Quantum dynamics and localization in fluctuating potentials

点击翻译按钮获取中文摘要

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.