Reply on `comment on our paper `Single two-level ion in an anharmonic-oscillator trap: Time evolution of the Q function and population inversion ''

We show here that the model Hamiltonian used in our paper for ion vibrating in a q-analog harmonic oscillator trap and interacting with a classical single-mode light field is indeed obtained by replacing the usual bosonic creation and annihilation operators of the harmonic trap model by their q-deformed counterparts. The approximations made in our paper amount to using for the ion-laser interaction in a q-analog harmonic oscillator trap, the operator F_{q}=exp{-(|\epsilon|^2}/2)}exp{i\epsilon A^{\dagger}}exp{i\epsilon A}, which is analogous to the corresponding operator for ion in a harmonic oscillator trap that is $F=exp{-(|\epsilon|^2 /2)}exp{i\epsilon a^{\dagger }}exp{i\epsilon a}$. In our article we do not claim to have diagonalized the operator, $F_q = exp{i \epsilon (A^{\dagger}+A)}$, for which the basis states |g,m> and |e,m> are not analytic vectors.Comment: Revtex, 4pages. To be Published in Physical Review A59, NO.4(April 99

Schr\"{o}dinger cat state of trapped ions in harmonic and anharmonic oscillator traps

We examine the time evolution of a two level ion interacting with a light field in harmonic oscillator trap and in a trap with anharmonicities. The anharmonicities of the trap are quantified in terms of the deformation parameter $\tau$ characterizing the q-analog of the harmonic oscillator trap. Initially the ion is prepared in a Schr\"{o}dinger cat state. The entanglement of the center of mass motional states and the internal degrees of freedom of the ion results in characteristic collapse and revival pattern. We calculate numerically the population inversion I(t), quasi-probabilities $Q(t),$ and partial mutual quantum entropy S(P), for the system as a function of time. Interestingly, small deformations of the trap enhance the contrast between population inversion collapse and revival peaks as compared to the zero deformation case. For \beta =3 and $4,($ determines the average number of trap quanta linked to center of mass motion) the best collapse and revival sequence is obtained for \tau =0.0047 and \tau =0.004 respectively. For large values of \tau decoherence sets in accompanied by loss of amplitude of population inversion and for \tau \sim 0.1 the collapse and revival phenomenon disappear. Each collapse or revival of population inversion is characterized by a peak in S(P) versus t plot. During the transition from collapse to revival and vice-versa we have minimum mutual entropy value that is S(P)=0. Successive revival peaks show a lowering of the local maximum point indicating a dissipative irreversible change in the ionic state. Improved definition of collapse and revival pattern as the anharminicity of the trapping potential increases is also reflected in the Quasi- probability versus t plots.Comment: Revised version, 16 pages,6 figures. Revte

Radiative and Seesaw Threshold Corrections to the S3S_3 Symmetric Neutrino Mass Matrix

We systematically analyze the radiative corrections to the $S_3$ symmetric neutrino mass matrix at high energy scale, say the GUT scale, in the charged lepton basis. There are significant corrections to the neutrino parameters both in the Standard Model (SM) and Minimal Supersymmetric Standard Model (MSSM) with large tan$\beta$, when the renormalization group evolution (RGE) and seesaw threshold effects are taken into consideration. We find that in the SM all three mixing angles and atmospheric mass squared difference are simultaneously obtained in their current 3$\sigma$ ranges at the electroweak scale. However, the solar mass squared difference is found to be larger than its allowed 3$\sigma$ range at the low scale in this case. There are significant contributions to neutrino masses and mixing angles in the MSSM with large tan$\beta$ from the RGEs even in the absence of seesaw threshold corrections. However, we find that the mass squared differences and the mixing angles are obtained in their current 3$\sigma$ ranges at low energy when the seesaw threshold effects are also taken into account in the MSSM with large tan$\beta$.Comment: 20 Pages, 2 Figures and 2 Table

Low temperature hopping magnetotransport in paramagnetic single crystals of cobalt doped ZnO

Long needle-shaped single crystals of Zn1-xCoxO were grown at low temperatures using a molten salt solvent technique, up to x=0.10. The conduction process at low temperatures is determined to be by Mott variable range hopping. Both pristine and cobalt doped crystals clearly exhibit a crossover from negative to positive magnetoresistance as the temperature is decreased. The positive magnetoresistance of the Zn1-xCoxO single crystals increases with increased Co concentration and reaches up to 20% at low temperatures (2.5 K) and high fields (>1 T). SQUID magnetometry confirms that the Zn1-xCoxO crystals are predominantly paramagnetic in nature and the magnetic response is independent of Co concentration. The results indicate that cobalt doping of single crystalline ZnO introduces localized electronic states and isolated Co2+ ions into the host matrix, but that the magnetotransport and magnetic properties are decoupled.Comment: 7 pages, 9 figures, submitted to Physical Review

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: An algorithm

We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted.Comment: To appear in Eur. Phys. J.

A procedure used for a ground truth study of a land use map of North Alabama generated from LANDSAT data

A land use map of a five county area in North Alabama was generated from LANDSAT data using a supervised classification algorithm. There was good overall agreement between the land use designated and known conditions, but there were also obvious discrepancies. In ground checking the map, two types of errors were encountered - shift and misclassification - and a method was developed to eliminate or greatly reduce the errors. Randomly selected study areas containing 2,525 pixels were analyzed. Overall, 76.3 percent of the pixels were correctly classified. A contingency coefficient of correlation was calculated to be 0.7 which is significant at the alpha = 0.01 level. The land use maps generated by computers from LANDSAT data are useful for overall land use by regional agencies. However, care must be used when making detailed analysis of small areas. The procedure used for conducting the ground truth study together with data from representative study areas is presented