4,813 research outputs found
On quadratic Hom-Lie algebras with equivariant twist maps and their relationship with quadratic Lie algebras
Hom-Lie algebras having non-invertible and equivariant twist maps are
studied. Central extensions of Hom-Lie algebras having these properties are
obtained and shown how the same properties are preserved. Conditions are given
so that the produced central extension has an invariant metric with respect to
its Hom-Lie product making its twist map self-adjoint when the original Hom-Lie
algebra has such a metric. This work is focused on algebras with these
properties and we call them quadratic Hom-Lie algebras. It is shown how a
quadratic Hom-Lie algebra gives rise to a quadratic Lie algebra and that the
Lie algebra associated to the given Hom-Lie central extension is a Lie algebra
central extension of it. It is also shown that if the 2-cocycle associated to
the central extension is not a coboundary, there exists a non-abelian and
non-associative algebra, the commutator of whose product is precisely the
Hom-Lie product of the Hom-Lie central extension. Moreover, the algebra whose
commutator realizes this Hom-Lie product is shown to be simple if the
associated Lie algebra is nilpotent. Non-trivial examples are provided
Decay by tunneling of Bosonic and Fermionic Tonks-Girardeau Gases
We study the tunneling dynamics of bosonic and fermionic Tonks-Girardeau
gases from a hard wall trap, in which one of the walls is substituted by a
delta potential. Using the Fermi-Bose map, the decay of the probability to
remain in the trap is studied as a function of both the number of particles and
the intensity of the end-cap delta laser. The fermionic gas is shown to be a
good candidate to study deviations of the non-exponential decay of the
single-particle type, whereas for the bosonic case a novel regime of
non-exponential decay appears due to the contributions of different resonances
of the trap
Suppression of Zeno effect for distant detectors
We describe the influence of continuous measurement in a decaying system and
the role of the distance from the detector to the initial location of the
system. The detector is modeled first by a step absorbing potential. For a
close and strong detector, the decay rate of the system is reduced; weaker
detectors do not modify the exponential decay rate but suppress the long-time
deviations above a coupling threshold. Nevertheless, these perturbing effects
of measurement disappear by increasing the distance between the initial state
and the detector, as well as by improving the efficiency of the detector.Comment: 4 pages, 4 figure
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