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Abstrak :
Tugas akhir ini membahas mengenai fungsi Green untuk persamaan Poisson. Fungsi Green ini akan diperoleh pada kondisi dimana suku nonhomogen dari persamaan Poisson merupakan fungsi Delta Diract atau merupakan kelipatan dari fungsi yang dicari.

Abstrak :
Pendekatan Hamiltonian tight binding digunakan untuk mempelajari sifat transport muatan di molekul DNA. Sifat transport muatan ini dipelajari dengan menggunakan dua model DNA yaitu model DNA Aperiodik dan model DNA G4. Model DNA Aperiodik terdiri dari 32 pasangan basa ATGC yang tersusun secara acak dengan sequence GCTAGTACGTGACGTAGCTAGGATATGCCTGA. Pada model ini dilakukan perhitungan menggunakan metode transfer matriks dan metode hamburan untuk mendapatkan probabilitas transmisi serta menghitung karakteristik I-V berdasarkan formula Landauer Büttiker dengan memvariasikan nilai kopling 𝛼 interstrand. Peningkatan nilai kopling 𝛼 interstrand memberikan dampak yang sangat baik terhadap transport muatan yaitu terjadinya peningkatan probabilitas transmisi dan karakteristik IV pada tegangan tinggi. Sedangkan, model DNA G4 terdiri dari 4 basa guanine yang tersusun membentuk struktur planar, g-quartet yang disusun secara bertumpuk. Pada model DNA ini dilakukan perhitungan panjang lokalisasi menggunakan metode transfer matriks dan perhitungan density of state (DOS) dan karakteristik I-V menggunakan pendekatan fungsi green di bawah pengaruh temperatur dan medan magnet. Temperatur menyebabkan terjadinya fluktuasi termal yang menurunkan panjang lokalisasi, density of state (DOS) dan karakteristik I-V di molekul DNA G4. Sedangkan, medan magnet menyebabkan terjadinya pergeseran fase keadaan elektron di jalur transport yang mempengaruhi panjang lokalisasi dan DOS yang berimbas pada peningkatan arus hingga di tegangan tinggi. ...... The tight binding Hamiltonian approach is used in studying charge transport properties DNA molecules. The charge transport properties are studied by using two DNA models, the Aperiodic DNA molecule and the G4 DNA molecule. The Aperiodic DNA model consist of 32 base pairs that ATGC arranged randomly with sequence GCTAGTACGTGACGT-AGCTAGGATATGCCTGA. In this model, transfer matrix method and scattering method are used in obtain transmission probability and calculating the I-V characteristic for various values of interstrand coupling α. The increase of α gives a very good impact on charge transport that is the increase of transmission probability and I-V characteristic at high voltages. G4 DNA model consists of planar structure of four guanine bases, g-quartet, which are stacked on top each other. In this DNA model, localization length is calculated using transfer matrix method and the density of state (DOS) as well as I-V characteristic are calculated using green function approach under the influence of temperature and magnetic field. The temperature causes thermal fluctuations that decreases the localization length, density of state (DOS) and I-V characteristics in G4 DNA molecule. Meanwhile, magnetic field causes a shift in electron wave phase along its travel path which is affecting the localization length and DOS which lead to current increament up to high voltage.

Abstrak :
Quarks are the main constituents of protons and neutrons and hence are important building blocks of all the matter that surrounds us. However, quarks have the intriguing property that they never appear as isolated single particles but only in bound states. This phenomenon is called confinement and has been a central research topic of elementary particle physics for the last few decades. In order to find the mechanism that forbids the existence of free quarks many approaches and ideas are being followed, but by now it has become clear that they are not mutually exclusive but illuminate the problem from different perspectives. Two such confinement scenarios are investigated in this thesis. Firstly, the importance of Abelian field components for the low-energy regime is corroborated, thus supporting the dual superconductor picture of confinement and secondly, the influence of the Gribov horizon on non-perturbative solutions is studied.