Titlebook: Advances in Quantum Mechanics; Contemporary Trends Alessandro Michelangeli,Gianfausto Dell‘Antonio Book 2017 Springer International Publis

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2281-518X the field.This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments

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stratum-corneum

Vo Tan Tai,Doan Ngoc Minh,Dang Xuan Baound state and orbital stability for the NLS equation on a general starlike graph with potentials, preprint arXiv:1608.01506) which covers the most general setting and we compare it with similar results.

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https://doi.org/10.1007/978-3-030-62324-1em and to highlight the techniques employed and the main ideas. In the final part we outline a few major open questions that concern the topical problem of the multiplicity of self-adjoint realisations of the model, and which are worth addressing in the future.

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R. Velumani,S. Bama,M. Victor Josecoupled system of non-linear Sch?dinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

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Prathima Guruprasad,Guruprasad K. S. Raoand of the scattering phase. In the case of Sturm-Liouville operators defined on compact graphs and in general for differential operators on compact star-graphs, unknown potentials can be recovered from the knowledge of the spectrum of operators obtained imposing different boundary conditions.

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https://doi.org/10.1007/978-981-15-8534-0rier Hamiltonian operator and where . and . are two test functions.?In particular, when . is close to a resonant state then explicit expression of the dominant terms of the survival probability defined as | 〈.,?...〉 |. is given.

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Abelian Gauge Potentials on Cubic Lattices,ds in a system of ultracold atoms in optical lattices. After reviewing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold set-ups, we study cubic lattice tight-binding models with commensurate flux. We finally discuss applications of gauge potentials in one-dimensional rings.