In this paper, we investigate Quantum Renormalization group theory in transverse Ising model on one dimensional chain of spin-1/2 particles. To this end, we employ recursion relations to Quantum Renormalization of coherence measure at ground state. Coherence measure diagram in terms of intensity of transverse field for higher Renormalization steps shows the detection of Quantum phase transition point for transverse Ising model which implies that the coherence measure can be a good indicator of Quantum phase transition in transverse Ising model. Also, we obtain the divergence behavior that governs the first derivative of the coherence measure behavior, near to critical point. Although the coherence measure depends on the basis of writing the density matrix, results show that the Quantum phase transition point detected by coherence measure is independent of selected basis.

This manuscript is the collection of lectures given in the summer school on strongly correlated electron systems held at Isfahan University of technology, June 2007. A short overview on Quantum magnetism and spin systems is presented. The numerical exact diagonalization (Lanczos) alghorithm is explained in a pedagogical ground. This is a method to get some ground state properties on finite cluster of lattice models. Two extensions of Lanczos method to get the excited states and also finite temperature properties of Quantum models are also explained. The basic notions of Quantum phase transition are discussed in term of Ising model in transverse field. Its phase diagram and critical properties are explained using the Quantum Renormalization group approach. Most of the topics are in tutorial level with hints to recent research activities.

In this paper, the Lifshitz formula for the Casimir energy between two dielectrics in zero temperature is derived using box Renormalization. Although there are several derivations for the force in this case in the literature, including Lifshitz’ s own proof, so far there has been no unambiguous and rigorous derivation for energy that we are aware of. Since energy becomes important in some cases, e. g. calculation of entropy or heat capacity, using the correct and precise definition of the Casimir energy, for the first time, we remove all of the infinities systematically without any ambiguity. This proof also shows the strength and accuracy of the box Renormalization scheme.

Currently, carbon Quantum dots have attracted considerable attention due to their unique properties and desirable advantages. High crystallinity, water solubility, good dispersibility, small size, low toxicity, inexpensive raw materials, high chemical stability, environmental compatibility, low cost, stability under light, desirable charge transfer with advanced electronic conductivity, as well as specific thermal and mechanical properties are some of these features. Carbon Quantum dots have various applications in different fields. Fabrication of precise chemical and biological sensors, bioimaging, solar cells, drug tracking, nanomedicine, light-emitting diodes (LEDs), and electrocatalysts are some of these applications. Biological sensors based on carbon Quantum dots are capable of detecting various metal ions, acids, proteins, biotin, polypeptides, DNA and miRNA, water pollutants, hematin, drugs, vitamins, and other chemicals. In the present study, the properties of carbon Quantum dots and some of their fabrication and applications methods have been addressed. In continuation of the paper, the effect of carbon Quantum dots on important factors in plants such as growth and development, photosynthesis, absorption and transportation of substances, resistance to biotic and abiotic stresses, as well as their application in agriculture has been investigated.

The recent observational data are strongly in favor of a positive acceleration of the present universe. In a first approximation, the background space-time that we live in, might be considered as a de Sitter space-time. If this is so, it is important to understand how Quantum gravity and should formulated in de Sitter space. We discusses the some properties of linear Quantum gravity necessitated to the indefinite metric quantization for preserving the de Sitter invariant and eliminating the infrared divergence in the graviton two points function. There appears two different types of negative norm states. The first one is similar to those non physical states dual to gauge states which appear in gauge Quantum field theory in Minkowski space. The other is due to the occurrence of negative frequency solutions in order to preserve de Sitter covariance. This is similar to the case of minimally coupled scalar field in dS space. We discuss the possibility of generalization to the Minkowskian limit and their consequences in the Renormalization theory.

