Bindu A. Bambah

Coherent states of nonlinear algebras: applications to quantum optics

We present a general unified approach for finding the coherent states (CSs) of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general procedure to map these deformed algebras to appropriate Lie algebras. This is used, for the noncompact cases, to obtain the annihilation operator eigenstates, by finding the canonical conjugates of these operators. Generalized CSs, in the Perelomov sense, also follow from this construction. This allows us to explicitly construct CSs associated with various quantum optical systems.

Yang-Mills Magnetofluid Unification

We generalize the hybrid magnetofluid model of a charged fluid interacting with an electromagnetic field to the dynamics of a relativistic hot fluid interacting with a non-Abelian field. The fluid itself is endowed with a non-Abelian charge and the consequences of this generalization are worked out. Applications of this formalism to the quark gluon plasma are suggested.

Three dimensional quadratic algebras : Some realizations and representations

Four classes of three-dimensional quadratic algebra of the type [Q0,Q±] = ±Q±, [Q+,Q-] = aQ02 + bQ0 + c, where (a,b,c) are constants or central elements of the algebra, are constructed using a generalization of the well known two-mode bosonic realizations of su(2) and su(1,1). The resulting matrix representations and single variable differential operator realizations are obtained. Some remarks on the mathematical and physical relevance of such algebras are given.

JORDAN–SCHWINGER-TYPE REALIZATIONS OF THREE-DIMENSIONAL POLYNOMIAL ALGEBRAS

A three-dimensional polynomial algebra of order m is defined by the commutation relations [P0,P±] = ± P±, [P+,P-] = ϕ(m)(P0) where ϕ(m) (P0) is an mth order polynomial in P0 with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders l and m can be combined to give two distinct (l+m+1)th order polynomial algebras. This procedure follows from a generalization of the well-known Jordan–Schwinger method of construction of su(2) and su(1,1) algebras from two mutually commuting boson algebras.

On a Raychaudhuri equation for hot gravitating fluids

We generalise the Raychaudhuri equation for the evolution of a self gravitating fluid to include an Abelian and non-Abelian hybrid magneto fluid at a finite temperature. The aim is to utilise this equation for investigating the dynamics of astrophysical high temperature Abelian and non-Abelian plasmas.

Classical gauge theories as dynamical systems—Regularity and chaos

In this review we present the salient features of dynamical chaos in classical gauge theories with spatially homogeneous fields. The chaotic behaviour displayed by both abelian and non-abelian gauge theories and the effect of the Higgs term in both cases are discussed. The role of the Chern-Simons term in these theories is examined in detail. Whereas, in the abelian case, the pure Chern-Simons-Higgs system is integrable, addition of the Maxwell term renders the system chaotic. In contrast, the non-abelian Chern-Simons-Higgs system is chaotic both in the presence and the absence of the Yang-Mills term. We support our conclusions with numerical studies on plots of phase trajectories and Lyapunov exponents. Analytical tests of integrability such as the Painlevé criterion are carried out for these theories. The role of the various terms in the Hamiltonians for the abelian Higgs, Yang-Mills-Higgs and Yang-Mills-Chern-Simons-Higgs systems with spatially homogeneous fields, in determining the nature of order-disorder transitions is highlighted, and the effects are shown to be counter-intuitive in the last-named system.

Order - chaos transitions in field theories with topological terms: a dynamical systems approach

We present a comparative study of the dynamical behaviour of topological systems of recent interest, namely the non-Abelian Chern - Simons Higgs system and the Yang - Mills Chern - Simons Higgs system. By reducing the full field theories to temporal differential systems by using the assumption of spatially homogeneous fields, we study the Lyapunov exponents for two types of initial conditions. We also examine in minute detail the behaviour of the Lyapunov spectra as a function of the various coupling parameters in the system. We compare our results with those for Abelian Higgs, Yang - Mills Higgs and Yang - Mills Chern - Simons systems which have been discussed recently by other authors. The role of the various terms in the Hamiltonians for such systems in determining the order - disorder transitions is emphasized and shown to be counter-intuitive in the Yang - Mills Chern - Simons Higgs systems.

Degeneracy Resolution Capabilities of NOνA and DUNE in the Presence of Light Sterile Neutrino

We investigate the implications of a sterile neutrino on the physics potential of the proposed experiment DUNE and future runs of NO A using latest NO A results. Using combined analysis of the disappearance and appearance data, NO A reported preferred solutions at normal hierarchy (NH) with two degenerate best-fit points: one in the lower octant (LO) and = 1.48 and the other in higher octant (HO) and = 0.74 . Another solution of inverted hierarchy (IH), which is 0.46 away from best fit, was also reported. We discuss chances of resolving these degeneracies in the presence of sterile neutrino.

Baryon asymmetry, inflation and squeezed states

We use the general formalism of squeezed rotated states to calculate baryon asymmetry in the wake of inflation through parametric amplification. We base our analysis on a B and CP violating Lagrangian in an isotropically expanding universe. The B and CP violating terms originate from the coupling of complex fields with non-zero baryon number to a complex background inflaton field. We show that a differential amplification of particle and antiparticle modes gives rise to baryon asymmetry.

Isospin squeezed states, disoriented chiral condensates and pion production: a dynamic group theoretical approach

Abstract We make a complete dynamical study of isotopic spin conservation effects on the multiplicity distributions of both hard and soft pions emitted in a quark gluon plasma undergoing a non-equilibrium phase transition.