arXiv subjects

Minjae Lee

Publications and source records attributed to Minjae Lee.

58 records · Page 4Linked to original sources

arXiv2016

Dirac cones for point scatterers on a honeycomb lattice

We investigate the spectrum and the dispersion relation of the Schrödinger operator with point scatterers on a triangular lattice and a honeycomb lattice. We prove that the low-level dispersion bands have conic singularities near Dirac points, which are the vertices of the first Brillouin Zone. The existence of such conic dispersion bands plays an important role in various electronic properties of honeycomb-structured materials such as graphene. We then prove that for a honeycomb lattice, the spectra generated by higher-level dispersion relations are all connected so the complete spectrum consists of at most three bands. Numerical simulations for dispersion bands with various parameters are also presented.

math-ph↗

arXiv2016

Eigenvalues of Šeba billiards with localization of low-energy eigenfunctions

We study the localization of eigenfunctions produced by a point scatterer on a thin rectangle. We find an explicit set of eigenfunctions localized to part of the rectangle by showing that the one-dimensional Schrödinger operator with a Dirac delta potential asymptotically governs the spectral properties of the two-dimensional point scatterer. We also find the rate of localization in terms of the aspect ratio of the rectangle. In addition, we present numerical results regarding the asymptotic behavior of the localization.

math-ph↗

arXiv2015

Online Keyword Spotting with a Character-Level Recurrent Neural Network

In this paper, we propose a context-aware keyword spotting model employing a character-level recurrent neural network (RNN) for spoken term detection in continuous speech. The RNN is end-to-end trained with connectionist temporal classification (CTC) to generate the probabilities of character and word-boundary labels. There is no need for the phonetic transcription, senone modeling, or system dictionary in training and testing. Also, keywords can easily be added and modified by editing the text based keyword list without retraining the RNN. Moreover, the unidirectional RNN processes an infinitely long input audio streams without pre-segmentation and keywords are detected with low-latency before the utterance is finished. Experimental results show that the proposed keyword spotter significantly outperforms the deep neural network (DNN) and hidden Markov model (HMM) based keyword-filler model even with less computations.

cs.CL↗

arXiv2015

Localization of low-energy eigenfunctions in Seba billiards

We investigate localization of low-energy modes of the Laplacian with a point scatterer on a rectangular plate. We observe that the point scatterer acts as a barrier confining the low-level modes to one side of the plate while assuming the Dirichlet boundary condition at a point does not induce this type of localization. This low-energy phenomenon extends to higher modes as we increase the eccentricity of the plate.

math-ph↗