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Abstrak :
Penelitian kali ini mencoba memodelkan materi gelap yang menggumpal menjadi objek mampat yang disebut bintang gelap dengan mempertimbangkan efek temperatur. Partikel berjenis fermion, boson dan parafermion digunakan untuk memodelkan partikel gelap. Penentuan suhu bintang dilakukan dengan 2 metode yaitu: i) menganggap suhu bin- tang seragam dan ii) temperatur berubah-ubah bergantung tekanan dengan menganggap entropinya tetap. Didapati bahwa pada temeratur tidak nol, jenis partikel sangat mem- pengaruhi sifat-sifat dari bintang gelap. Pada kasus fermion, efek temperatur dan en- tropi membuat persamaan keadaannya lebih lunak dan didapatkan bintang yang memiliki massa dan radius lebih besar. Pada kasus boson, efek temperatur dan entropi tidak terlalu signifikan. Sedangkan pada kasus parafermion didapat persamaan keadaan tidak stabil dan perlu telaah lebih lanjut.

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In this work we model dark matter that clumps into a compact object called a dark stars, the effects of temperature is considered. We use Fermi-Dirac, Bose-Einstein and Parafermion statistics to model dark matter particles. To determine the temperature of the star 2 methods are used, i) Assume the temperature is uniform throughout the star and ii) the temperature varies depending on pressure by assuming that the entropy is constant. It was found that in the case of finite temeratures, the type of particle statisticss greatly affects the properties of dark stars. In the case of fermions, the effects temperature and entropy make the equation of state(EoS) softer and have larger mass and radius. In the case of bosons, the effect of temperature and entropy is not too significant. Whereas in the case of parafermion, the results obtained unstable equations of state and need further study.

Abstrak :
Kami telah membahas fungsi partisi dari kondensasi Bose-Einstein di dalam perangkap parabola yang dinyatakan oleh persamaan Gross-Pitaevskii satu dimensi. Fungsi partisi itu sendiri dirumuskan hanya dengan meninjau semua tingkat-tingkat energi dari osilator kuantum makroskopik yang mirip seperti di dalam mekanika statistika. Solusi-solusi dari tingkat-tingkat energi untuk kasus ini dapat diturunkan dengan mengikuti metode yang menggunakan teori perturbasi bebas waktu. Pada kasus ini, persamaan Gross-Pitaevskii satu dimensi dapat diperlakukan sebagai osilator kuantum makroskopik dengan menerapkan kondisi bahwa faktor nonlinearnya sangat kecil. Selain itu, perumusan analitik untuk energi tingkat dasar dapat diperoleh dengan menggunakan metode tersebut. Namun demikian, tingkat-tingkat eksitasinya tidak diberikan secara eksplisit. Saat ini, kami melanjutkan pekerjaan sebelumnya untuk menurunkan tingkat-tingkat keadaan lainnya supaya dapat merumuskan fungsi partisi. Akan tetapi, kami tidak mendapatkan bentuk analitik dari fungsi partisi karena integral dari suku-suku nonlinear tidak dapat membentuk hubungan rekursif. Akibatnya, tidak hanya fungsi partisi tetapi juga energi bebas Helmholtz dan entropi harus dikaji ulang untuk memeriksa sifat konvergennya. ......We have discussed the partition function of the Bose-Einstein condensation in parabolic trap associated to the one-dimensional Gross-Pitaevskii equation. The partition function itself is constructed by considering all the energy levels of the macroscopic quantum oscillator which is similar to statistical mechanics. The solutions of the energy levels for this case can be derived by pursuing the method that applies the time-independent perturbation theory. In this case, the one-dimensional Gross Pitaevskii equation can be treated as the one-dimensional macroscopic quantum oscillator on condition that the nonlinearity is very small. Moreover, the analytical expression for the ground state energy can be obtained by applying the method. However, the higher level states were not explicitly provided. In this research we followed up on the former work to derive explicitly the other states in order to formulate the partition function. However, we did not find the closed form of the partition function since the results of nonlinear term integral could not form the recursion relation. As a consequence, not only should the partition function but also the Helmholtz free energy and entropy should be reevaluated to check their convergences.

Abstrak :
We consider the correction of ground state energy of one-dimensional Gross-Pitaevskii equation by adding a gain-loss term as a time-dependent external potential. The interesting purpose of this term is that it can be used to explain the experimental results especially in the nonlinear fiber optics regarding the pulse propagation and collapse-revival of the condensate in the Bose-Einstein condensation. In the Bose-Einstein condensation itself, the function can represent that condensate can interact with the normal atomic cloud. Some analytical solutions have been obtained by choosing anansatz solution of the wave function and its solution can be dark or bright soliton. Since the Gross-Pitaevskii equation can be treated as a macroscopic quantum oscillator, we can use time-dependent perturbation theory as in ordinary quantum mechanics to find the ground state energy correction if we assume other terms to be very small. In addition, time-dependent potential allows a transition from one energy level to others. In this case, we expand the solution of nonstationary one-dimensional wave function as a linear superposition of harmonic oscillator normalized eigen functions. To get the recursive formulas, we suggest an option to formulate the coefficients after inserting the initial condition which must be satisfied such as in quantum mechanics.

Abstrak :
ABSTRACT
Penulis mempelajari sifat-sifat bintang gelap menggunakan model interaksi diri, model pertukaran meson vektor dan model kondensat Bose-Einstein. Bintang gelap merupakan kumpulan dari materi gelap boson. Materi gelap boson berada dalam keadaan dasar. Sifat-sifat dari bintang gelap yang dipelajari oleh penulis yaitu massa dan jari-jari bintang, deformasi pasang-surut, momen inersia dan hubungan I-Love-Q. Dengan diketahui sifat-sifat tersebut, penulis dapat mengetahui interaksi yang terjadi pada materi gelap boson. Massa materi gelap boson ditetapkan yaitu 300 MeV dan 400 MeV. Nilai konstanta kopling pada model interaksi diri, nilai massa interaksi pada model pertukaran meson vektor dan nilai panjang hamburan pada model kondensat Bose-Einstein diambil dari hasil simulasi numerik materi gelap dingin dan tidak bertumbukan CCDM yang memenuhi persamaan 0.1 ?cm?^2/g le; ?/m_b le;1 ?cm?^2/g.

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ABSTRACT
We study properties of dark stars on self interaction model, exchange vector meson model and Bose Einstein condensate model. Dark stars are compact objects formed from bosonic dark matter. Bosonic dark matter is in ground state. The properties of the dark stars studied by us are the mass and radius of stars, tidal deformation, inertia moment, and I Love Q relation. By knowing these properties, we can see the interactions that occur in bosonic dark matter. Bosonic dark matter mass is set at 300 MeV and 400 MeV. Coupling constant on self interaction model, interaction mass on exchange vector meson model, and scattering length on Bose Einstein condensate model determined by the result of numerical simulations CCDM which requires 0.1 ?cm?^2/g le; ?/m_b le;1 ?cm?^2/g.

Abstrak :
Interferometry, the most precise measurement technique known today, exploits the wave-like nature of the atoms or photons in the interferometer. As expected from the laws of quantum mechanics, the granular, particle-like features of the individually independent atoms or photons are responsible for the precision limit, the shot noise limit. However this “classical” bound is not fundamental and it is the aim of quantum metrology to overcome it by employing entanglement among the particles. This work reports on the realization of spin-squeezed states suitable for atom interferometry. Spin squeezing was generated on the basis of motional and spin degrees of freedom, whereby the latter allowed the implementation of a full interferometer with quantum-enhanced precision.