Results and Discussion

Yu Watanabe

M. Moshińsky

Group theoretical techniques are pointed out which are effective for dealing with some many body problems. While Group Theory provides the backbone of all of the following discussion, vety little of its abstract formalism is used. The part used is either discussed in the text or the results for the group under discussion are stated pointing out the analogy between these results and those of the familiar rotation group. (auth)

Harkirat Singh

The thesis started with a short introduction about my research work and discussed about the systems I worked on. Later, it discussed about the experimental techniques that I have learned during the course of my work. This chapter includes the experimental approaches that I have used in sample preparation, characterization and measurements that I performed on my samples. In third chapter, I introduced about my first research work i.e. experimental quantification of entanglement in CN using magnetic susceptibility and heat capacity. In the fourth chapter, I briefly discussed about the magnetic field and temperature dependence of entanglement estimated using heat capacity. A good agreement with the theoretical predictions of our experimental results was also discussed. The fifth chapter consists of experimental study of quantum discord in CN quantified using magnetic susceptibility and heat capacity. In this chapter also I have discussed that our experimental results exhibits good correspondence with theoretical predictions and earlier reported results. In the sixth and last chapter of my thesis, I have discussed an experimental study we performed to investigate the magnetic properties of NiCr2O4 nanoparticles. Our experimental results have shown development of 2D spin-glass like phase in the nanoparticles of NiCr2O4. The parameter values we obtained by fitting the experimental data with the existing theoretical model for spin-glasses matches well with the reported values.

Laura Ortiz Martín

Ian Jauslin

In this chapter, we will review the results obtained thus far by Eric A. Carlen, Elliott H. Lieb, and me on a Simplified Approach to the Bose gas. The Simplified Approach yields a family of effective one-particle equations, which capture some non-trivial physical properties of the Bose gas at both low and high densities, and even some of the behavior at intermediate densities. In particular, the Simplified Approach reproduces Bogolyubov’s estimates for the ground state energy and condensate fraction at low density, as well as the mean-field estimate for the energy at high densities.We will also discuss a phase that appears at intermediate densities with liquid-like properties. The simplest of the effective equations in the Simplified Approach can be studied analytically, and we will review several results about it; the others are so far only amenable to numerical analysis, and we will discuss several numerical results. We will start by reviewing some results and conjectures on the Bose gas and then introduce the Simplified Approach and its derivation from the Bose gas.We will then discuss the predictions of the Simplified Approach and compare these to results and conjectures about the Bose gas. Finally, we will discuss a few open problems about the Simplified Approach.

Fei Yan, Salvador Elías Venegas-Andraca