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.
آدمی موت سے ڈرتے ہیں جیسا کہ بچے اندھیرے میں جانے سے ڈرتے ہیں۔ اور جیسا کہ کہانیوں سے بچوں کا فطری ڈر بڑھ جاتا ہے۔ یہی حال موت کا ہے یقیناً موت کی سوچ ، کہ یہ گناہوں کی اجرت ہے۔ اور دوسری دنیا کا راستہ مقدس اور مذہبی ہے۔ لیکن یہ انسانی فطرت کے قانون کے مطابق واقع ہوگی یہ ڈر کمزور ہے۔ تاہم مذہبی غور وفکر میں یہ بعض اوقات تکبر اور تو ہم پرستی ہوتی ہے۔ آپ نے کچھ پادریوں کی نفس کشی کی کتابیں پڑھی ہوں گی کہ ایک آدمی اپنے آپ میں سوچتا ہے کہ انگلی کو دبانے اور ایک اذیت دینے سے ہم درد کیوں محسوس کرتے ہیں؟ اور اس سے ہم تصور کر سکتے ہیں کہ موت کے درد کیا ہوں گے ۔ جب سارا جسم تباہ اور تحلیل ہوتا ہے جب بہت مرتبہ موت ایک عضو کی اذیت سے کم درد کے ساتھ گزرتی ہے تو بہت زیادہ اہم حصوں میں تیز حِس نہیں ہوتی ۔ اور اس سے جو محض ایک فلاسفر اور فطری آدمی کے طور پر کہتا ہے ، یہ بڑا اچھا کہا گیا تھا ۔ موت کی مذہبی رسومات کی رفاقت موت سے زیادہ خوف ناک ہوتیں ہیں ۔ آہیں، پریشانیاں اور بے رنگ چہرہ اور دوستوں کا رونا اور سیاہ کپڑے اور رسومات موت کو خوفناک دکھاتے ہیں یہ مشاہدہ کرنے کے قابل کہ انسان کے ذہن میں کوئی جذبہ اتنا کمزور نہیں۔ لیکن یہ موت کے ڈر کو زیر اور مغلوب کرتا ہےاور اس لیے موت خوفناک دشمن نہیں ہے۔ جب ایک آدمی کے پاس موت کے لیے بہت سے جذبات ہوں جو کہ موت کی جنگ سے جیت سکتے ہیں۔ بدلہ موت سے جیت جاتا ہے محبت اس کی پرواہ نہیں کرتی۔ مرتبہ اس کی خواہش کرتا ہے غم اس کو...
تعمیرِسماج کا اسلامی منہج : حضرت عمر فاروقؓ کی فکر و بصیرت کی روشنی میں تجزیاتی مطالعہ The modern era is considered as advanced and humanized in terms of materialized advancement only. Today the leading societies of the world have created a self-sufficient religion in the name of humanism and have set standards ignoring Divine guidance. Thus, man has the right to decide the rules and norms of society on his own goodwill. As a result, the breaking of family system, appearance of gay and homosexual relations, etc. Are being considered as legitimate in many countries where religion is no more considered a guiding principle. On the other hand, revealed religions have focus on the development of humanity in terms of both the ethical and materialistic perspectives. Islam as religion has provided a model of such an advancement and social change in history that has proven that Divine guidance is major source for betterment and development of civilization and humanity. This was practically proven in the time of Muslim golden rule in the world. The caliph Umar (R.A) was the man who introduced for the first time, the principles and values, which has changed the Arabs to a civilized and humanized nation. This huge change was made possible in the light of Divine guidance. In this academic article all such norms, values, and principles that were introduced by Sayyīdnā Umar (R.A) which brought a social change in his Era are discussed. Facts have been collected from historic books and presented following the descriptive and analytical method. Although, the information was narrated and scattered in the books, no proper study was introduced where the role of these reforms in the social construction was analyzed. The aim of the study has to investigate the historic facts of social change in the era of the righteous Caliph Sayyidna Umar bin Khattāb and prepare a guideline for the humanity in present era.
In this thesis ―Purification, Characterization and Binding of Metals to Zinc Alpha 2-Glycoprotein (ZAG) by Employing Various Techniques‖ the development of several techniques were carried out to analyze the interaction of biologically important metals of Irving William Series. The expression and purification of the ZAG protein was also optimized for the preparation of samples. The folding to the native conformation was also carried out. That ZAG protein is present in almost all fluids of the body. Since the discovery of ZAG, several studies have been carried out. The importance of ZAG as an important biochemical agent is known long before. The growing number of literature since today demonstrates that it’s an important biomarker for the cancer cachexia, prostate cancer, lipid mobilizing agent and obesity suppressor. The crystal structure of ZAG reveals that the fold and distribution of domains are similar to the Major histocompatibility complex-I (MHC-I) molecules. This class is known for their immune regulation and thus ZAG is believed as a central player in the immune system and cellular signaling. There is no clear evidence of ZAG participation in the cancerous conditions but over expression is dealt as a biomarker. The study shows that the ZAG interacts with several ligands. There interaction with metals is known for boosting the bioactivity of ZAG. Although, it’s believed long ago that the ZAG is an important protein that participate in several biochemical processes and little is known to understand the ligands bound conformations of ZAG with their targets like peptides and metals. In this current project, we were focused to get the good expression and purification procedure for the preparation of ZAG. The unnative aggregated fold of ZAG from the inclusion bodies was transformed into the native fold using refolding and dialysis method optimization. The introduction of histidine tag to the C-terminal and their successful removal by the Carboxypeptidase Y enzyme was also carried out. The results of the cleavage of histidine tag were evaluated with gel electrophoresis, Mass Spectrometry and Fluorescence Spectroscopy. The confirmation of native fold and bioactivity was also confirmed from DAUDA binding affinity using fluorescence emission. The formation of metal complex of Irving William Series with ZAG and their respective complexation analysis was also studies using MALDI-TOF MS and Fluorescence Spectroscopy. xiii It was found that the ZAG has multiple binding sites that interact with metals even in the presence of DAUDA. The X-ray tube analysis using FPXRF shows that Fe (III) and Co (II) has similar concentration of atoms bound to ZAG molecules.