Articles written in Pramana – Journal of Physics
Volume 8 Issue 6 June 1977 pp 545-562 Mathematical Physics
We consider a graded algebra with two products (
With the retention of the gradation structure and the possible choice of two ε-factors we recover the algebras of the canonical formalism of boson and fermion systems for the above classical and quantum theories. We also recover in this case the algebra of anticommutative classical systems considered by Martin along with its quantum analogue.
Volume 10 Issue 3 March 1978 pp 273-282 Classical Mechanics
A Bose type of classical Hamilton algebra, i.e., the algebra of the canonical formalism of classical mechanics, is represented on a linear space of functions of phase space variables. The symplectic metric of the phase space and possible algorithms of classical mechanics (which include the standard one) are derived. It is shown that to each of the classical algorithms there is a corresponding one in the phase space formulation of quantum mechanics.
Volume 10 Issue 4 April 1978 pp 413-427 Solids
Using the Green function method of lattice statics, the lattice distortion in the neighborhood of a vacancy in magnesium has been calculated in three different axially-symmetric (AS) host lattice models and also in a model derived from an empirical interatomic pair potential. The variations in the lattice distortion and the relaxation energy of the vacancy are studied as the size of the defect space is allowed to vary from two to four surrounding neighbors. The perfect static lattice Green functions are computed up to 19 neighbors in the 4 models and the values obtained are shown to be not very sensitive to the model chosen. The lattice relaxation is found to be negligible in all models except in a four-neighbor AS model. The relaxation energies in these four models are computed to be 0.0027 eV, 0.034 eV, 0.28 eV and 0.0069 eV respectively. Results for the monovacancy formation energy, the elastic dipole tensor and the volume change of the crystal due to the vacancy are also presented.
Volume 17 Issue 3 September 1981 pp 257-270 Solid State Physics
Following the standard Green’s functions matrix partitioning technique, the force constant changes needed to explain the translational (6.8 THz) and torsional (10.1 THz) modes occurring in the KCl:NH4+ system are calculated. Three different defect site symmetries are considered for the ammonium ion impurity. These are (i)
Volume 23 Issue 1 July 1984 pp 69-77 Statistical Physics
We calculate the Rayleigh-Brillouin spectrum of a Newtonian fluid undergoing a planar Poiseuille-Couette flow using the fluctuating hydrodynamic approach of Landau and Lifshitz. Our results reduce to the corresponding results for pure Couette flow when the pressure gradient is made to vanish. The Brillouin spectrum is obtainable from that appropriate to Couette flow by a simple rescaling. There are very minute corrections which impart asymmetry to the Brillouin lines as well as the Rayleigh line, and these can be selectively picked up by suitable choice of the scattering geometry.
Volume 35 Issue 4 October 1990 pp 349-354
The fluctuating hydrodynamics theory of a fluid possessing internal rotation is set up following the Landau-Lifshitz approach.
Volume 40 Issue 1 January 1993 pp 1-16
Abstracting from Nambu’s work  on the generalization of Hamiltonian mechanics, we obtain the concept of a classical Nambu algebra of type I (CNA-I). Consistency requirement of time evolution of the trilinear Nambu bracket leads to a new five point identity (FPI). Incorporating the FPI into CNA-I, we obtain a classical Nambu algebra of type II (CNA-II). Nambu’s algorithm for generalized classical mechanics turns out to be compatible with CNA-II. Tensor product composition of two CNA-I’s results in another CNA-I whereas that of two CNA-II’s does not. This implies that interacting systems cannot be consistently treated in Nambu’s framework. It is shown that the recent generalization of Nambu mechanics based on an arbitrary Lie group (instead of the particular case of the rotation group as in the case of Nambu’s original algorithm) suggested by Biyalinicki-Birula and Morrison , is compatible with CNA-I but not with CNA-II. Relaxation of the commutative and associative observable product by making it nonassociative so as to arrive at the quantum counterpart meets with serious difficulties from the view point of tensor product composition property. Thus neither CNA-I nor CNA-II have quantum counterparts. Implications of our results are discussed with special reference to existing work on Nambu mechanics in the literature.
Volume 41 Issue 2 August 1993 pp 125-137 Research Articles
There exists a coassociative and cocommutative coproduct in the linear space spanned by the two algebraic products of a classical Hamilton algebra (the algebraic structure underlying classical mechanics ). The transition from classical to quantum Hamilton algebra (the algebraic structure underlying quantum mechanics) is an
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