M. Sabir

Function projective synchronization in chaotic and hyperchaotic systems through open-plus-closed-loop coupling

Recently introduced function projective synchronization in which chaotic systems synchronize up to a scaling function has important applications in secure communications. We design coupling function for unidirectional coupling in identical and mismatched oscillators to realize function projective synchronization through open-plus-closed-loop coupling method. Numerical simulations on Lorenz system, Rossler system, hyperchaotic Lorenz, and hyperchaotic Chen system are presented to verify the effectiveness of the proposed scheme.

Temperature dependence of coupling constants

We study the temperature-dependence of coupling constants at the one-loop level for massive ϕ4 theory and massive scalar electrodynamics (SED). It is found that the scalar coupling constant λ for m2 > 0 decreases with temperature leading to a phase transition to a non-interacting phase. In a model with m2 < 0, λ increases as 1n T. The gauge coupling constant of SED increases uniformly with temperature.

Path integral analysis of harmonic oscillators with time-dependent mass

Two cases of forced harmonic oscillators with time dependent mass for which exact propagators can be evaluated are presented. From the exact propagators, normalized solutions of the corresponding Schrödinger equations are arrived at. Time-dependent invariants are also found.

Non-integrability of SU(2) Yang-Mills and Yang-Mills-Higgs systems

The spherically symmetric time-dependent SU(2) Yang-Mills equations and Yang-Mills-Higgs equations are shown to be non-integrable by using the Weiss, Tabor and Carnevale (1983) method of Painleve analysis. Reduced equations corresponding to these systems are also found to be non-integrable.

A bag model study ofD mesons

An investigation of the newly discovered charmed mesonsD 0 andD +, particularly their non-leptonic decay modes, is carried out in the framework of the MIT bag model. The amplitude for a number of two-body final state decays are explicitly evaluated and compared with other available estimates.

Chaos and curvature in a quartic Hamiltonian system

Chaotic behaviour of a quartic oscillator system given byH l/2(p12+p22)+ (1/12)(1 -α) (q14+q24)+1/2q12q22 is studied. Though the Riemannian curvature is positive the system is nonintegrable except when S/B α = 0. Calculation of maximal Lyapunov exponents indicates a direct correlation between chaos and negative curvature of the potential boundary.

Integrability of two-dimensional homogeneous potentials

Combining the extended Painleve conjecture with Yoshidas singularity and stability analyses (1986) it is shown that, for two-dimensional homogeneous potentials of degree 2m, integrability restricts Kowalevskaya exponents and integrability coefficients to discrete sets of values. This result is made use of in the analysis of integrability of symmetric potentials with m=2, 3 and 4. Direct construction of additional first integrals is successful only in special cases which can be transformed to known integrable ones.

Relativistic non-covariance in interacting spin-1 field theories

Acausal interactions of a massive spin-1 field such as symmetric tensor and quadrupole moment couplings are not covariant at the basic c-number level. Curiously enough, certain causal derivative couplings are also non-covariant.

Transition from order to chaos in SU(2) Yang-Mills-Higgs system

Time-dependent spherically symmetricSU(2) Yang-Mills-Higgs system is shown to be chaotic near the ’t Hooft-Polyakov monopole solution by calculating the maximal Lyapunov exponents. A phase transition like behaviour from order to chaos is observed as a parameter depending on the self interaction constant of scalar fields increases.

Reformulation of Einstein gravity as a flat space gauge theory

Based on an algebraic decomposition of a fourth rank tensor in terms of second rank tensors we suggest a reformulation of Einstein’s gravitational theory as a flat space gauge theory. This has been done by associating a curved manifold with a flat space U(2)×U(2) gauge theory. It is shown that while, in order to reproduce Einstein field equations one has to use a non-Yang-Mills action, the linearized equations follow from a Yang-Mills action. A relation between the metric and gauge fields is obtained. The consistency of the postulates is also verified.