Triple solutions for the one-dimensional p-Laplacian

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions to the two point boundary value problem (|u\u27|p -2 u\u27) = q(t) f(t,u,u\u27) on (0,1), u(0) = u(1) = 0

Oscillation of higher order difference equations via comparison

In this paper we shall present some new oscillation criteria for difference equations of the form x(n) + q(n)f(x[n - ]) = 0 and x(n) = q(t)f(x[n - ]) + p(n)F(x[n + ]) via comparison with some difference equations of lower order whose oscillatory behavior are known

A Fresh Approach to the Study of Atmosphere Turbidity

The problem of assessment of atmospheric turbidity caused by aerosol particles, viz., dust, smoke, haze, and other atmospheric pollutants, apart from the effect of variable water vapour content of the atmosphere, has been studied afresh. The basic concept underlying Linke's turbidity factor, T has been found to be theoretically sound, although its quantitative formulation suffers from one major defect, viz, its 'virtual variation' with air mass. This error has been traced to defective formulation of the quantitative expression for T. A 'Rational turbidity factor', Tr, has been proposed which is likely to overcome the limitations of Linke's turbidity factor, T. A nomogram has been development for quick evaluation of Tr, and the effect of altitude has also been considered

Topological transitions in dissipatively coupled Su-Schrieffer-Heeger models

Non-Hermitian topological phenomena have gained much interest among physicists in recent years. In this paper, we expound on the physics of dissipatively coupled Su-Schrieffer-Heeger (SSH) lattices, specifically in systems with bosonic and electrical constituents. In the context of electrical circuits, we demonstrate that a series of resistively coupled LCR circuits mimics the topology of a dissipatively coupled SSH model. In addition, we foreground a scheme to construct dissipatively coupled SSH lattices involving a set of non-interacting bosonic oscillators weakly coupled to engineered reservoirs of modes possessing substantially small lifetimes when compared to other system timescales. Further, by activating the coherent coupling between bosonic oscillators, we elucidate the emergence of non-reciprocal dissipative coupling which can be controlled by the phase of the coherent interaction strength precipitating in phase-dependent topological transitions and skin effect. Our analyses are generic, apropos of a large class of systems involving, for instance, optical and microwave settings, while the circuit implementation represents the most straightforward of them.Comment: 10 pages, 9 figure

Robust transmission of non-Gaussian entanglement over optical fibers

We show how the entanglement in a wide range of continuous variable non-Gaussian states can be preserved against decoherence for long-range quantum communication through an optical fiber. We apply protection via decoherence-free subspaces and quantum dynamical decoupling to this end. The latter is implemented by inserting phase shifters at regular intervals $\Delta$ inside the fiber, where $\Delta$ is roughly the ratio of the speed of light in the fiber to the bath high-frequency cutoff. Detailed estimates of relevant parameters are provided using the boson-boson model of system-bath interaction for silica fibers, and $\Delta$ is found to be on the order of a millimeter.Comment: 9 pages, 2 figures, RevTeX4, submitted to PR

Exact time evolution and master equations for the damped harmonic oscillator

Using the exact path integral solution for the damped harmonic oscillator it is shown that in general there does not exist an exact dissipative Liouville operator describing the dynamics of the oscillator for arbitrary initial bath preparations. Exact non-stationary Liouville operators can be found only for particular preparations. Three physically meaningful examples are examined. An exact new master equation is derived for thermal initial conditions. Second, the Liouville operator governing the time-evolution of equilibrium correlations is obtained. Third, factorizing initial conditions are studied. Additionally, one can show that there are approximate Liouville operators independent of the initial preparation describing the long time dynamics under appropriate conditions. The general form of these approximate master equations is derived and the coefficients are determined for special cases of the bath spectral density including the Ohmic, Drude and weak coupling cases. The connection with earlier work is discussed.Comment: to be published in Phys. Rev.

An analysis of dynamical suppression of spontaneous emission

It has been shown recently [see, for example, S.-Y. Zhu and M. O. Scully, Phys. Rev. Lett. {\bf 76}, 388 (1996)] that a dynamical suppression of spontaneous emission can occur in a three-level system when an external field drives transitions between a metastable state and {\em two} decaying states. What is unusual in the decay scheme is that the decaying states are coupled directly by the vacuum radiation field. It is shown that decay dynamics required for total suppression of spontaneous emission necessarily implies that the level scheme is isomorphic to a three-level lambda system, in which the lower two levels are {\em both} metastable, and each is coupled to the decaying state. As such, the total suppression of spontaneous emission can be explained in terms of conventional dark states and coherent population trapping.Comment: 8 pages, 3 figure