M A Rastkhadiv has completed BS and MS from Shiraz University and now is finalizing his PhD from Shiraz University, School of Science. He is interested in statistical mechanics and is researching on quantum many body systems in nano dimensions.
Liquid 3He injected in a carbon nanotube is of high interests due to different behavior of the liquid helium in the quasi-one dimensional system. In this work, a variational approach based on the cluster expansion of energy has been performed to calculate some thermodynamic properties of this quantum system. In order to do so, a single-walled carbon nanotube (SWCN) containing liquid 3He is considered, applying the Lennard-Jones and Stan-Cole potentials for 3He-3He and 3He-C interactions, respectively. We have done our calculations for density range 0.1-1.0 nm-1 and radii R=0.3, 0.48 and 0.8 nm. At first, we have calculated the one-body (E1) and the two-body (E2) energies, then the total energy (E=E1+E2) has been obtained. Our results show that the one-body energy has negative values while the two-body energy has positive values, although both of them increase by increasing density. To compare our results with other works, we have calculated single particle energy states ε(kρ,φ) for a single 3He atom in a SWCN in ground state nρ=1 , nφ=0 equal (-231.671 K) for radius R=0.48 nm, where there is a good agreement between our results and Vranjes et al. The total energy is negative for all the densities. We have calculated the equation of state for the system, and have found out that the pressure increases by increasing the density and nanotube radius. Our results for incompressibility show that the system can have a liquid state for higher densities (higher than 1.0 nm-1) for R=0.48 and 0.8 nm whereas for R=0.3 nm cannot have a liquid-gas phase transition. These transition points occur in densities about 1.2 and 2.1 nm-1 for 0.8 and R=0.48 nm-1 radii, respectively; which are very low densities. In other words, liquid 3He in a carbon nanotube is the lowest density liquid one has ever seen. This helps us to make 3He liquid in very low densities in comparison with three dimensional systems.
Suraka Bhattacharjee has completed her BSc from University of Calcutta and MSc from Presidency University in the year 2014. Currently, she is pursuing her PhD from S N Bose National Centre for Basic Sciences, India, under the supervision of Dr. Ranjan Chaudhury. Her first paper has been recently published in Physica B.
The doped quantum Heisenberg antiferromagnets are extremely alluring for their interesting magnetic properties and inherent itinerant character. Even the magnetic behaviors of the one-dimensional and two-dimensional antiferromagnets are quite distinct which is in contrast to the age old idea of the theoreticians and experimentalists. The strongly correlated t-J model is the simplest model that has paramount importance in describing these itinerant systems starting from the slightly less than half-filled band limit. My work is primarily based on the calculation of generalized spin stiffness constant for low-dimensional doped antiferromagnets corresponding to the t-J model. The results can vividly elucidate on the characteristic magnetic features of doped La2-xSrxCuO4 or YBa2Cu3O6+x which are known to exhibit high temperature superconductivity at optimal doping concentration. While the generalized spin stiffness constant for 2-D systems shows a monotonous fall with increase in doping concentration, the spin stiffness in 1-D shows a peak in the lower doping region. The comparison of my results with other theoretical and experimental results substantiates the inextricable role of spin stiffness constant as effective exchange constant for these doped itinerant antiferromagnets at least in the low doping region. Moreover, the plot of spin stiffness constant versus doping concentration for 2-D systems shows a cross-over or a point of inflexion near 61% doping concentration, signifying a possible quantum phase transition, as was previously shown by Emery et al. Finally, it can be concluded that my formalism also puts forward a novel scheme for determining the exchange constant and magnetic correlations in the strongly correlated itinerant magnetic systems.