A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen Values

We consider a PT Symmetric Partner to Khare Mandal's recently proposed non-Hermitian potential with complex eigen values. Our potential is Quasi-Exactly solvable and is shown to possess only real eigen values.Comment: 10 page

Simulation and theory of vibrational phase relaxation in the critical and supercritical nitrogen: Origin of observed anomalies

We present results of extensive computer simulations and theoretical analysis of vibrational phase relaxation of a nitrogen molecule along the critical isochore and also along the gas-liquid coexistence. The simulation includes all the different contributions [atom-atom (AA), vibration-rotation (VR) and resonant transfer] and their cross-correlations. Following Everitt and Skinner, we have included the vibrational coordinate ($q$) dependence of the interatomic potential. It is found that the latter makes an important contribution. The principal important results are: (a) a crossover from a Lorentzian-type to a Gaussian line shape is observed as the critical point is approached along the isochore (from above), (b) the root mean square frequency fluctuation shows nonmonotonic dependence on the temperature along critical isochore, (c) along the coexistence line and the critical isochore the temperature dependent linewidth shows a divergence-like $\lambda$-shape behavior, and (d) the value of the critical exponents along the coexistence and along the isochore are obtained by fitting. The origin of the anomalous temperature dependence of linewidth can be traced to simultaneous occurrence of several factors, (i) the enhancement of negative cross-correlations between AA and VR contributions and (ii) the large density fluctuations as the critical point (CP) is approached. The former makes the decay faster so that local density fluctuations are probed on a femtosecond time scale. A mode coupling theory (MCT) analysis shows the slow decay of the enhanced density fluctuations near critical point. The MCT analysis demonstrates that the large enhancement of VR coupling near CP arises from the non-Gaussian behavior of density fluctuation and this enters through a nonzero value of the triplet direct correlation function.Comment: 35 pages, 15 figures, revtex4 (preprint form

On input/output maps for nonlinear systems via continuity in a locally convex topology

In this paper we show that the output of a nonlinear system with inputs in () whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results

The detectability of eccentric binary pulsars

Studies of binary pulsars provide insight into various theories of physics. Detection of such systems is challenging due to the Doppler modulation of the pulsed signal caused by the orbital motion of the pulsar. We investigated the loss of sensitivity in eccentric binary systems for different types of companions. This reduction of sensitivity should be considered in future population synthesis models for binary pulsars. This loss can be recovered partially by employing the `acceleration search' algorithm and even better by using the `acceleration-jerk search' algorithm.Comment: 2 pages. To appear in the proceeding of "The Metrewavelength Sky Conference" held at NCRA-TIFR, Pune, from December 9-13 2013, to mark 50 years of radio astronomy research at the Tata Institute of Fundamental Research (TIFR), as well as 10 years of operation of the Giant Metrewave Radio Telescope (GMRT) as an international observator

New approach to (quasi)-exactly solvable Schrodinger equations with a position-dependent effective mass

By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schr\"odinger equation with a position-dependent effective mass. In the latter case, SUSYQM techniques provide us with some additional new potentials.Comment: 11 pages, no figur

Effective-mass Schroedinger equation and generation of solvable potentials

A one-dimensional Schr\"odinger equation with position-dependent effective mass in the kinetic energy operator is studied in the framework of an $so(2,1)$ algebra. New mass-deformed versions of Scarf II, Morse and generalized P\"oschl-Teller potentials are obtained. Consistency with an intertwining condition is pointed out.Comment: 9 pages, no figure, communication at "2nd International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics", Prague, Czech Republic, June 14-16,200

Reduced-dimension linear transform coding of distributed correlated signals with incomplete observations

We study the problem of optimal reduced-dimension linear transform coding and reconstruction of a signal based on distributed correlated observations of the signal. In the mean square estimation context this involves finding he optimal signal representation based on multiple incomplete or only partial observations that are correlated. In particular this leads to the study of finding the optimal Karhunen-Loeve basis based on the censored observations. The problem has been considered previously by Gestpar, Dragotti and Vitterli in the context of jointly Gaussian random variables based on using conditional covariances. In this paper, we derive the estimation results in the more general setting of second-order random variables with arbitrary distributions, using entirely different techniques based on the idea of innovations. We explicitly solve the single transform coder case, give a characterization of optimality in the multiple distributed transform coders scenario and provide additional insights into the structure of the problm

Field Theories on Null Manifolds

We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed an action for the electric sector of the theory. This action is the first example for an interacting conformal Carrollian Field Theory. The proposed action respects the finite and infinite conformal Carrollian symmetries in d = 4. We calculate conserved charges corresponding to these finite and infinite symmetries and then rewrite the conserved charges in terms of the canonical variables. We finally compute the Poisson brackets for these charges and confirm that infinite Carrollian conformal algebra is satisfied at the level of charges

Tax breaks for the small scale sector: An appraisal.

Small scale sector ; Taxation

Raising the tax ratio by reining in the "Tax-Breaks": An agenda for action.

Taxation