Effective Evolution Equations from Quantum Dynamics

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Quantum Theory
Cover of the book Effective Evolution Equations from Quantum Dynamics by Niels Benedikter, Marcello Porta, Benjamin Schlein, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Niels Benedikter, Marcello Porta, Benjamin Schlein ISBN: 9783319248981
Publisher: Springer International Publishing Publication: November 4, 2015
Imprint: Springer Language: English
Author: Niels Benedikter, Marcello Porta, Benjamin Schlein
ISBN: 9783319248981
Publisher: Springer International Publishing
Publication: November 4, 2015
Imprint: Springer
Language: English

These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.           

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.           

More books from Springer International Publishing

Cover of the book Slow Viscous Flow by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Handbook of DSM-5 Disorders in Children and Adolescents by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Sustainable Growth in the EU by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Recommendations for Fatigue Design of Welded Joints and Components by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Modelling and Simulation for Autonomous Systems by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Youngsters Solving Mathematical Problems with Technology by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book CEOs and White-Collar Crime by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Job Scheduling Strategies for Parallel Processing by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Foundations of Heterogeneous Integration: An Industry-Based, 2.5D/3D Pathfinding and Co-Design Approach by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Klaus von Beyme by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Rethinking Social Studies Teacher Education in the Twenty-First Century by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Rehabilitation Medicine for Elderly Patients by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Reflected Brownian Motions in the KPZ Universality Class by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Characterizing Stellar and Exoplanetary Environments by Niels Benedikter, Marcello Porta, Benjamin Schlein
Cover of the book Democracy after the Internet - Brazil between Facts, Norms, and Code by Niels Benedikter, Marcello Porta, Benjamin Schlein
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy