Fundamental Theory of Quantum Scattering

A.S. Davydov

Manuel Valiente, Nikolaj Thomas Zinner

In this chapter, we begin by introducing some basic concepts in quantum mechanics, mostly with the purpose of setting the notation and definitions. We then build the standard non-relativistic scattering theory, which is very important throughout the rest of the book.

Christian Gérard, Izabella Łaba

Fundamentals Geometrical methods I The Mourre theory Basic propagation estimates Geometrical methods II Wave operators and scattering theory Open problems Appendix Bibliography Index.

Dževad Belkić

Yahui Chai, Arianna Crippa, Karl Jansen +4 more

Collider experiments play a central role in understanding the subatomic structure of matter, as well as developing and verifying the fundamental theory of elementary particle interactions. However, comprehending scattering processes at a fundamental level in theory remains a significant challenge. The necessary involved time evolution and the with time rapidly increasing bond dimension in Tensor Networks make simulating the scattering process with this classical method challenging. On the other hand, quantum computers hold great promise to efficiently simulate real-time dynamics of lattice field theories. In this work, we take the first step in this direction toward simulating fermionic scattering using a digital-quantum computing approach. Specifically, we propose a method based on Givens rotation to prepare the initial state of the fermionic scattering process, which consists of two fermionic wave packets with opposite momenta. With a time evolution operator based on the underlying Hamiltonian acting on the initial state, the two fermionic wave packets propagate and interact with each other. Using the lattice Thirring model as the test bed and the Qiskit Statevector simulator, we observe an elastic scattering between fermions and antifermions in the strong interaction region. In addition, we clearly observe an entanglement production in the scattering process. We consider our work also as an indispensable step towards a quantum simulation of a scattering process on a real quantum device.