The aim of this study was to examine Renormalization of Kyriacou and Sutcliffe's teachers' stress prevalence, source and symptoms scale (TSS) through factor analysis and assessing its validity and reliability. 430 male and female teachers, consisting of both physical education and non- physical education high school teachers at West Azarbaijan province filled out the TSS questionnaire. Diffluent and convergent validity of TSS were computed through determining coefficient of correlation by Mental Health Inventory (MHI) as well as Job Descriptive Index (JDI). TSS reliability was calculated through tester test and internal consistency. Reliability and validity indices obtained for TSS were satisfactory and significant at p<0.01. Seven factors were obtained by factor analysis applying varimax method. These factors had eigenvalues higher than I and 49041 percent of the total variance was explained by them. The seventh factor was removed because its reliability was lower than 0.7. The Remaining six factors are: teacher's inappropriate socioeconomic and family statues, issues concerning the school’s atmosphere and facilities, students' behavior problems and difficulties, teachers' professional qualifications, students' low amount of educational motivation and time pressure. Regarding the source and symptoms of stress, criterion validity concerning those who had stressful experiences during the past 12 months yielded that there was significance difference between two groups with low and high stress. Results showed that 8.2, 18.1, 40.0, 30.5 and 3.2 percent of the teachers were at non-risk, low risk, average risk, high risk and extreme risk areas, respectively, but none of them were at the critical area. According to the results of the research, TSS scale had necessary psychometrics characteristics to be applied at psychological research and clinical diagnosis in investigation of the teachers' stress.

The effects of higher order excitations on the bandgap Renormalization of quasi-one dimensional semiconductor systems within the dynamical random phase approximation is studied. The contribution of the first and second excited states wave functions is incorporated in the calculation of the bandgap narrowing due to many-body exchangecorrelation effects. It is shown that incorporation of the higher order excitations leads to the result that absolute values of the bandgap narrowing in these cases are larger than the corresponding Renormalization which is calculated by only considering the ground state wave function.

Spontaneous symmetry breaking occurs when the underlying laws of a physical system are symmetric, but the vacuum state chosen by the system is not. The (3+1)d $\phi^4$ theory is relatively simple compared to other more complex theories, making it a good starting point for investigating the origin of non-trivial vacua. The adaptive perturbation method is a technique used to handle strongly coupled systems. The study of strongly correlated systems is useful in testing holography. It has been successful in strongly coupled QM and is being generalized to scalar field theory to analyze the system in the strong-coupling regime. The unperturbed Hamiltonian does not commute with the usual number operator. However, the quantized scalar field admits a plane-wave expansion when acting on the vacuum. While quantizing the scalar field theory, the field can be expanded into plane-wave modes, making the calculations more tractable. However, the Lorentz symmetry, which describes how physical laws remain the same under certain spacetime transformations, might not be manifest in this approach. The proposed elegant resummation of Feynman diagrams aims to restore the Lorentz symmetry in the calculations. The results obtained using this method are compared with numerical solutions for specific values of the coupling constant $\lambda = 1, 2, 4, 8, 16$. Finally, we find evidence for Quantum triviality, where self-consistency of the theory in the UV requires $\lambda = 0$. This result implies that the $\phi^4$ theory alone does not experience SSB, and the $\langle \phi\rangle = 0$ phase is protected under the RG-flow by a boundary of Gaussian fixed-points.

The focus of this study is on developing a framework for a Quantum Algorithm Processing Unit (QAPU) with the hybrid architecture for classical-Quantum algorithms. The framework is used to increase the implementation performance of Quantum algorithms and design Quantum Processing Units (QPU). The framework shows a general plan for the architecture of Quantum processors who is capable of run the Quantum algorithms. In particular, the QAPU can be used as a Quantum node to design a Quantum multicomputer. At first, the hybrid architecture is designed for the Quantum algorithms. Then, the relationship between the classical and the Quantum part of hybrid algorithms is extracted, and main stages of the hybrid algorithm are developed. Next, the framework of the QAPU is designed.Furthermore, the framework is implemented and simulated for the existing Quantum algorithms on a classic computer.It is shown that the framework is appropriate for Quantum algorithms.