• C L Mehta

Articles written in Pramana – Journal of Physics

• Hölder’s inequality for matrices

We prove that for arbitraryn×n matricesA1,A2,…,Am and for positive real numbersp1,p2,…,pm withp1−1+p2−1+…+pm/−1=1, the inequality$$|Tr(A_1 A_2 ...A_m )^2 |&lt; \mathop {II}\limits_{k = 1}^m [Tr(A_k^\dag A_k )^{p_k } ]P_k^{ - 1}$$ holds.

• Evanescent waves and the van Cittert Zernike theorem in cylindrical geometry

The cylindrical angular spectrum of the wavefield is introduced. In this representation the field consists of homogeneous as well as evanescent waves. The representation is applied to propagation problems and an analogue of van Cittert Zernike theorem is obtained in cylindrical geometry.

• Extremum uncertainty product and sum states

We consider the states with extremum products and sums of the uncertainties in non-commuting observables. These are illustrated by two specific examples of harmonic oscillator and the angular momentum states. It shows that the coherent states of the harmonic oscillator are characterized by the minimum uncertainty sum 〈(Δq)2〉 + 〈(Δp)2〉. The extremum values of the sums and products of the uncertainties of the components of the angular momentum are also obtained.

• Intensity fluctuations in thermal light with orthogonally polarised multiple-peak spectrum

The moment generating function of the integrated light intensity of thermal radiation having multiple peak spectrum is obtained. Cases of two-peak and three-peak spectra where different peaks are in orthogonal states of polarisation are considered. The moment generating function is shown to be the product of two simpler generating functions.

• Two-mode para-Bose number states

Two-mode para-Bose number states are discussed. The two-mode system has been chosen as it is a representative of the multi-mode system. Salient properties like normalization, orthogonality and degeneracy of these states have also been discussed.

• Squeezed vacuum as an eigenstate of two-photon annihilation operator

We introduce the inverse annihilation and creation operatorsâ−1 andâ+-1 by their actions on the number states. We show that the squeezed vacuum exp(1/2;ξâ+2]|0&gt; and squeezed first number state exp[1/2;ξâ+2]|n=1&gt; are respectively the eigenstates of the operators (â†−1â) and (ââ+-1) with the eigenvalue ξ.

• # Pramana – Journal of Physics

Volume 94, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019