1,072 research outputs found
Dirac equation in the magnetic-solenoid field
We consider the Dirac equation in the magnetic-solenoid field (the field of a
solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm
solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using
von Neumann's theory of deficiency indices. We find self-adjoint extensions of
the Dirac Hamiltonian in both above dimensions and boundary conditions at the
AB solenoid. Besides, for the first time, solutions of the Dirac equation in
the magnetic-solenoid field with a finite radius solenoid were found. We study
the structure of these solutions and their dependence on the behavior of the
magnetic field inside the solenoid. Then we exploit the latter solutions to
specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm
solenoid.Comment: 23 pages, 2 figures, LaTex fil
Reduction of quantum noise in optical interferometers using squeezed light
We study the photon counting noise in optical interferometers used for
gravitational wave detection. In order to reduce quantum noise a squeezed
vacuum state is injected into the usually unused input port. Here, we
specifically investigate the so called `dark port case', when the beam splitter
is oriented close to 90{\deg} to the incoming laser beam, such that nearly all
photons go to one output port of the interferometer, and only a small fraction
of photons is seen in the other port (`dark port'). For this case it had been
suggested that signal amplification is possible without concurrent noise
amplification [R.Barak and Y.Ben-Aryeh, J.Opt.Soc.Am.B25(361)2008]. We show
that by injection of a squeezed vacuum state into the second input port,
counting noise is reduced for large values of the squeezing factor, however the
signal is not amplified. Signal strength only depends on the intensity of the
laser beam.Comment: 8 pages, 1 figur
On the AKSZ formulation of the Rozansky-Witten theory and beyond
Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action
for the Rozansky-Witten model, which can be defined for any complex manifold
with a closed (2,0)-form. We also construct the holomorphic version of
Rozansky-Witten theory defined over Calabi-Yau 3-fold.Comment: 12 page
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