaries and/or periodic boundaries. In addition, we apply this method to a realizable three-dimensional system in which a silica sphere is stably suspended in a fluid above an indented metallic substrate. More generally, the method allows off-the-shelf FDTD software, already supporting a wide variety of materials (including dielectric, magnetic, and even anisotropic materials) and boundary conditions, to be exploited for the Casimir problem.

We propose a method of achieving large temperature T sensitivity in the Casimir force that involves measuring the stable separation between dielectric objects immersed in a fluid. We study the Casimir force between slabs and spheres using realistic material models, and find large >2 nm=K variations in their stable separations (hundreds of nanometers) near room temperature. In addition, we analyze the effects of Brownian motion on suspended objects, and show that the average separation is also sensitive to changes in T. Finally, this approach also leads to rich qualitative phenomena, such as irreversible transitions, from suspension to stiction, as T is varied. DOI: 10.1103/PhysRevLett.105.060401 PACS numbers: 12.20.Ds, 42.50.Lc Casimir forces between macroscopic objects arise from thermodynamic electromagnetic fluctuations, which persist even in the limit of zero temperature due to quantummechanical effects (the Bose-Einstein distribution of the photon fluctuations) [1]. In most vacuum-separated geometries, such as parallel metal plates, the force is attractive and decaying as a function of plate-plate separation [1], becoming readily observable at micron and submicron separations. For a nonzero temperature T, the force is predicted to change as a consequence of the changing photon thermal distribution, but this change is typically negligible near room temperature and submicron separations [2,3] and is only a few percent for $100 K changes in T at 1-2 m separations where Casimir forces are barely observable [2][3][4]. Therefore, despite theoretical interest in these T effects [2,5], it has proven difficult for experiments to unambiguously observe T corrections to the Casimir force [4]. Other attempts to measure T Casimir corrections have focused on nonequilibrium situations that differ conceptually from forces due purely to equilibrium fluctuations [6]. A clear experimental verification of a T Casimir correction would be important in order to further validate the foundation of Lifshitz theory for Casimir effects [2,3].In this Letter, we propose a method for obtaining strongly temperature-dependent Casimir effects by exploiting geometries involving fluid-separated dielectric objects (with separations in the hundreds of nanometers). In fluid-separated geometries, the Casimir force can be repulsive [1,7], and can even lead to stable suspensions of objects due to force-sign transitions from material dispersion [8,9] or gravity [9,10]. We show that, by a proper choice of materials or geometries, this stable separation d can depend dramatically on T (2 nm=K is easily obtainable), and there can even be transitions where d jumps discontinuously at some T. Essentially, a stable separation arises from a delicate cancellation of attractive and repulsive contributions to the force from fluctuations at different frequencies, and this cancellation is easily altered or upset by the T corrections. This appears to be the first prediction of a strong T-dependent Casimir phenomenon at submicron separations where Casimir effect...

As autonomous driving systems mature, motion forecasting has received increasing attention as a critical requirement for planning. Of particular importance are interactive situations such as merges, unprotected turns, etc., where predicting individual object motion is not sufficient. Joint predictions of multiple objects are required for effective route planning. There has been a critical need for highquality motion data that is rich in both interactions and annotation to develop motion planning models. In this work, we introduce the most diverse interactive motion dataset to our knowledge, and provide specific labels for interacting objects suitable for developing joint prediction models. With over 100,000 scenes, each 20 seconds long at 10 Hz, our new dataset contains more than 570 hours of unique data over 1750 km of roadways. It was collected by mining for interesting interactions between vehicles, pedestrians, and cyclists across six cities within the United States. We use a high-accuracy 3D auto-labeling system to generate high quality 3D bounding boxes for each road agent, and provide corresponding high definition 3D maps for each scene. Furthermore, we introduce a new set of metrics that provides a comprehensive evaluation of both single agent and joint agent interaction motion forecasting models. Finally, we provide strong baseline models for individualagent prediction and joint-prediction. We hope that this new large-scale interactive motion dataset will provide new opportunities for advancing motion forecasting models.