96 research outputs found
Wave Propagation in Random and Topological Media
This thesis discusses wave propagation in two kinds of systems, random media and topological insulators. In a disordered system, the wave is randomized by multiple scattering. The scattering matrix and associated delay times are powerful tools with which to describe wave transport. We discuss the relation among the Wigner time, the transmission time, and energy density in a lossless or lossy system. We propose the zeros of the transmission matrix and show how to manipulate the zero-transmission mode in a nonunitary system. In a photonic topological insulator, we realize an edge mode and discuss its robustness in the face of various types of disorder.
There is a powerful relation between time delay and the density of states (DOS) in a lossless system. The Wigner time equals the DOS in a reciprocal lossless system, which is one half the transmission time. It is therefore sufficient to measure the transmission matrix to obtain the DOS. There are two approaches to obtain the local DOS (LDOS), measuring the imaginary part of local Green’s function or calculating the sum of intensity when the sample is excited in all incoming channels with unit flux.
Here, we will discuss the relations between the time delay and the DOS in a nonunitary system. Although the dwell time no longer equals the DOS, we show using the Feshbach formalism that the energy excited by all incident channels can still be expressed as a superposition of Lorentzian lines related to the quasi-normal modes.
Based on the connection between the scattering matrix and the Green’s function, the determinants of both the scattering and reflection matrices can be expressed as a ratio of zeros and poles. In this work, we show that the determinant of the transmission matrix can also be expressed in terms of zeros and poles. We find the structure of the zeros in the complex energy plane. In a unitary reciprocal system, the zeros of transmission either fall on the real axis in the energy plane or appear as conjugate pairs symmetrically disposed relative to the real axis, This leads to the equivalence between transmission time and DOS. Loss or gain breaks the symmetry of zeros of transmission. Differences between the transmission time and the DOS is related to the positions of zeros. This allows us to realize zero-transmission in a random system. We predict that the average transmission time will decrease with increasing loss because more zeros of transmission would be pulled into the lower half of the complex plane.
We also study the edge mode at the interface between quantum-valley-Hall (QVH) and quantum-spin-Hall (QSH) systems. The counterpart of the QSH effect in a photonic system is realized experimentally in a 2D meta-waveguide. We demonstrate valley-dependent waveguiding in a system in which the edge mode is endowed with both the pseudo-spin and valley degrees of freedom. When the edge mode couples to a cavity in the bulk, we observe in experiments that the reflection effect is evident. Based on the coupled-mode theory, we estimate the reflection rate and explain the negative transmission time. We also find the statistics of time delay and find the modes of the medium in the analysis of the transmitted field and the field inside the medium in the presence of a coherent background
The Ethics of AI-Generated Maps: A Study of DALLE 2 and Implications for Cartography
The rapid advancement of artificial intelligence (AI) such as the emergence
of large language models including ChatGPT and DALLE 2 has brought both
opportunities for improving productivity and raised ethical concerns. This
paper investigates the ethics of using artificial intelligence (AI) in
cartography, with a particular focus on the generation of maps using DALLE 2.
To accomplish this, we first create an open-sourced dataset that includes
synthetic (AI-generated) and real-world (human-designed) maps at multiple
scales with a variety settings. We subsequently examine four potential ethical
concerns that may arise from the characteristics of DALLE 2 generated maps,
namely inaccuracies, misleading information, unanticipated features, and
reproducibility. We then develop a deep learning-based ethical examination
system that identifies those AI-generated maps. Our research emphasizes the
importance of ethical considerations in the development and use of AI
techniques in cartography, contributing to the growing body of work on
trustworthy maps. We aim to raise public awareness of the potential risks
associated with AI-generated maps and support the development of ethical
guidelines for their future use.Comment: 8 pages, 2 figures, GIScience 2023 conferenc
Dynamics of transmission in disordered topological insulators
Here we show in simulations of the Haldane model that pulse propagation in
disordered topological insulators is robust throughout the central portion of
the band gap where localized modes do not arise. Since transmission is robust
in topological insulators, the essential field variable is the phase of the
transmitted field, or, equivalently, its spectral derivative, which is the
transmission time. Except near resonances with bulk localized modes that couple
the upper and lower edges of a topological insulator, the transmission time in
a topological insulator is proportional to the density of states and to the
energy excited within the sample. The average transmission time is enhanced in
disordered TIs near the band edge and slightly suppressed in the center of the
band gap. The variance of the transmission time at the band edge for a random
ensemble with moderate disorder is dominated by fluctuations at resonances with
localized states, and initially scales quadratically. When modes are absent,
such as in the center of the band gap, the transmission time self-averages and
its variance scales linearly. This leads to significant sample-to-sample
fluctuations in the transmission time. However, because the transmission time
is the sum of contributions from the continuum edge mode, which stretches
across the band gap, and far-off-resonance modes near the band edge, there are
no sharp features in the spectrum of transmission time in the center of the
band gap. As a result, ultrashort, broadband pulses are faithfully transmitted
in the center of the band gap of topological insulators with moderate disorder
and bent paths. This allows for robust signal propagation in complex
topological metawaveguides for applications in high-speed optoelectronics and
telecommunications
LSTM-TrajGAN: A Deep Learning Approach to Trajectory Privacy Protection
The prevalence of location-based services contributes to the explosive growth of individual-level trajectory data and raises public concerns about privacy issues. In this research, we propose a novel LSTM-TrajGAN approach, which is an end-to-end deep learning model to generate privacy-preserving synthetic trajectory data for data sharing and publication. We design a loss metric function TrajLoss to measure the trajectory similarity losses for model training and optimization. The model is evaluated on the trajectory-user-linking task on a real-world semantic trajectory dataset. Compared with other common geomasking methods, our model can better prevent users from being re-identified, and it also preserves essential spatial, temporal, and thematic characteristics of the real trajectory data. The model better balances the effectiveness of trajectory privacy protection and the utility for spatial and temporal analyses, which offers new insights into the GeoAI-powered privacy protection
Transmission Zeros with Topological Symmetry in Complex Systems
Understanding vanishing transmission in Fano resonances in quantum systems and metamaterials and perfect and ultralow transmission in disordered media, has advanced the understanding and applications of wave interactions. Here we use analytic theory and numerical simulations to understand and control the transmission and transmission time in complex systems by deforming a medium and by adjusting the level of gain or loss. Unlike the zeros of the scattering matrix, the position and motion of the zeros of the determinant of the transmission matrix in the complex plane of frequency and field decay rate have robust topological properties. In systems without loss or gain, the transmission zeros appear either singly on the real axis or as conjugate pairs in the complex plane. As the structure is modified, two single zeros and a complex conjugate pair of zeros may interconvert when they meet at a square root singularity in the rate of change of the distance between the transmission zeros in the complex plane with sample deformation. The transmission time is the spectral derivative of the argument of the determinant of the transmission matrix. It is a sum over Lorentzian functions associated with the resonances of the medium, which is the density of states, and with the zeros of the transmission matrix. Transmission vanishes, and the transmission time diverges as zeros are brought near the real axis. Monitoring the transmission and transmission time when two zeros are close may open up new possibilities for ultrasensitive detection
- …