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Consistent Mori-Projector Theory in Two Dimensions

二维一致森投影理论

基本信息

批准号：
EP/N009428/1
负责人：
Michael Hartmann
金额：
$ 12.69万
依托单位：
Heriot-Watt University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2015
资助国家：
英国
起止时间：
2015 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FN009428%2F1
关键词：
Consistent Mori Projector Theory Two

项目摘要

Quantum many-body systems are traditionally studied in thermal equilibrium where the methodology of statistical mechanics has proven very successful in describing them. In recent years, an increasing number of experiments in diverse technologies including superconducting circuits, semiconductors and atomic Rydberg media are however giving rise to a new, largely unexplored class of quantum many-body systems with interacting particles in driven and dissipative, non-equilibrium regimes. These pose a new scientific challenge and thus generate a need to develop novel techniques that are capable of modelling them efficiently and accurately. I recently started to develop a new technique called consistent Mori Projectors (c-MoP) which derives coupled but non-linear equations of motion for the reduced density matrices of the subsystems of a many-body system and thus leads to an efficient description of local quantities. Starting from my promising initial results, I will in this project derive a powerful theory for the efficient description of two-dimensional systems in non-equilibrium scenarios that is based on the c-MoP concept. I expect this achievement to open up possibilities for modelling two-dimensional quantum many-body systems that hitherto defy a tractable but accurate description. As first applications that exploit these new possibilities I will employ the developed techniques for calculating stationary states and their phase diagram for driven-dissipative Bose-Hubbard and Jaynes-Cummings-Hubbard models, which play a central role among driven-dissipative quantum many-body systems. The results of the project will provide a basis for my future research plans and and will lay foundations for future technologies that exploit quantum effects.

量子多体系统传统上是在热平衡中研究的，统计力学的方法论已经被证明在描述它们方面非常成功。然而，近年来，包括超导电路、半导体和原子里德堡介质在内的各种技术中越来越多的实验正在产生一种新的、基本上未被探索的量子多体系统，其相互作用的粒子处于驱动和耗散的非平衡状态。这些都提出了新的科学挑战，因此需要开发能够有效和准确地对它们进行建模的新技术。我最近开始开发一种名为一致Mori投影(c-MOP)的新技术，它为多体系统的子系统的约化密度矩阵推导出耦合的非线性运动方程，从而导致对局域量的有效描述。从我有希望的初步结果出发，我将在这个项目中推导出一个强大的理论，用于在非平衡场景中有效地描述二维系统，它是基于c-MOP概念的。我期待这一成就为二维量子多体系统的建模开辟了可能，到目前为止，这种系统还无法用简单但准确的描述来描述。作为利用这些新可能性的第一个应用，我将使用开发的技术来计算驱动耗散Bose-Hubbard和Jaynes-Cummings-Hubbard模型的驻定态及其相图，这两个模型在驱动耗散量子多体系统中扮演着核心角色。该项目的结果将为我未来的研究计划提供基础，并将为未来利用量子效应的技术奠定基础。