Times of arrival: Bohm beats Kijowski

We prove that the Bohmian arrival time of the 1D Schroedinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time. We derive an inequality relating the average Bohmian arrival time to the one of Kijowksi. We prove that the average Bohmian arrival time is less than Kijowski's one if and only if the wave packet leads to position probability backflow through x. Otherwise the two average arrival times coincide.Comment: 9 page

Natural History Of Atopic Disease In Early Childhood: Is Cord Blood IgE A Prognostic Factor?

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68008/2/10.1177_000992289203100411.pd

Diffraction in time of a confined particle and its Bohmian paths

Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial wavefunctions. In each case Bohmian trajectories of the particles are computed and also the mean arrival time at a given location is studied as a function of the initial state.Comment: 8 pages, 6 figure

A new approach to quantum backflow

We derive some rigorous results concerning the backflow operator introduced by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not compact. Thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator. From the position representation of the backflow operator we obtain a more efficient method to determine the backflow constant. Finally, detailed position probability flow properties of a numerical approximation to the (perhaps improper) wave function of maximal backflow are displayed.Comment: 12 pages, 8 figure

Time of Arrival from Bohmian Flow

We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity and monotonicity properties are established. We show that our detection probability improves and generalises earlier proposals by Leavens and McKinnon. The difference between the two notions is illustrated through application to a free wave packet.Comment: 18 pages, 8 figures, to appear in Journ. Phys. A; representation of ref. 5 improved (thanks to Rick Leavens

Demonstrating Advantages of Neuromorphic Computation: A Pilot Study

Neuromorphic devices represent an attempt to mimic aspects of the brain's architecture and dynamics with the aim of replicating its hallmark functional capabilities in terms of computational power, robust learning and energy efficiency. We employ a single-chip prototype of the BrainScaleS 2 neuromorphic system to implement a proof-of-concept demonstration of reward-modulated spike-timing-dependent plasticity in a spiking network that learns to play the Pong video game by smooth pursuit. This system combines an electronic mixed-signal substrate for emulating neuron and synapse dynamics with an embedded digital processor for on-chip learning, which in this work also serves to simulate the virtual environment and learning agent. The analog emulation of neuronal membrane dynamics enables a 1000-fold acceleration with respect to biological real-time, with the entire chip operating on a power budget of 57mW. Compared to an equivalent simulation using state-of-the-art software, the on-chip emulation is at least one order of magnitude faster and three orders of magnitude more energy-efficient. We demonstrate how on-chip learning can mitigate the effects of fixed-pattern noise, which is unavoidable in analog substrates, while making use of temporal variability for action exploration. Learning compensates imperfections of the physical substrate, as manifested in neuronal parameter variability, by adapting synaptic weights to match respective excitability of individual neurons.Comment: Added measurements with noise in NEST simulation, add notice about journal publication. Frontiers in Neuromorphic Engineering (2019

Bohmian trajectories and Klein's paradox

We compute the Bohmian trajectories of the incoming scattering plane waves for Klein's potential step in explicit form. For finite norm incoming scattering solutions we derive their asymptotic space-time localization and we compute some Bohmian trajectories numerically. The paradox, which appears in the traditional treatments of the problem based on the outgoing scattering asymptotics, is absent.Comment: 14 pages, 3 figures; minor format change

Bohmian arrival time without trajectories

The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wave function and its spatial derivative, both restricted to the boundary of the detector's spacetime volume, is derived for the general case, where the probability current at the detector's boundary may vary its sign.Comment: 20 pages, 12 figures; v2: reference added, extended introduction, published versio

A planar hybrid transceiving mixer at 76.5GHz for automotive radar applications

A growing number of applications for radar systems in automobiles demands for low-cost radar front-ends. A planar monostatic radar front-end is particularly suited for low cost applications as it uses only one antenna for transmission and reception and, thus, minimizes the needed chip area. Generally, in a standard homodyne radar a radio-frequency (RF) signal generated by an oscillator is used for both, the transmitted signal and the local oscillator (LO). Well controlled distribution of the input power between antenna and mixer is crucial. A transceiving mixer at 76.5GHz is presented, where this distribution is done by use of a rat-race coupler. In a conventional transceiver the oscillator signal is split into the transmitted and in the LO signal by a directional coupler. A second directional coupler is needed in order to merge the received and the LO signal at the mixer. In our design the purpose of splitting and merging the signals is realized with only one coupler. Elimination of the second coupler reduces losses significantly. The received signal is down-converted to the intermediate frequency (IF) by use of a balanced mixer. For small relative speed in a CW-Doppler-radar or short distance in a FMCWradar the IF is very small. Therefore 1/f noise is a significant value. In order to achieve good 1/f noise characteristics, Schottky diodes were used. The diodes were flip-chip bonded onto a microstrip circuit on a Al2O3 substrate. The assembled transceiver was measured on-waver. An input power of 7 dBm was applied. The measured output power was 3 dBm and the conversion loss 9 dB. A noise figure of 15.3 dB was measured at 100 kHz

Implications of Lorentz covariance for the guidance equation in two-slit quantum interference

It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wavefunction is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie-Bohm ones, such as crossing of the axis of symmetry.Comment: 27 pages including 6 pages of figure