This book serves as an introduction to the growing field of quantum many-body transport in interacting nanojunctions. It delves into a theoretical approach based on a general density-matrix formulation for open quantum systems. In the book, relevant transport observables, like the current or its higher order cumulants, are obtained by evaluating quantum statistical averages. This approach requires the knowledge of the reduced density matrix of the interacting nanosystems.

The formulation for addressing transport problems, based on the evolution of the reduced density operator in Liouville space, is highly versatile. It enables the treatment of charge and spin transport across various realistic nanostructures. Topics encompass standard Coulomb blockade, cotunneling phenomena in quantum dots, vibrational and Franck-Condon effects in molecular junctions, as well as many-body interference observed in double quantum dots or carbon nanotubes.

Derived from lectures tailored for graduate and advanced students at the University of Regensburg in Germany, this book is enriched with exercises and step-by-step derivations.

Combining a theoretical framework for modeling systems with realistic experimental set-ups Numerous step-by-step derivations aid readers in comprehending key results effortlessly Enriched with exercises at the end of each chapter, providing essential tools for independent research

Autorentext

Andrea Donarini is an apl. professor within the Quantum Transport and Spintronics chair at the University of Regensburg (Germany), where he teaches and conducts research in the field of quantum transport at the nanoscale. He graduated from the University of Milan (Italy) before earning his PhD in Physics at the Technical University of Denmark (Lyngby). Since then, he has advanced his career at the University of Regensburg, being appointed an apl. Professor in 2020. Prof. Donarini's research primarily focuses on the transport characteristics of complex interacting nanojunctions. Specifically, he has explored various aspects of the interplay between interference and interaction in single molecule junctions and quantum dot structures. His quest to identify markers of many-body interference phenomena, both in current and noise, has led him to investigate single electron transistors, STM single molecule junctions, nanoelectromechanical systems, and most recently, lightwave-STM junctions. Milena Grifoni is a professor of Theoretical Physics at the University of Regensburg (Germany), where she leads a research group studying non-equilibrium properties of open quantum systems. She obtained her Master's degree and PhD at the University of Genoa (Italy). Following a post-doctoral phase in Germany, she became a permanent staff member at the Technical University of Delft (The Netherlands). In 2003, she assumed a chair for theoretical physics in Regensburg. Prof. Grifoni's work has predominantly focused on the dynamical and stationary properties of open quantum systems. This includes investigating dissipative properties of quantum particles interacting with bosonic thermal reservoirs, as well as electronic transport in non-equilibrium fermionic environments. She is recognized for influential contributions to the driven spin-boson problem, which have found recent applications in superconducting qubit platforms. Additionally, her studies on the non-equilibrium Kondo effect and other many-body phenomena in carbon nanotubes, molecules, and other low-dimensional systems have made significant contributions to the field.

Inhalt

Part I: Transport Theory.- 1. Preliminary Concepts.- 2. The Quantum Transport Problem.- 3. Linear Transport within Kubo Formalism.- 4. Density Matrix Methods for Quantum Transport.- 5. Diagrammatic Formulation of Transport in Liouville space.- Part II: Interacting Nanojunctions.- 6. The Single Impurity Anderson Model.- 7. Double Quantum Dots.- 8. Quantum Dot Molecules.- 9. Junctions with Ferromagnetic Electrodes.- 10. Transport in Molecular Junctions.- 11. Junctions with Superconducting Leads.- 12. Solutions.