Volume 45, Issue 4
October 1995, pages 305-376
pp 305-309 October 1995
Painlevé analysis and integrability of the damped anharmonic oscillator equation
The Painlevé analysis is applied to the anharmonic oscillator equation$$\ddot x + d\dot x + Ax + Bx^2 + Cx^3 = 0$$. The following three integrable cases are identified: (i)C=0,d^{2}=25A/6,A>0,B arbitrary, (ii)d^{2}=9A/2,B=0,A>0,C arbitrary and (iii)d^{2}=−9A/4,C=2B^{2}/(9A),A<0,C<0,B arbitrary. The first two integrable choices are already reported in the literature. For the third integrable case the general solution is found involving elliptic function with exponential amplitude and argument.
pp 311-317 October 1995
The particle in a box problem inq-quantum mechanics
G Vinod K Babu Joseph K M Valsamma
Aq-deformed,q-Hermitian kinetic energy operator is realised and hence aq-Schrödinger equation (q-SE) is obtained. Theq-SE for a particle confined in an infinite potential box is solved and the energy spectrum is found to have an upper bound.
pp 319-326 October 1995
G Ramachandran A R Usha Devi N S Saandeep Kannada Vardhana
Following the recent work of Chandleret al on quasi probability distributions for spin-1/2 particles, we show that polarized light can be interpreted in terms of trivariate probability distributions in two different ways by choosing the variates to correspond to (i) the co-ordinates on the Poincare sphere, (ii) the components of the spin operator of the photon. In either case, it is shown that the Margenau-Hill procedure leads to probability mass functions while the Wigner-Weyl approach leads to probability density functions and the well-known Stokes parameters are also realised as appropriate averages with respect to these distribution functions.
pp 327-331 October 1995
On the Dirac equation with anomalous magnetic moment term in a beam of electromagnetic wave
The object of the paper is to obtain the solution of the Dirac equation with the Pauli-term in an electromagnetic field depending on the single variable (ct -nr) along the directionn.
pp 333-342 October 1995
Fermilab top mass and modified Fritzsch mass matrices
Fritzsch like mass matrices with non-zero 22-elements both in U sector and D sector have been investigated in the context of latest data regardingm_{t}^{phys}, |V_{ub}|, |V_{cb}|, |V_{td}| and |V_{ts}|. Unlike several other phenomenological models, the present model not only accommodates the value ofm_{t}^{phys} in the range 150–240 GeV, encompassing the CDF and D0 values, but is also able to reproduce |V_{cb}| ≊0.040 and |V_{ub}/V_{cb}| = 0.08±0.02 and |V_{td}| is predicted to lie in the range 0.005–0.014. Further, the angles of the unitarity triangle, related to the CP-violating asymmetries, are calculated to be in the ranges −1.0⩽sin2α⩽−0.1, 0.6 ⩽sin2α⩽1.0 and 0.48⩽sin2β⩽0.56, which are in agreement with other recent calculations.
pp 343-353 October 1995
Vacuum structure, chiral symmetry breaking and electric dipole moment of neutron
Considering a CP-violating QCD interaction, the electric dipole moment of neutron (EDMN) is estimated in a quark model of light mesons with a dynamical breaking of chiral symmetry through a non-trivial vacuum structure. Pion and kaon, being treated consistently within the model, yield to the constituent quark wave functions as well as the dynamical quark masses and thus determine the constituent quark field operators with respect to light quark flavors. Using the translationally invariant hadronic states and these constituent quark field operators, the EDMN estimated here remains well within the recent experimental bound ofD_{n}<11 × 10^{−26} e-cm with the CP-violation parameter |ϑ|=10^{−8}, which in fact accounts for a strong CP-violation.
pp 355-368 October 1995
Controlling chaos: Stabilization of unstable orbits using exponential control for maps and flows
We demonstrate that chaos can be controlled using multiplicative exponential feedback control. Unstable fixed points, unstable limit cycles and unstable chaotic trajectories can all be stabilized using such control which is effective both for maps and flows. The control is of particular significance for systems with several degrees of freedom, as knowledge of only one variable on the desired unstable orbit is sufficient to settle the system onto that orbit. We find in all cases that the transient time is a decreasing function of the stiffness of control. But increasing the stiffness beyond an optimum value can increase the transient time. We have also used such a mechanism to control spatiotemporal chaos is a well-known coupled map lattice model.
pp 369-376 October 1995
Macroscopic equation of motion in inhomogeneous media: A microscopic treatment
A M Jayannavar Mangal C Mahato
The dynamical evolution of a Brownian particle in an inhomogeneous medium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative stability of states in nonequilibrium systems which has been a subject of debate for over several decades. The theoretical treatments adopted so far are mostly phenomenological in nature. In this work we give a microscopic treatment of this problem. We derive the Langevin equation of motion and the associated Fokker-Planck equation. The correct reduced description of the Kramers equation in the overdamped limit (Smoluchowski equation) is obtained. Our microscopic treatment may be helpful in understanding the working of thermal ratchets, a problem of much current interest.
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