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

Thesis Info

Access Option

External Link

Author

Iqbal, Shahid

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2014

Thesis Completion Status

Completed

Subject

Physics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2518/1/2576S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727057564

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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.
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ہجر فراق سوہنے یار دے وچ: ۶

سی حرفی ۔۶
الف
الٰہی بھیج ماہی نوں تھکے نین وچاری دے
لگی سانگ سینے وچ ڈاہڈی، کیتے قول اقراری دے
برہوں بن رسولی پنگرے، جاگے پھٹ بیماری دے
آکھ حنیف نہ ملیا ماہی، ٹُٹے جوش خماری دے

ب
برباد کیتا چا نیناں ، لگے وانگ کٹاری دے
نیوں لگا چخہ چڑھ بہنا، رونے عمراں ساری دے
نین نشیلے کردے حیلے، چھوپے پا دل داری دے
آکھ حنیف نہ ملیا ماہی، لکھے لیکھ لکھاری دے

ت
توے تے روٹی سڑدی جیوں کر ہِکے پاسے تے
دل جگر تے چکی چلے ، غلہ جیویں خراسے تے
عاشق نال رقیب سڑیندے جیویں معشوق دے ہاسے تے
آکھ حنیف نہ ملیا ماہی، جیوندے رہے دلاسے تے

ث
ثمر جے پیار دا چاہویں، عاجز پکڑ حلیمی نوں
گھر آئے دی عزت کرنی ہو کے کھڑا تعظیمی نوں
ونڈیں پیار جگت وچ بہتا، بھلیں نہیں کریمی نوں
آکھ حنیف نہ ملیا ماہی، سِک دے یار قدیمی نوں
ج
جوانی ایویں گزری، کدی نہ سدیا یاراں نے
رُٹھے یار ، غماں رُت آئی، موڑے منہ بہاراں نے
وچ حیرانی، سرگردانی، فانی ہوئے ہزاراں نے
آکھ حنیف نہ ملیا ماہی، ہو گئے حال بیماراں نے

ح
حاصل کی محبت اندر، سر بدنامیاں چائیاں نی
نعمت کھانے ، صاف پوشاکاں، مڈھوں منوں بھلائیاں نی
چنتے ، فکر، اندیشے آئے ، کر دے غم، چڑھائیاں نی
آکھ حنیف نہ ملیا ماہی، کیتیاں بے وفائیاں نی

خ
خدا دی ذات نرالی ویکھے ایس بیماری نوں
عشق ازل دا روگ اولا، کھاندا برہوں ماری نوں
وچ جدائی رہی ترہائی، وصل نہ درداں ماری نوں
آکھ حنیف نہ ملیا ماہی، بخشیں اوگنہاری نوں

د
دوائی روگ میرے دی، باہجھوں نہیں سجن دے کو
دے دیدار مرے دل دارا، موتی آس دے...

Post-Covid 19, Online consumer purchase behavior in Pakistan

Since Covid-19, there has been a rise in e-commerce and online brands' influence on consumer buying behavior. It is crucial to investigate the factors that impact online consumer purchase behavior. Applying the theory of reasoned action (TRA), our study seeks to assess the extent to which customer satisfaction and perceived risks build trust and how trust, consumer engagement, and ease of purchase would act as reasons for consumers to engage in e-commerce in Pakistan. Using data gathered from 400 respondents via a questionnaire, we have demonstrated the precise relationship between these six constructs. Results indicate that customer satisfaction positively influences trust while perceived risks negatively affect it and that trust and consumer engagement positively and directly impact purchase behavior. Online retailers should improve these factors and modify the online environment to increase sales from their e-channels and improve customer retention

Seroprevalence of Toxoplasmosis, Hematological and Serum Biochemical Profile in Sheep in Multan and Khanewal Districts, Punjab Pakistan .

