First Detected Arrival of a Quantum Walker on an Infinite Line.

Phys Rev Lett

Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.

Published: January 2018

The first detection of a quantum particle on a graph is shown to depend sensitively on the distance ξ between the detector and initial location of the particle, and on the sampling time τ. Here, we use the recently introduced quantum renewal equation to investigate the statistics of first detection on an infinite line, using a tight-binding lattice Hamiltonian with nearest-neighbor hops. Universal features of the first detection probability are uncovered and simple limiting cases are analyzed. These include the large ξ limit, the small τ limit, and the power law decay with the attempt number of the detection probability over which quantum oscillations are superimposed. For large ξ the first detection probability assumes a scaling form and when the sampling time is equal to the inverse of the energy band width nonanalytical behaviors arise, accompanied by a transition in the statistics. The maximum total detection probability is found to occur for τ close to this transition point. When the initial location of the particle is far from the detection node we find that the total detection probability attains a finite value that is distance independent.

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.120.040502DOI Listing

Publication Analysis

Top Keywords

detection probability
20
detection
8
initial location
8
location particle
8
sampling time
8
total detection
8
probability
5
detected arrival
4
quantum
4
arrival quantum
4

Similar Publications

While recent studies suggested a potential causal link between type 1 diabetes mellitus (T1DM) but not type 2 diabetes mellitus (T2DM) and idiopathic pulmonary fibrosis (IPF), the involved mechanism remains unclear. Here, using a Mendelian randomization (MR) approach, we verified the causal relationship between the two types of diabetes mellitus and IPF and investigated the possible role of inflammation in the association between diabetes mellitus and IPF. Based on genome-wide association study (GWAS) summary data of T1DM, T2DM, and IPF, the univariable MR, multivariable MR (MVMR), and mediation MR were successively used to analyze the causal relationship.

View Article and Find Full Text PDF

Chronic coronary artery disease (CAD) remains a significant global healthcare burden. Current risk assessment methods have notable limitations in early detection and risk stratification. Hence, there is an urgent need for innovative biomarkers that facilitate the premature CAD diagnosis, ultimately leading to reduction in associated morbidity and mortality rates.

View Article and Find Full Text PDF

Introduction: To interact with the environment, it is crucial to distinguish between sensory information that is externally generated and inputs that are self-generated. The sensory consequences of one's own movements tend to induce attenuated behavioral- and neural responses compared to externally generated inputs. We propose a computational model of sensory attenuation (SA) based on Bayesian Causal Inference, where SA occurs when an internal cause for sensory information is inferred.

View Article and Find Full Text PDF

Surface water plays a vital role in the spread of infectious diseases. Information on the spatial and temporal dynamics of surface water availability is thus critical to understanding, monitoring and forecasting disease outbreaks. Before the launch of Sentinel-1 Synthetic Aperture Radar (SAR) missions, surface water availability has been captured at various spatial scales through approaches based on optical remote sensing data.

View Article and Find Full Text PDF

Anomaly detection is crucial in areas such as financial fraud identification, cybersecurity defense, and health monitoring, as it directly affects the accuracy and security of decision-making. Existing generative adversarial nets (GANs)-based anomaly detection methods overlook the importance of local density, limiting their effectiveness in detecting anomaly objects in complex data distributions. To address this challenge, we introduce a generative adversarial local density-based anomaly detection (GALD) method, which combines the data distribution modeling capabilities of GANs with local synthetic density analysis.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!