Abstract
The primary aims of this chapter are twofold: i) To present a brief description of the beginnings of an exact theory of quantum solitons on lattices, and ii) To describe the Hartree approximation for this exact theory, which is useful when the number of freedoms (lattice points) and the quantum level become large. These discussions are presented in the context of several ongoing collaborations in the study of the ways that the linear theory of quantum mechanics represents the nonlinear behaviors of classical lattices in the corresponding limit.
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Eilbeck, J.C., Scott, A.C. (1994). Quantum Lattices. In: Spatschek, K.H., Mertens, F.G. (eds) Nonlinear Coherent Structures in Physics and Biology. NATO ASI Series, vol 329. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1343-2_1
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