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Rajneesh Atre

Publications and source records attributed to Rajneesh Atre.

8 recordsLinked to original sources
arXiv2012

Solving Linear Differential Equations: A Novel Approach

We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the equations under study, as well as that of the solutions are made transparent. We demonstrate the efficacy of the method by showing the common structure of the solution space of a wide variety of differential equations viz. Hermite, Laguerre, Jocobi, Bessel and hypergeometric etc. We also illustrate the use of the procedure to develop approximate solutions, as well as in finding solutions of many particle interacting systems.

math-ph↗
arXiv2010

Controlling Grey Solitons in a Trap

Experimentally observed grey solitons are analytically extracted from a physically viable \GP equation. Associated Lieb and Bogoliubov modes are calculated for these class of solitons. It is observed that, these nonlinear excitations have strong coupling with the trap at low momenta and hence can be effectively isolated from the Bogoliubov sound modes, which responds weakly to harmonic confinement. This strong coupling with the trap also makes the grey soliton amenable for control and manipulation through both trap modulation and temporal variation of the two-body interaction.

cond-mat.other↗
arXiv2007

Complex solitons with power law behaviour in Bose-Einstein condensates near Feshbach resonance

Complex, localized stable solitons, characterized by a power law behaviour, are found for a quasi-one-dimensional Bose-Einstein condensate near Feshbach resonance. Both dark and bright solitons can be excited in the experimentally allowed parameter domain, when two and three-body interactions are respectively repulsive and attractive. These solutions are obtained for non-zero chemical potential, unlike their unstable real counterparts which exist in the limit of vanishing $μ$. The dark solitons travel with constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity can exist for specified interaction strengths.

cond-mat.other↗
arXiv2006

Controlling pulse propagation in optical fibers through nonlinearity and dispersion management

In case of the nonlinear Schrödinger equation with designed group velocity dispersion, variable nonlinearity and gain/loss; we analytically demonstrate the phenomenon of chirp reversal crucial for pulse reproduction. Two different scenarios are exhibited, where the pulses experience identical dispersion profiles, but show entirely different propagation behavior. Exact expressions for dynamical quasi-solitons and soliton bound-states relevant for fiber communication are also exhibited.

nlin.SI↗
arXiv2005

A new class of exact solitary wave solutions of one dimensional Gross-Pitaevskii equation

We present a large family of {\it{exact}} solitary wave solutions of the one dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain/loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map on to a {\it{linear}} Schrödinger eigenvalue problem, thereby enabling one to find analytically the effect of a wide variety of temporal variations in the control parameters, which are experimentally realizable. Corresponding to each solvable quantum mechanical system, one can identify a soliton configuration. These include soliton trains in close analogy to experimental observations of Strecker {\it{et al.,}} [Nature {\bf{417}{150}{2002}], spatio-temporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates and analytical expression of two-soliton bound states, to name a few.

cond-mat.other↗
arXiv2004

Information Entropy and Correlation of the Hooke's Atom

We provide an algebraic procedure to find the eigenstates of two-charged particles in an oscillator potential, known as {\it{Hooke's}} atom. For the planar Hooke's atom, the exact eigenstates and single particle densities for arbitrary azimuthal quantum number, are obtained analytically. Information entropies associated with the wave functions for the relative motion are then studied systematically, since the same incorporates the effect of the Coulomb interaction. The {\it{quantum pottery}} of the information entropy density reveals a number of intricate structures, which differ significantly for the attractive and repulsive cases. We indicate the procedure to obtain the approximate eigen states. Making use of the relationship of this dynamical system with the quasi-exactly solvable systems, one can also develop a suitable perturbation theory, involving the Coulomb coupling $Z$, for the approximate wave functions.

quant-ph↗
arXiv2003

Quantum information entropies of the eigenstates and the coherent state of the Pöschl-Teller potential

The position and momentum space information entropies, of the ground state of the Pöschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the Pöschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.

quant-ph↗