Self-consistent projection operator theory for quantum many-body systems

2013/07/31 by Peter Degenfeld-Schonburg, Michael J. Hartmann · 7 citations
Mathematics · Physics and Astronomy · #Algorithm #Biology #Cold Atom Physics and Bose-Einstein Condensates #Mathematics #Operator (biology) #Physics #Projection (relational algebra) #Quantum #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #cond-mat.quant-gas #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1103/physrevb.89.245108

published as Phys. Rev. B 89, 245108 (2014) · 13 pages, 4 figures

openalex publication_date 2014/06/09 · arxiv created 2014/06/11 · arxiv updated 2014/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient analytical and numerical approach. Besides its practical use it provides an interpretation and systematic extension of mean-field approaches and an adaption of open quantum systems theory to settings where a dynamically evolving environment has to be taken into account. We show its high accuracy for two significant classes of complex quantum many-body dynamics, unitary evolutions of nonequilibrium states in closed and stationary states in driven-dissipative systems.

Citations

• Many-body physics with ultracold gases
• Correlator expansion approach to stationary states of weakly coupled cavity arrays
• Laser cooling of trapped ions in a standing wave
• What DO we know about high Tc?
• An open-system quantum simulator with trapped ions
• Topological Insulators
• Transport, Collective Motion, and Brownian Motion
• Non-Abelian anyons and topological quantum computation
• The density-matrix renormalization group
• Open Quantum Systems. An Introduction

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