A K Rajagopal
Articles written in Pramana – Journal of Physics
Volume 1 Issue 3 September 1973 pp 135-146 Solids
A simple derivation of the three magnon bound state equation
Chanchal K Majumdar G Mukhopadhyay A K Rajagopal
A simple derivation of the equation for determining the bound states of three magnons in the Heisenberg linear chain with longitudinal anisotropy is given. The present method utilizes nothing more than the Schrödinger equation and Faddeev’s three body equations, and avoids the introduction of the ideal spin wave Hilbert space.
Volume 4 Issue 3 March 1975 pp 140-152 Solids
Some results in the theory of interacting electron systems
The expressions for the longitudinal dielectric function, spin and orbital susceptibilities in the static, long wavelength limit are evaluated by solving the corresponding linearized vertex functions exactly in this limit. The plasma dispersion relation to leading order in the long wave limit is similarly obtained. These are compared with the corresponding results obtained previoulsy by us by a variational solution to the same vertex equations. It is established that the variational method gives the exact results in the static, zero wave vector limit, involving the proper renormalizations. The plasma dispersion relation is found to be the same as in the exact calculation whereas the coefficient of q^{2} in the static density correlation function has an important additional contribution to the variational result. Applications of these results are briefly discussed.
Volume 33 Issue 3 September 1989 pp 347-358 Mathematical Physics
Bivariate averaging and the Wigner distribution function
In order to gain insight into the nature of the Wigner and related distribution functions, bivariate averaging functions of real unbounded variables with absolutely continuous marginals that are ordinary probabilities are considered. Accordingly variables are chosen to be phase space variables that are respectively eigenvalues of position and momentum operators. The impact of the condition that the marginals are squared magnitudes of amplitudes that are Fourier transforms of one another is emphasized by the delay of the introduction of this Fourier transform condition until after the form for a bivariate distribution with the given marginals is obtained. When the respective amplitudes are fourier transforms of one another, special cases of the bivariate averaging function correspond to generalized Wigner functions characterized by a parameter
Volume 38 Issue 3 March 1992 pp 233-247
We first draw attention to the fact that the position operator,$$\hat X$$, its translation generator,$$\hat P$$, and its scale generator,$$\hat D$$, form an important group of triplet of operators that appear in the Heisenberg uncertainty relation stated in its most general form. The pair$$(\hat X,\hat P)$$ forms the phase-space and they have led to Fourier transform pair, the autocorrelation function, the Wiener-Khinchine theorem, and the Wigner function with many different applications to wave phenomena. The importance of the pairs$$(\hat X,\hat D)$$ and$$(\hat P,\hat D)$$ has been pointed out by Moses and Quesada (1972, 1973, 1974) who showed that we must then consider a Mellin transform pair, a scale autocorrelation function, and a corresponding Wiener-Khinchine theorem. In the present paper, we define and explore properties of a bivariate averaging function defined in a new “phase-space” involving the Mellin transform variable and its partner which can either be the position or momentum, analogous to the Wigner function. The not-necessarily positive feature of the bivariate averaging functions is traced to the general Heisenberg uncertainty mentioned above. The properties and their inter-relationships among the averaging functions are given. We hope this will be of use in discussing physical phenomena involving fractals, turbulence, and near phase transitions where the scaling properties are of importance.
Volume 39 Issue 6 December 1992 pp 615-631
A theoretical framework for treating the effects of magnetic field
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