Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

Astronomy and Cosmogony

Geometry in Physics

Cubic–quartic optical solitons in Kerr and power law media

Dark-in-the-Bright solitary wave solution of higher-order nonlinear Schrödinger equation with non-Kerr terms

We analytically solve the higher-order nonlinear Schr\"odinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and obtain results for bright and dark solitary wave solutions. The functional form of these solutions are different from the traditional sech and tanh bright and dark solitons. Periodic wave solutions are also presented. Going over to the traveling coordinate, we reduce the complicated HNLS equation to the Hamiltonian form and treat the resulting equations by the dynamical systems theory. The results of our study demonstrate that the equation can, in general, support both soliton (bright and dark) and periodic solutions. We estimate the size of the derivative non-Kerr nonlinear coefficients. The results are in good agreement with those of the waveguide made of highly nonlinear optical materials. Our calculated values can be used as model parameters for sub-10 fs pulse propagation.

Higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms: A model for sub-10-fs-pulse propagation

We have studied the modulational instability (MI) of the higher-order nonlinear Schrodinger (HNLS) equation with non-Kerr nonlinearities in an optical context and presented an analytical expression for MI gain to show the effects of non-Kerr nonlinearities and higher-order dispersions on MI gain spectra. In our study, we demonstrate that MI can exist not only for the anomalous group-velocity dispersion (GVD) regime, but also in the normal GVD regime in the HNLS equation in the presence of non-Kerr quintic nonlinearities. The non-Kerr quintic nonlinear effect reduces the maximum value of the MI gain and bandwidth and plays a sensitive role over the Kerr nonlinearity, which leads to continuous wave breaking into a number of stable wave trains of ultrashort optical pulses that can be used to generate the stable supercontinuum white-light coherent sources.

Impact of dispersion and non-Kerr nonlinearity on the modulational instability of the higher-order nonlinear Schrödinger equation

Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background

We derive results for two constants of the motion of a one-dimensionaldamped harmonic oscillator with position-dependent frictional coeﬃcientand use them to obtain two alternative Lagrangian representations, whichare not connected by a gauge term. The Hamiltonians corresponding tothese Lagrangianslead tocanonicallyinequivalent phase-spacedescriptions.We could, however, make use of a perturbation theoretic approach to quan-tize the classical motion using both Hamiltonians and thus demonstratethat the corresponding quantum systems are entirely diﬀerent.PACS numbers: 03.20.+i, 03.30.+p, 03.65.–w

Amitava Choudhuri

Papers

Dark-in-the-Bright solitary wave solution of higher-order nonlinear Schrödinger equation with non-Kerr terms

Higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms: A model for sub-10-fs-pulse propagation

Impact of dispersion and non-Kerr nonlinearity on the modulational instability of the higher-order nonlinear Schrödinger equation

Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background

On the quantization of damped harmonic oscillator