The Wigner Function in Science and Technology

This book describes Wigner functions and its applications in various fields of science where it has been found to be very useful in wide range of modern disciplines, including quantum information, coherent optics, and superconducting qubits.

This book is designed to give a background to the origins and development of Wigner functions, as well as its mathematical underpinnings. Along the way the authors emphasise the connections, and differences, from the more popular non-equilibrium Green’s function approaches. But, the key importance lies in inclusion of applications of the Wigner function to various fields of science, including quantum information, coherent optics, and superconducting qubits. These disciplines approach it differently, and the goal here is to give a unified background and highlight how it is utilized in the different disciplines.

1. Introduction 2. Approaches to quantum transport 3. Wigner functions 4. Effective potentials 5. Numerical solutions 6. Particle approaches 7. Collisions and the Wigner function 8. Entanglement 9. Quantum chemistry 10. Semi-classical communications 11. Quantum optics 12. Quantum physics