Ijtihad As a Legislative Function: Role of Ijtihad, Ifta and Taqleed in Legislative Process

In Islamic legislation Ijtihad plays an important role and has central position in the whole process. Demands of life change day by day thus it become necessary to take on the structural review of Islamic laws keeping in mind the spirit and discipline of Islamic. Ijtihad thus play as a perfect tool for legislation. Regarding fatawas the jurists followed the methodologies of companions, tabieen, and taba Tabaeen. In cases in which they did not find any legal opinion of their teachers related to a specific problem they themselves tried to find out the solution for that problem from the relevant Texts and formulate their own fatawa. In Pakistan the Judiciary that performs the task of interpretation for law-making, Majlis-e-Shura and various Ulama are exercising the job of Ifta. The Council of Islamic Ideology is the official legislative body of fatawa. Taqleed is also an acceptable mode of legislation whose proofs are evident from Quran and Sunnah. It has been used as a source of legislation in Pakistan as well. In constitution of Pakistan article 189 and 201 are related to Taqlid. Article 189 and 201 makes the decisions of Supreme Court binding on all courts and the High court judgments binding on all subordinate courts. Thus the legislative process in Islam employs the methods of Ijtihad, Ifta and Taqlid as a perfect tool of legislation.

Quantum Chaos in Driven Power-Law Potentials: Generalized Coherent States to Wave Packet Evolution

Quantum wave packets generally spread in their time evolution except in the special case of harmonic oscillator. In bounded Hamiltonian systems, the wave packet reconstructs itself under the condintion of phase matching and manifests the phenomena of quantum revivals and fractional revivals. In an earlier work, Gazeau and Klauder proposed a formalism to construct the quantum states (generalized coherent states) for general Hamiltonian systems with discrete and continuous spectra, and proclaimed them as ‘temporally stable’, i.e. they do not spread under time evolution. In this thesis we study, first, the dispersion of Gazeau-Klauder’s ‘temporally stable’ states, and then study how to overcome the dispersion and to build non-dispersive wave packets for nonlinear dynamical systems by the use of external periodic modulation. Gazeau-Klauder coherent states are developed for power-law potentials and their evolution in space and time is analyzed. We show that these states follow classical dynamics as long as the underlying energy spectrum is linear, otherwise they follow a classical-like evolution upto a few classical periods and disperse thereafter, despite their special construction. The auto-correlation function and probability density as a function of space and time explain the spatio-temporal behavior of these states. The analysis of the wave packet dynamics and resulting recurrence phe- nomena is extended to periodically driven power-law potentials. In the pres- ence of an external periodically modulating force, these potentials may ex- hibit classical and quantum chaos. We show that the dynamics of a quantum wave packet in the modulated power law potentials manifests quantum re- currences at various time scales. We develop general analytical relations for these times and discuss their parametric dependence. We use the recurrence phenomenon as a probe to find out the signatures of nondispersive wave packets in the periodically driven systems.