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Springer eBooks

Quantum Collision Theory of Nonrelativistic Particles

Reiner M. Dreizler, Tom Kirchner, Cora S. Lüdde

Published Jan 1, 2022• 1 citation
Publisher
DOI
10.1007/978-3-662-65591-7

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In the framework of nonstationary scattering theory, we study the formation of an entangled state of two identical nonrelativistic spin- 1/2 particles as a result of their elastic scattering. The measure of particle entanglement in the final channel is described using pair concurrence. For the indicated quantitative criterion, we obtain general expressions in terms of the direct and exchange scattering amplitudes in the cases of pure and mixed spin states of the pair in the initial channel. We consider the violation of Bell’s inequality in the final channel. We show that as a result of a collision between unpolarized particles, a Werner spin state of the pair forms, which is entangled if the singlet component of the angular differential scattering cross section in the center-of-mass reference frame exceeds the triplet component. We use the process of free electron-electron scattering as an example to illustrate the developed formalism.
Abstract The salient features of generalized second‐quantization representations for nonrelativistic systems of composite particles are reviewed and their application to a reformulation of the quantum theory of reactive collisions is discussed. Such representations allow the properties of the bound composite states to be built explicitly into the algebra of states and observables. A single unperturbed Hamiltonian simultaneously describes the free propagation of the various species of bound composites as well as of their unbound constituents, while the interaction Hamiltonian describes only true scattering and reaction processes. The inclusion of the binding of all composites in the unperturbed Hamiltonian cures the divergences in the Born series arising from bound‐state poles. Unstable composites can be included in a natural way, leading to an explicit representation for the kinematics and dynamics of their decay and their contribution to collision phenomena.