arXiv subjects
Publications and source records attributed to S. Chaturvedi.
An interpolation between the canonical partition functions of Bose, Fermi and Maxwell-Boltzmann statistics is proposed. This interpolation makes use of the properties of Jack polynomials and leads to a physically appealing interpolation between the statistical weights of the three statistics. This, in turn, can be used to define a new exclusion statistics in the spirit of the work of Haldane.
Eigenstates of the linear combinations $a^2+βa^{\dagger2}$ and $ab+βa^\dagger b^\dagger$ of two boson creation and annihilation operators are presented. The algebraic procedure given here is based on the work of Shanta et al. [Phys. Rev. Lett. {\bf 72}, 1447, 1994] for constructing eigenstates of generalized annihilation operators.
A direct proof of the resolution of the identity in the odd sector of the Fock space in terms of squeezed number states $D(ξ)|2m+1>; D(ξ) = \exp((ξa^{\dagger2}-ξ^*{a^2})/2)$ is given. The proof entails evaluation of an integral involving Jacobi polynomials. This is achieved by the use of Racah identities.
A general formula for the grand canonical partition function for a para Fermi system of any order and of any number of levels is derived.
A new proof for the completeness of the coherent states $D(α)\mid f>$ for the Heisenberg Weyl group and the groups $SU(2)$ and $SU(1,1)$ is presented. Generalizations of these results and their consequences are disussed.