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Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime
We consider a hydrogen atom confined in time-dependent trap created by a
spherical impenetrable box with time-dependent radius. For such model we study
the behavior of atomic electron under the (non-adiabatic) dynamical confinement
caused by the rapidly moving wall of the box. The expectation values of the
total and kinetic energy, average force, pressure and coordinate are analyzed
as a function of time for linearly expanding, contracting and harmonically
breathing boxes. It is shown that linearly extending box leads to de-excitation
of the atom, while the rapidly contracting box causes the creation of very high
pressure on the atom and transition of the atomic electron into the unbound
state. In harmonically breathing box diffusive excitation of atomic electron
may occur in analogy with that for atom in a microwave field
Local normal forms for c-projectively equivalent metrics and proof of the Yano-Obata conjecture in arbitrary signature. Proof of the projective Lichnerowicz conjecture for Lorentzian metrics
Two K\"ahler metrics on a complex manifold are called c-projectively
equivalent if their -planar curves coincide. These curves are defined by the
property that the acceleration is complex proportional to the velocity. We give
an explicit local description of all pairs of c-projectively equivalent
K\"ahler metrics of arbitrary signature and use this description to prove the
classical Yano-Obata conjecture: we show that on a closed connected K\"ahler
manifold of arbitrary signature, any c-projective vector field is an affine
vector field unless the manifold is with (a multiple of) the
Fubini-Study metric. As a by-product, we prove the projective Lichnerowicz
conjecture for metrics of Lorentzian signature: we show that on a closed
connected Lorentzian manifold, any projective vector field is an affine vector
field.Comment: comments are welcom
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