Many-body ground state localization and coexistence of localized and extended states in an interacting quasiperiodic system

We study the localization problem of one-dimensional interacting spinless fermions in an incommensurate optical lattice, which changes from an extended phase to a nonergoic many-body localized phase by increasing the strength of the incommensurate potential. We identify that there exists an intermediate regime before the system enters the many-body localized phase, in which both the localized and extended many-body states coexist, thus the system is divided into three different phases, which can be characterized by normalized participation ratios of the many-body eigenstates and distributions of natural orbitals of the corresponding one-particle density matrix. This is very different from its noninterating limit, in which all eigenstaes undergo a delocaliztion-localization transtion when the strength of the incommensurate potential exceeds a critical value.Comment: 5 pages, 6 figure

To Copy Verbatim, Paraphrase or Summarize:Listeners’ Methods of Discourse Representation While Recalling Academic Lectures

It is unanimously agreed that comprehension of academic lectures is cognitively demanding; however, few studies have focused on a listener’s real-time discourse representation of a lecture. Based on the qualitative analysis of the verbal protocols, the present study investigated sixteen Chinese university students’ verbal recall of an academic mini-lecture to explore how they made sense of the lecture and represented its discourse when they recalled it episode by episode, and to what extent they differed in discourse representation. The results show that listeners’ discourse representation involved a range of cognitive processes such as paraphrasing, summarizing, and verbatim copying. Paraphrasing and summarizing were the main methods of discourse representation used by the participants when they verbally recalled the lecture. Those who correctly paraphrased more idea units recalled more content of the lecture. They were able to select and retain more idea units in their short-term memory, build more associations between the selected idea units, integrate them with the existing discourse structures and ensure contextual coherence in the construction of the local discourse structures. The findings of the study contribute to a better understanding of how listeners comprehend academic lectures and confirm that improving students’ paraphrasing skills and hierarchical discourse construction in recall are conducive to better comprehension of academic lectures.<br/

Dirichlet Boundary Value Problems for Second Order pp-Laplacian Difference Equations

In this paper, the solutions to second order Dirichlet boundary value problems of $p$-Laplacian difference equations are investigated. By using critical point theory, existence and multiplicity results are obtained. The proof is based on the Mountain Pass Lemma in combination with variational techniques