Operator formalism for the Wigner phase distribution

The probability distribution for finding a state of the radiation field in a particular phase is described by a multitude of theoretical formalisms; the phase-sensitivity of the Wigner quasi-probability distribution being one of them. We construct a hermitian phase operator for this Wigner phase. We show that this operator is complete and also elucidate a set of complete but non-orthogonal states that seems to be naturally associated with such an operator. Further we show that our operator satisfies a weak equivalence relation with the Pegg-Barnett operator, thus showing that the essential phase information furnished by both formalisms are the same. It is also shown that this operator gives results which are in correct agreement with the expected uniform phase distribution of a Fock state.Comment: 5 page

The sustainability of Suranga irrigation in South Karnataka and northern Kerala, India

This paper reports the preliminary findings from an on-going research project that is exploring the resilience and sustainability of suranga irrigation technology found in the Western Ghats of south Karnataka and northern Kerala, India. The suranga are traditional adit water harvesting systems that tap ground waters. They have been constructed mainly by individual land owners to provide both drinking and irrigation water. This paper compares traditional suranga irrigation technology with that of more modern irrigation technology, first introduced during the green revolution, in terms of their impacts on livelihood strategies and water use efficiency. The paper also describes some of the recent adaptations made by farmers to suranga systems based on response to new crop growing opportunities and the availability of new conveyance and distribution technologies and materials. The paper concludes by exploring the resilience and sustainability of the traditional system from a catchment based perspective as the region faces the duel pressures of population increase and climate change.Submitted Versio

Quantum-limited amplification and parametric instability in the reversed dissipation regime of cavity optomechanics

Cavity optomechanical phenomena, such as cooling, amplification or optomechanically induced transparency, emerge due to a strong imbalance in the dissipation rates of the parametrically coupled electromagnetic and mechanical resonators. Here we analyze the reversed dissipation regime where the mechanical energy relaxation rate exceeds the energy decay rate of the electromagnetic cavity. We demonstrate that this regime allows for mechanically-induced amplification (or cooling) of the electromagnetic mode. Gain, bandwidth, and added noise of this electromagnetic amplifier are derived and compared to amplification in the normal dissipation regime. In addition, we analyze the parametric instability, i.e. optomechanical Brillouin lasing, and contrast it to conventional optomechanical phonon lasing. Finally, we propose an experimental scheme that realizes the reversed dissipation regime using parametric coupling and optomechanical cooling with a second electromagnetic mode enabling quantum-limited amplification. Recent advances in high-Q superconducting microwave resonators make the reversed dissipation regime experimentally realizable.Comment: 5+3 pages, 5 figures, 1 tabl

Phase properties of operator valued measures in phase space

The Wigner Phase Operator (WPO) is identified as an operator valued measure (OVM) and its eigen states are obtained. An operator satisfying the canonical commutation relation with the Wigner phase operator is also constructed and this establishes a Wigner distribution based operator formalism for the Wigner Phase Distribution. The operator satisfying the canonical commutation relation with the Wigner Phase Operator valued measure (WP-OVM) is found to be not the usual number operator. We show a way to overcome the non-positivity problem of the WP-OVM by defining a positive OVM by means of a proper filter function, based on the view that phase measurements are coarse-grained in phase space, leading to the well known Q-distribution. The identification of Q phase operator as a POVM is in good agreement with the earlier observation regarding the relation between operational phase measurement schemes and the Q-distribution. The Q phase POVM can be dilated in the sense of Gelfand-Naimark, to an operational setting of interference at a beam-splitter with another coherent state - this results in a von Neumann projector with well-defined phase

Evidence of robust 2D transport and Efros-Shklovskii variable range hopping in disordered topological insulator (Bi2Se3) nanowires

We report the experimental observation of variable range hopping conduction in focused-ion-beam (FIB) fabricated ultra-narrow nanowires of topological insulator (Bi2Se3). The value of the exponent in the hopping equation was extracted as ~ 1/2 for different widths of nanowires, which is the proof of the presence of Efros-Shklovskii hopping transport mechanism in a strongly disordered system. High localization lengths (0.5nm, 20nm) were calculated for the devices. A careful analysis of the temperature dependent fluctuations present in the magnetoresistance curves, using the standard Universal Conductance Fluctuation theory, indicates the presence of 2D topological surface states. Also, the surface state contribution to the conductance was found very close to one conductance quantum. We believe that our experimental findings shed light on the understanding of quantum transport in disordered topological insulator based nanostructures.Comment: 14pages, 4 figure

Effect of non-magnetic impurities on the magnetic states of anatase TiO2_2

The electronic and magnetic properties of TiO$_2$, TiO$_{1.75}$, TiO$_{1.75}$N$_{0.25}$, and TiO$_{1.75}$F$_{0.25}$ compounds have been studied by using \emph{ab initio} electronic structure calculations. TiO$_2$ is found to evolve from a wide-band-gap semiconductor to a narrow-band-gap semiconductor to a half-metallic state and finally to a metallic state with oxygen vacancy, N-doping and F-doping, respectively. Present work clearly shows the robust magnetic ground state for N- and F-doped TiO$_2$. The N-doping gives rise to magnetic moment of $\sim$0.4 $\mu_B$ at N-site and $\sim$0.1 $\mu_B$ each at two neighboring O-sites, whereas F-doping creates a magnetic moment of $\sim$0.3 $\mu_B$ at the nearest Ti atom. Here we also discuss the possible cause of the observed magnetic states in terms of the spatial electronic charge distribution of Ti, N and F atoms responsible for bond formation.Comment: 11 pages, 4 figures To appear J. Phys.: Condens. Matte

Gravitational baryogenesis of cosmological constant dominated universe

In this paper, we have studied the gravitational baryogenesis of isotropic and homogeneous universe in the frame-work of general relativity. We investigate an exact and new solution of Einstein's field equations for FRW metric. Our solution represents a transitioning model of the universe which was expanding in decelerated mode and it transit in accelerated mode after dominance of cosmological constant $\Lambda$. We observe that gravitational baryogenesis occurs in the derived universe and derived baryon entropy ratio is in good agreement with its observational value.Comment: 8 Pages, 4 Figures, Accepted in Gravitation and Cosmolog