A method to investigate many-body Liouvillian spectra beyond the steady state

Westhoff, Philipp (29. Oktober 2025): A method to investigate many-body Liouvillian spectra beyond the steady state. Masterarbeit, Fakultät für Physik, Ludwig-Maximilians-Universität München.

Abstract

Open quantum systems, where quantum dynamics is influenced by (non-)Markovian environments, have attracted increasing attention due to their rich physical properties. Understanding phenomena such as non-equilibrium phases, anomalous thermalization, and dissipative state preparation requires the knowledge of the low-lying eigenvalues and eigenstates of the Lindbladian. In this thesis, we introduce a framework that systematically computes not only steady states but also low-lying excited states in large, dissipative, interacting quantum many-body systems. The framework is based on tensor-network methods and utilizes recent advances in complex-time Krylov spaces. Extending these ideas to the challenging non-Hermitian eigenvalue problem ubiquitous in open quantum systems enables simulations at unprecedented Hilbert space dimensions. We employ the framework to analyze a dissipative state preparation protocol for Bose-Einstein condensates (BECs) on optical lattices. Analytical and numerical studies allow us to characterize the steady state and perform a finite-size scaling of the dissipative gap, uncovering strong evidence for non-linear hydrodynamics described by the Kardar-Parisi-Zhang universality class. Furthermore, we show analytically that the dissipative state preparation can be substantially accelerated via the quantum Mpemba effect. Our approach exploits weak symmetries to analytically identify a class of simple, experimentally realizable states that converge exponentially faster to the steady state than typical random initializations. Overall, this work establishes a versatile framework for the spectral analysis of generic open quantum many-body systems, enabling the analysis of complex collective phenomena and additionally paving the way toward faster dissipative preparation of highly entangled states in analog quantum simulators.

• Dokumententyp: LMU München: Studienabschlussarbeit
• Fakultät: Physik > Theoretische Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• Sprache: Englisch