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

A dynamical inconsistency of Horava gravity

The dynamical consistency of the non-projectable version of Horava gravity is investigated by focusing on the asymptotically flat case. It is argued that for generic solutions of the constraint equations the lapse must vanish asymptotically. We then consider particular values of the coupling constants for which the equations are tractable and in that case we prove that the lapse must vanish everywhere -- and not only at infinity. Put differently, the Hamiltonian constraints are generically all second-class. We then argue that the same feature holds for generic values of the couplings, thus revealing a physical inconsistency of the theory. In order to cure this pathology, one might want to introduce further constraints but the resulting theory would then lose much of the appeal of the original proposal by Horava. We also show that there is no contradiction with the time reparametrization invariance of the action, as this invariance is shown to be a so-called "trivial gauge symmetry" in Horava gravity, hence with no associated first-class constraints.Comment: 28 pages, 2 references adde

Q-phonon description of low lying 1^- two-phonon states in spherical nuclei

The properties of 1^-_1 two-phonon states and the characteristics of E1 transition probabilities between low-lying collective states in spherical nuclei are analysed within the Q-phonon approach to the description of collective states. Several relations between observables are obtained. Microscopic calculations of the E1 0^+_1 -> 1^-_1 transition matrix elements are performed on the basis of the RPA. A satisfactory description of the experimental data is obtained.Comment: 16 pages, 2 figures, 9 table

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