B Talukdar
Articles written in Pramana – Journal of Physics
Volume 60 Issue 3 March 2003 pp 483-490
Momentum densities and Compton profiles of alkali-metal atoms
Pranab Sarkar Anupam Sarkar S N Roy B Talukdar
It is assumed that the dynamics of valence electrons of alkali-metal atoms can be well accounted for by a quantum-defect theoretic model while the core electrons may be supposed to move in a self-consistent field. This model is used to study the momentum properties of atoms from^{3}Li to^{37}Rb. The numerical results obtained for the momentum density, moments of momentum density and Compton profile are found to be in good agreement with the results of more detailed configuration-interaction calculations for the atom^{3}Li. Similar results for^{11}Na,^{19}K and^{37}Rb are compared with the corresponding Hartree-Fock-Roothaan values only, for want of data from other realistic calculations
Volume 61 Issue 1 July 2003 pp 99-107
Canonical structure of evolution equations with non-linear dispersive terms
The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The specific results presented refer to the third- and fifth-order equations of the so-called distinguished subclass.
Volume 61 Issue 1 July 2003 pp 161-165
Matrix factorization method for the Hamiltonian structure of integrable systems
S Ghosh B Talukdar S Chakraborti
We demonstrate that the process of matrix factorization provides a systematic mathematical method to investigate the Hamiltonian structure of non-linear evolution equations characterized by hereditary operators with Nijenhuis property.
Volume 70 Issue 4 April 2008 pp 657-667 Research Articles
Symmetries and conservation laws of the damped harmonic oscillator
Amitava Choudhuri Subrata Ghosh B Talukdar
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.
Volume 72 Issue 2 February 2009 pp 445-450 Brief Reports
S K Golam Ali B Talukdar Aparna Saha
We make use of a coordinate-free approach to implement Vakhitov–Kolokolov criterion for stability analysis in order to study the effects of three-body atomic recombination and lattice potential on the matter–wave bright solitons formed in Bose–Einstein condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number by a factor of $\sqrt{1 − b_{g3}$ with $g_{3}$ the coupling constant of the lattice potential and $b = 0.7301$.
Volume 72 Issue 6 June 2009 pp 939-950 Research Articles
Evolution of optical pulses in the presence of third-order dispersion
Debabrata Pal S K Golam Ali B Talukdar
We model the propagation of femtosecond pulses through optical fibres by a nonlinear Schrödinger (NLS) equation involving a perturbing term arising due to third-order dispersion in the medium. The perturbative effect of this higher-order dispersion causes the usual NLS soliton to emit a radiation field. As a result, the given initial pulse propagating through the fibre exhibits nonsolitonic behaviour. We make use of a variational method to demonstrate how an initial pulse by the interaction with the emitted radiation can evolve into a soliton. We also demonstrate that the effect of interaction between the initial pulse and radiation field can be accounted for by including, in the evolution equation, terms associated with self-steepening and stimulated Raman scattering that characterize the optical medium.
Volume 75 Issue 3 September 2010 pp 471-483 Research Articles
Electron Rydberg wave packets in one-dimensional atoms
Supriya Chatterjee Amitava Choudhuri Aparna Saha B Talukdar
An expression for the transition probability or form factor in one-dimensional Rydberg atom irradiated by short half-cycle pulse was constructed. In applicative contexts, our expression was found to be more useful than the corresponding result given by Landau and Lifshitz. Using the new expression for the form factor, the motion of a localized quantum wave packet was studied with particular emphasis on its revival and super-revival properties. Closed form analytical expressions were derived for expectation values of the position and momentum operators that characterized the widths of the position and momentum distributions. Transient phase-space localization of the wave packet produced by the application of a single impulsive kick was explicitly demonstrated. The undulation of the uncertainty product as a function of time was studied in order to visualize how the motion of the wave packet in its classical trajectory spreads throughout the orbit and the system becomes nonclassical. The process, however, repeats itself such that the atom undergoes a free evolution from a classical, to a nonclassical, and back to a classical state.
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