Fast Converging Path Integral Approach to Bose-Einstein Condensation Bilateral project with Germany2009-2010 |

A Bose–Einstein condensate (BEC) is a state of matter of bosons confined in an external potential and cooled to temperatures very near to absolute zero. Under such conditions, a large fraction of the atoms collapse into the lowest quantum state of the external potential, at which point quantum effects become apparent on a macroscopic scale. This state of matter was first predicted by Satyendra Nath Bose and Albert Einstein in 1924-25. Seventy years later, the first gaseous condensate was produced by Eric Cornell and Carl Wieman in 1995 at the University of Colorado at Boulder NIST-JILA lab, using a gas of rubidium atoms cooled to 170 nK. Cornell, Wieman, and Wolfgang Ketterle at MIT were awarded the 2001 Nobel Prize in Physics for their achievements.

SCL's two-year bilateral research project "Fast Converging Path Integral Approach to Bose-Einstein Condensation" is funded through the joint program by the Serbian Ministry of Science and German DAAD agency for the period 2009-2010. This project provides support to the ongoing collaboration established between SCL's path integral group, led by Dr. Aleksandar Bogojevic, and a research group of Dr. Axel Pelster from the University of Duisburg-Essen, Germany. One of the central aspects of the proposed project is the participation of young scientists in the planned research. A total of four PhD students (two from each partner) will participate in short-term visits and all research activities. The key aspect of their visits is to receive training relevant for their work on the joint research programme and to acquire relevant expertise.

The planned research aims to develop a new method for efficiently calculating path integrals by combining previously developed approaches of the two partners: higher order effective actions approach (Serbian group), and recursive diagrammatical approach (German group). The integrated method will be then applied to the study of Bose-Einstein condensation phenomenon. This research will analyze in detail the relation of the new method to other established approaches, such as Variational Perturbation Theory. We also plan to extend our existing Monte Carlo codes so as to implement the above approaches to the study of Bose-Einstein condensation in non-inertial and electromagnetic traps, and in related experimental setups.

SCL's two-year bilateral research project "Fast Converging Path Integral Approach to Bose-Einstein Condensation" is funded through the joint program by the Serbian Ministry of Science and German DAAD agency for the period 2009-2010. This project provides support to the ongoing collaboration established between SCL's path integral group, led by Dr. Aleksandar Bogojevic, and a research group of Dr. Axel Pelster from the University of Duisburg-Essen, Germany. One of the central aspects of the proposed project is the participation of young scientists in the planned research. A total of four PhD students (two from each partner) will participate in short-term visits and all research activities. The key aspect of their visits is to receive training relevant for their work on the joint research programme and to acquire relevant expertise.

The planned research aims to develop a new method for efficiently calculating path integrals by combining previously developed approaches of the two partners: higher order effective actions approach (Serbian group), and recursive diagrammatical approach (German group). The integrated method will be then applied to the study of Bose-Einstein condensation phenomenon. This research will analyze in detail the relation of the new method to other established approaches, such as Variational Perturbation Theory. We also plan to extend our existing Monte Carlo codes so as to implement the above approaches to the study of Bose-Einstein condensation in non-inertial and electromagnetic traps, and in related experimental setups.

**Papers:**- A. Balaz, I. Vidanovic, A. Bogojevic and A. Pelster:
*Phys. Lett.*A**374**(2010) 1539

doi: 10.1016/j.physleta.2010.01.034, arxiv: 1001.1463 - I. Vidanovic, A. Bogojevic, A. Balaz, and A. Belic:

*Phys. Rev.*E**80**(2009) 066706

doi: 10.1103/PhysRevE.80.066706, arxiv: 0911.5154

- I. Vidanovic, A. Bogojevic, and A. Belic:

*Phys. Rev.*E**80**(2009) 066705

doi: 10.1103/PhysRevE.80.066705, arxiv: 0911.5145

- A. Balaz, A. Bogojevic, I. Vidanovic, and A. Pelster:

*Phys. Rev. E***79**(2009) 036701

doi: 10.1103/PhysRevE.79.036701, arxiv: 0806.4774

**Activities and news related to the project:**