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V. Srinivasan

Publications and source records attributed to V. Srinivasan.

27 records · Page 2Linked to original sources
arXiv1999

Coherent States for the Deformed Algebras

We provide a unified approach for finding the coherent states of various deformed algebras, including quadratic, Higgs and q-deformed algebras, which are relevant for many physical problems. For the non-compact cases, coherent states, which are the eigenstates of the respective annihilation operators, are constructed by finding the canonical conjugates of these operators. We give a general procedure to map these deformed algebras to appropriate Lie algebras. Generalized coherent states, in the Perelomov sense, follow from this construction.

quant-ph↗
arXiv1998

Congruences and Canonical Forms for a Positive Matrix: Application to the Schweinler-Wigner Extremum Principle

It is shown that a $N\times N$ real symmetric [complex hermitian] positive definite matrix $V$ is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in $SO(m,n)$ [ $SU(m,n)$], for any choice of partition $N=m+n$. It is further shown that the method of proof in this context can easily be adapted to obtain a rather simple proof of Williamson's theorem which states that if $N$ is even then $V$ is congruent also to a diagonal matrix modulo a symplectic matrix in $Sp(N,{\cal R})$ [$Sp(N,{\cal C})$]. Applications of these results considered include a generalization of the Schweinler-Wigner method of `orthogonalization based on an extremum principle' to construct pseudo-orthogonal and symplectic bases from a given set of linearly independent vectors.

math-ph↗
arXiv1998

Quantum phase space distributions in thermofield dynamics

It is shown that the the quantum phase space distributions corresponding to a density operator $ρ$ can be expressed, in thermofield dynamics, as overlaps between the state $\mid ρ>$ and "thermal" coherent states. The usefulness of this approach is brought out in the context of a master equation describing a nonlinear oscillator for which exact expressions for the quantum phase distributions for an arbitrary initial condition are derived.

quant-ph↗
arXiv1998

A new orthogonalization procedure with an extremal property

Various methods of constructing an orthonomal set out of a given set of linearly independent vectors are discussed. Particular attention is paid to the Gram-Schmidt and the Schweinler-Wigner orthogonalization procedures. A new orthogonalization procedure which, like the Schweinler- Wigner procedure, is democratic and is endowed with an extremal property is suggested.

quant-ph↗
arXiv1997

Degeneracy Structure of the Calogero-Sutherland Model: an Algebraic Approach

The degeneracy structure of the eigenspace of the N-particle Calogero-Sutherland model is studied from an algebraic point of view. Suitable operators satisfying SU(2) algebras and acting on the degenerate eigenspace are explicitly constructed for the two particle case and then appropriately generalized to the N-particle model. The raising and lowering operators of these algebras connect the states, in a subset of the degenerate eigenspace, with each other.

hep-th↗
arXiv1996

An interpolation between Bose, Fermi and Maxwell-Boltzmann statistics based on Jack Polynomials

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.

hep-th↗