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This concise book introduces and discusses the basic theory of
conical intersections with applications in atomic, molecular and
condensed matter physics. Conical intersections are linked to the
energy of quantum systems. They can occur in any physical system
characterized by both slow and fast degrees of freedom - such as
e.g. the fast electrons and slow nuclei of a vibrating and rotating
molecule - and are important when studying the evolution of quantum
systems controlled by classical parameters. Furthermore, they play
a relevant role for understanding the topological properties of
condensed matter systems. Conical intersections are associated with
many interesting features, such as a breakdown of the
Born-Oppenheimer approximation and the appearance of nontrivial
artificial gauge structures, similar to the Aharonov-Bohm effect.
Some applications presented in this book include - Molecular
Systems: some molecules in nonlinear nuclear configurations undergo
Jahn-Teller distortions under which the molecule lower their
symmetry if the electronic states belong to a degenerate
irreducible representation of the molecular point group. - Solid
State Physics: different types of Berry phases associated with
conical intersections can be used to detect topologically
nontrivial states of matter, such as topological insulators, Weyl
semi-metals, as well as Majorana fermions in superconductors. -
Cold Atoms: the motion of cold atoms in slowly varying
inhomogeneous laser fields is governed by artificial gauge fields
that arise when averaging over the fast internal degrees of freedom
of the atoms. These gauge fields can be Abelian or non-Abelian,
which opens up the possibility to create analogs to various
relativistic effects at low speed.
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