Quantum dynamics and localization in fluctuating potentials

波动势中的量子动力学和局域化

• 批准号: 446279579
• 负责人: Professorin Dr. Barbara Drossel
• 金额: --
• 依托单位: Arbeitsgruppe Theorie komplexer Systeme
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/446279579?language=en
• 关键词: Quantum; dynamics; localization; fluctuating; potentials

Condensed matter theory treats atoms and electrons in finite-temperature media as objects with a limited spatial extension that remain spatially concentrated under time evolution. This is in contrast to what the Schrödinger equation for a system of many interacting particles predicts, where the interaction between the particles leads to the linear superposition of different many-particle states. The question of how to resolve this puzzle is closely related to the problem of interpreting quantum measurement, where time evolution leads to a stochastic localization of the measured particle such that one of the possible measurement outcomes is observed. In this proposal, we pursue the hypothesis that thermal fluctuations localize quantum particles in a finite-temperature system, with thermal fluctuations being modeled as a classically fluctuating potential. This is again motivated by condensed matter physics, where the influence of the environment beyond some short distance is usually treated as an external potential, i.e., as a classical potential.We therefore consider a one-dimensional lattice model for an electron in a spatiotemporally fluctuating potential. The Lindblad equation for the time evolution of the density matrix of the electron can be unravelled in terms of a stochastic equation for the wave function in many different ways, part of which lead to spatially localized wave functions, and part of which lead to spatially extended wave functions. In this project, we will (i) compare these different unravellings and evaluate the extent of localization and phase coherence of the respective wave functions (ii) include a feedback from the wave function on the potential, such that the time evolution becomes nonlinear in the wave function. We expect that this will lift the degeneracy between the different unravellings and lead to a dynamics where the wave function retains a limited spatial extension(iii) discuss the interesting philosophical issues arising from these investigations. These issues related to the interpretation of wave functions and density matrices, and to the relation between the quantum and classical world.

凝聚态物质理论将有限温度介质中的原子和电子视为具有有限空间扩展的物体，在时间演化中保持空间集中。这与由许多相互作用的粒子组成的系统的Schrödinger方程所预测的相反，在这个系统中，粒子之间的相互作用导致不同的多粒子状态的线性叠加。如何解决这个难题的问题与解释量子测量的问题密切相关，在量子测量中，时间演化导致被测量粒子的随机定位，从而观察到可能的测量结果之一。在这个提议中，我们追求热涨落在有限温度系统中的量子粒子局域化的假设，热涨落被建模为经典的涨落势。这又是由凝聚态物理引起的，在凝聚态物理中，超出一定短距离的环境影响通常被视为外部势，即作为经典势。因此，我们考虑一个一维晶格模型的电子在一个时空波动的势。电子密度矩阵的时间演化的Lindblad方程可以用波函数的随机方程以许多不同的方式展开，其中一部分导致空间局域波函数，一部分导致空间扩展波函数。在这个项目中，我们将(i)比较这些不同的解开并评估各自波函数的局部化和相位相干性的程度（ii）包括波函数对势的反馈，使得波函数中的时间演化成为非线性的。我们期望这将解除不同展开之间的简并并导致波函数保持有限空间扩展的动力学（iii）讨论从这些研究中产生的有趣的哲学问题。这些问题涉及波函数和密度矩阵的解释，以及量子世界和经典世界之间的关系。