LEAPS-MPS: Investigating Emergent Gravity in Combinatorial Quantum Systems

LEAPS-MPS：研究组合量子系统中的涌现引力

• 批准号: 2138323
• 负责人: Kassahun Betre
• 金额: $ 17.21万
• 依托单位: San Jose State University Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2138323&HistoricalAwards=false
• 关键词: LEAPS; MPS; Investigating; Emergent; Gravity

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).This award funds the research activities of Professor Kassahun Betre at San Jose State University. Space and time are perhaps the most fundamental aspects of physical reality. However, a deeper explanation of their nature is still a mystery. Many possible approaches toward addressing this issue have been pursued in recent years; these are usually grouped under names such as String Theory, Loop Quantum Gravity, and Causal Dynamical Triangulation. As part of this project, Professor Betre will pursue a complementary approach called Emergent Background-Independent Quantum Gravity (EBIQG). This approach posits that the building blocks of space and time are certain quantum-mechanical relationships that can be expressed in the form of graphs. Within such an approach, space and time emerge only as macroscopic averages. Professor Betre will build numerical tools that simulate the statistical and thermodynamic properties of the graph-theoretic quantum systems, and construct a model for the emergence of dimension and geometry in a two-dimensional quantum gravity. This project is also envisioned to have significant broader impacts. San Jose State University is a minority-serving institution, and undergraduate and masters students participating in this research project will develop not only analytical research skills but also practical skills in conducting numerical simulations. This project will also provide these students the experience and confidence to succeed in STEM fields. More technically, this research will bring two important new directions to the field of EBIQG. First, it highlights the emergence of the uniform dimension of space itself as a starting point. A graph-theoretic generalization of the dimension of Euclidean space called inductive dimension is used as a dynamical quantity of the graph microstates that course-grains into the emergent dimension of smooth manifolds. Second, this research project models discretized space using all geometric graphs --- graph-theoretic analogues of triangulations of surfaces --- rather than just regular lattices and regular graphs. With this approach, the emergence of quantum gravity from the graph models appears as a degenerate zero- temperature ground state. Such research will therefore help to pave the way towards a concrete model for emergent integer dimension and geometry from a non-geometric graph-theoretic Hilbert space.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。该奖项资助圣何塞州立大学Kassahun berte教授的研究活动。空间和时间可能是物理现实中最基本的方面。然而，对其性质的更深层次解释仍然是一个谜。近年来，已经采取了许多可能的方法来解决这个问题；这些通常被归类为诸如弦理论、环量子引力和因果动态三角测量等名称。作为该项目的一部分，伯特教授将寻求一种补充方法，称为新兴背景无关量子引力（EBIQG）。这种方法假定空间和时间的构建块是某些量子力学关系，这些关系可以用图形的形式表示。在这种方法中，空间和时间只表现为宏观平均值。伯特教授将建立数值工具来模拟图论量子系统的统计和热力学性质，并为二维量子引力中维度和几何的出现构建一个模型。预计该项目还将产生更广泛的重大影响。圣何塞州立大学是一所为少数民族服务的大学，参与本研究项目的本科生和硕士生不仅要培养分析研究技能，还要培养进行数值模拟的实践技能。该项目还将为这些学生提供在STEM领域取得成功的经验和信心。从技术上讲，本研究将为EBIQG领域带来两个重要的新方向。首先，它突出了空间本身的统一维度作为起点的出现。利用欧几里得空间维数的一种图论推广——归纳维数作为图微态向光滑流形突现维的动态量。其次，本研究项目使用所有几何图来建模离散空间——曲面三角形的图论类似物——而不仅仅是规则格和规则图。用这种方法，量子引力在图模型中的出现表现为简并的零温度基态。因此，这样的研究将有助于为从非几何图论希尔伯特空间中出现的整数维和几何的具体模型铺平道路。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。