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"The dependence on the choice of these projections is studied in detail here and a method to overcome this ambiguity in DFT+U, by self-consistently determining the projections, is introduced. The author shows how nonorthogonal representations for electronic states may be used to construct these projections and, furthermore, how DFT+U may be implemented with a linearly increasing cost with respect to system size. The use of nonorthogonal functions in the context of electronic structure calculations is extensively discussed and clarified, with new interpretations and results, and, on this topic."

"Mekanika kuantum banyak benda menjadi suatu topik khusus dalam fisika dan memiliki banyak aplikasi di bidang fisika partikel, fisika nuklir, maupun fisika zat yang termampatkan. Hal ini tidak terlepas dari sistem yang ditinjau, yakni banyak partikel yang memungkinkan saling berinteraksi. Pada sistem materi termampatkan, hal yang menarik untuk ditinjau adalah interaksi elektron yang terkorelasi kuat. Berdasarkan teknik banyak benda yang diturunkan dari diagram Feynman, kami mengimplementasikan pendekatan ladder diagram untuk menangkap efek interaksi elektron-elektron. Kami menginvestigasi bagaimana efek korelasi ini mempengaruhi sifat yang bergantung suhu pada sistem metal terkorelasi dengan kuat. Sistem yang dipelajari adalah sifat material yang bergantung pada suhu, maka metode ladder diagram perlu diaplikasikan pada domain frekuensi Matsubara untuk mendapatkan self-energy yang self-consistent. Kami melakukan perhitungan kerapatan keadaan density of state dengan menggunakan algoritma ladder diagram untuk sistem metal.

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Quantum mechanics of many body problems has been a special topic in physics and may have many applications in particle physics, nuclear physics, and condensed matter physics. This condition comes because the system which is observed, that many particle with their interaction. In condensed matter physics, the strongly interaction of electrons are fascinating. Based on many body Feynman diagram, we implement the ladder diagram approximation for the electron interaction. We investigate the temperature dependent to capture the physical properties of the system. We formulated the Matsubara self energy then transform to the real frequency use Pad approximant."

"The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field, V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity, R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices, J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability, finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights."

"There have been many recent and important developments based on effective field theory and the renormalization group in atomic, condensed matter, nuclear and high-energy physics. These powerful and versatile methods provide novel approaches to study complex and strongly interacting many-body systems in a controlled manner. The six extensive lectures gathered in this volume combine selected introductory and interdisciplinary presentations focused on recent applications of effective field theory and the renormalization group to many-body problems in such diverse fields as BEC, DFT, extreme matter, Fermi-liquid theory and gauge theories. "

"ABSTRAKHasil eksperimen pada feromagnetis TiO2 yang didopinging dengan beberapa elemen tanah jarang menjadi topik yang diminati sebagai bahan semikonduktor feromagnetis diatas suhu kamar. TiO2 mengalami perubahan sifat material dari nonmagnetis menjadi magnetis akibat adanya formasi vakansi Ti yang diinduksikan penambahan atom Ta. Mekanisme terjadinya sifat feromagnetis diduga akibat interaksi Ruderman-Kittel-Kasuya-Yosida RKKY . Dalam penelitian ini, kami melakukan studi teoritis untuk memprediksi suhu Curie feromagnetis dari sistem berdasarkan kesimpulan-kesimpulan dari studi-studi sebelum ini. Kami menggunakan algoritma metode Dynamical Mean Field Theory DMFT yang mengambil hasil perhitungan Density Functional Theory DFT untuk memberikan nilai-nilai parameter fisis yang sesuai dengan keadaan material sebenarnya. Hasil penelitian ini menunjukkan bahwa TiO2:Ta memiliki bentuk semikonduktor tipe-n dan besar TC dari TiO2:Ta berkisar antara 480 - 596 K.

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ABSTRACTRecent experimental reports on ferromagnetism in TiO2 doped with certain rare earth elements have renewed interest in the search of optimal room temperature ferromagnetic semiconductors. TiO2 undergoes a change in its properties from nonmagnetic to magnetic which is attributed to formation of Ti vacancies induced by the addition of Ta atoms. The mechanism leading to ferromagnetic is believed to be governed by Ruderman Kittel Kasuya Yosida RKKY . Here we conduct a theoretical study to calculate and predict the ferromagnetic Curie temperature of the system based on conclusions of previous studies. We use Dynamical Mean Field Theory DMFT algorithm which employs result of Density Functional Theory DFT calculation to provide the proper physical parameters. Our results show that TiO2 Ta has a n type semiconductor and has TC value ranges from 480 to 596 K."

"Terinspirasi dari bentuk fungsi densitas probabilitas distribusi sekan hiperbolik, ditemukan fungsi survival dari sebuah distribusi kontinu baru dengan 2 parameter yakni rate parameter r dan parameter t. Distribusi baru tersebut kemudian diberi nama distribusi Krison Lengkap (berasal dari nama penemu distribusi sendiri) dengan notasi Krison(r,t). Selanjutnya ditentukan karakteristik dari distribusi Krison Lengkap yang meliputi fungsi densitas probabilitas, fungsi distribusi kumulatif, fungsi survival, mean, median, modus, kuantil, fungsi hazard, fungsi hazard kumulatif, dan fungsi pembangkit momen. Dalam skripsi ini, juga dibahas lebih lanjut kasus khusus dari distribusi Krison Lengkap ketika parameter t = 2 yang disebut sebagai distribusi Krison Generik. Pendekatan matematis yang komprehensif terhadap distribusi yang diusulkan disediakan, termasuk perumusan variansi, koefisien variasi, koefisien skewness, koefisien kurtosis, dan momen. Adapun parameter dari distribusi Krison Generik diestimasi dengan menggunakan metode maximum likelihood estimation. Terakhir, model distribusi Krison Generik dan beberapa model distribusi pembanding seperti distribusi Rayleigh, Lindley, dan Bilal diterapkan pada tiga dataset yaitu dataset pendapatan, waktu survival, dan tingkat kematian. Diperoleh hasil bahwa model distribusi Krison Generik dapat bekerja dengan baik pada ketiga dataset dibandingkan model distribusi Rayleigh, Lindley, dan Bilal.

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Inspired by the probability density function of the hyperbolic secant distribution, a new continuous distribution with two parameters, the rate parameter r and parameter t, was discovered. This new distribution is then named the complete Krison distribution (derived from the name of the discoverer of the distribution) with the notation Krison (r,t). Subsequently, the characteristics of the Complete Krison distribution are determined, including the probability density function, cumulative distribution function, survival function, mean, median, mode, quantiles, hazard function, cumulative hazard function, and moment generating function. In this thesis, further exploration is conducted on the special case of the Complete Krison distribution when the parameter t = 2 referred to as the Generic Krison distribution. A comprehensive mathematical approach to the proposed distribution is provided, including the formulation of variance, coefficient of variation, skewness coefficient, kurtosis coefficient, and moments. Moreover, the parameters of the Generic Krison distribution are estimated using the maximum likelihood estimation method. Finally, the Generic Krison distribution model and several comparative distribution models such as the Rayleigh, Lindley, and Bilal distributions are applied to three datasets: income, survival time, and mortality rate. The results indicate that the generic Krison distribution model performs well on all three datasets compared to the Rayleigh, Lindley, and Bilal distribution models."