Non-equilibrium dynamics and single-particle spectral functions in low-dimensional fermion systems

点击翻译按钮获取中文摘要

This proposal targets the exploration of dynamical processes in strongly correlated quantum matter. To this end I will study interacting electrons in low dimensional geometries. The properties of these electrons will be analyzed numerically and analytically in real space and real time. The aspired results will provide new insights into how power and quantum information is distributed in matter and therefore be highly relevant for the development of future quantum devices. Low-dimensional electron systems exhibit a number of intriguing correlation effects. In one dimension, for example, Luttinger liquid theory predicts the remarkable phenomenon of separate spin- and charge-density waves as the fundamental low-energy excitations. The enormous progress in the experimental realization of low-dimensional systems of the last years has in many cases gone hand in hand with precise theoretical predictions. This overall picture will be further completed in this project.A focus of current interest is the dynamics of strongly correlated systems out of equilibrium. Recently, experimentalists with ultra-cold gases impressively succeeded to observe an isolated quantum system far away from equilibrium. However, from the theory point of view to fully understand the dynamical processes in non-equilibrium the entire spectrum of excitations has to be known, a challenge that is far beyond the present state of knowledge. The extension of the Luttinger liquid theory by a mobile impurity, though, enables the calculation of the single-particle spectral function at higher energies. Additionally, the advent of efficient algorithms allows for numerically tracking the time dependence of observables in one dimension. I will use both methods to answer fundamental open questions on one-dimensional systems of interacting fermions in non-equilibrium. How do the spin- and charge density waves in ultra-cold gases evolve in time after a local single-particle excitation? This problem will also be generalized to two-dimensional systems. How does the system evolve if at some initial time the particle density of one spin direction is locally projected onto zero? What are the characteristics of the local single-particle spectral function at higher energies?