70 research outputs found
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 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
- …