The present study was conducted to determine the seroprevalence of toxoplasmosis, hematological and serum biochemical changes in sheep naturally infected with Toxoplasma gondii and compared between T. gondii positive and negative sheep in Multan and Khanewal districts, Punjab (Pakistan).Blood samples were collected from 500 sheep and T. gondii antibodies were tested by latex agglutination test (LAT) and Enzyme Linked Immunosorbent Assay (ELISA).Information related to hosts and herds were recorded on questionnaire basis such as gender, age of animals, aborted or non-aborted sheep, cats association with herd, method of disposing aborted fetuses and herd size.The overall prevalence of toxoplasmosis in sheep was 33.6% by latex agglutination test (LAT) and 27.4% by ELISA (P-value = 0.033, OR = 1.341, 95 % CI = 1.023, 1.757).The area wise prevalence of toxoplasmosis was 34.02% and 33. 01 % by LAT (P-value = 0.813, OR = 1.031, 95 % CI = 0.802, 1.324) in Multan and Khanewal and 28.12 % and 26.41 % by ELISA (P-value = 0.672, OR = 1.065, 95 % CI = 0.796, 1.424) in Multan and Khanewal respectively.Difference was statistically non-significant (P>0.05).The seroprevalence of toxoplasmosis was compared between aborted and non-aborted sheep and according to these results infection rate was 51.66% and 31.10% in aborted and non-aborted sheep by LAT (P-value = 0.002, OR = 1.661, 95 % CI = 1.248, 2.211) and 41.66 % and 26.22% in aborted and non-aborted sheep by ELISA (P-value = 0.013, OR = 1.589, 95 % CI = 1.128, 2.238) respectively.Difference was statistically significant (P<0.05) by both techniques.The relationship between sex of sheep and toxoplasmosis showed that infection was 31.37% and 33.85 % by LAT (P-value = 0.722, OR = 0.927, 95 % CI = 0.605, 1.419) in males and females respectively.Similarly prevalence was 19.6 % and 28.28% by ELISA (P-value = 0.188, OR = 0.693, 95 % CI = 0.390, 1.232) in males and females respectively.The prevalence was higher in females than males and difference was statistically non-significant (P>0.05) by both techniques.The prevalence of T. gondii was compared between different age groups and according to these findings infection rate was higher in age group 60-73 months (64.5% and 38.7%) and lowest in age group 4-17 months (26.4% and 22.4%) by LAT (P-value = 0.001) and ELISA (P-value = 0.404).Difference was statistically significant (P<0.05) by LAT and non-significant (P>0.05) by ELISA.Risk factors associated with prevalence of toxoplasmosis in sheep were also studied and according to these results a large flock size, presence of cats, and the aborted fetuses openly left on ground were all statistically significant (P≤0.05) risk factors that were positively associated with prevalence of toxoplasmosis in sheep flocks.Hematological and serum biochemical parameters were studied between T. gondii positive and negative sheep andaccording to these results mean values of haemoglobin, glucose, cholesterol, AST, ALT and LDH were 9.5 ± 2.6 g/dL, 50.6 ± 11.3 mg/dL, 211.6 ± 79.6 mg/dL, 216.4 ± 144.4 U/L, 79.0 ± 64.1 U/L, 613.9 ± 297.2 U/L in T. gondii positive sheep by LAT and 9.9 ± 3.1 g/dL, 52.3 ± 11.3 mg/dL, 198.5 ± 73.6 mg/dL, 209.44 ± 629.3 U/L, 98.7 ± 228.7 U/L, 578.3 ± 292.9 U/L in T. gondii negative sheep respectively.Similarly mean values of haemoglobin, glucose, cholesterol, AST, ALT and LDH were 9.5 ± 2.5 g/dL, 50.6 ± 11.3 mg/dL, 214.6 ± 79.9 mg/dL, 217.3 ± 140.7 U/L, 77.8 ± 66.4 U/L, 606.8± 291.5 U/L in T. gondii positive sheep by ELISA and 9.9 ± 3.1 g/dL, 52.3 ± 11.2 mg/dL, 198.4± 73.8 mg/dL, 209.6 ± 605.1 U/L, 97.6 ± 219.8 U/L, 583.8 ± 295.7 U/L in T. gondii negative sheep respectively.Hemoglobin, glucose and ALT concentration was lower in T. gondii positive sheep as compared to T. gondii negative sheep.Cholesterol, AST and LDH concentration was higher in T. gondii positive sheep than T. gondii negative sheep.Haemoglobin, Glucose, AST, ALT and LDH values varied statistically non-significantly (P>0.05) between T. gondii positive and negative sheep whereas cholesterol level varied statistically significantly (P<0.05) between T. gondii positive and negative sheep. In conclusion, cholesterol level was found higher in sheep infected with toxoplasmosis which may lead to certain complications including coronary artery diseases, myocardial infarction, atherosclerosis, hypertension, hemorrhage and vascular thrombosis in infected sheep.T. gondii is a blood parasite which can cause abortion, fetal death, stillbirth, neonatal death in sheep which can lead toward economic losses such as reduction in fur, wool, meat, milk and other dairy products etc. The results indicated the overall high rates of seroprevalence of T. gondii in sheep that warranted the threat to public health especially farmers and abattoir workers via zoonotic transmission of toxoplasmosis.Keeping in view, the medical and veterinary importance of T. gondii it is recommended that human population (especially farmers and abattoir workers), other livestock species and stray cats present in study area must also be screened for the Toxoplasma infection in the public interest.