# PREVIOUS PROJECTS

Here we have a short list of the abstracts of previous PDRP projects.

The ABC’s of BEC’s An Overview of Confined Atom Interferometry with Bose-Einstein Condensates

Throughout the paper, I cover the "ABC’s" of Bose-Einstein condensate (BEC) interferometry. Specifically, I talk about atom interferometry as a whole. Relevant topics pertaining to interference, apparatus, identical particles, and cold atoms are included in this section. The next section is on Bose-Einstein condensates, what they are, and their advantages and disadvantages in terms of atom interferometry. The third section is on confined atom interferometry, which covers the typical setup, the use of BEC’s, and their advantages and disadvantages. Finally, I include a brief section on additional experiments using BEC interferometry, as well as other types of atom interferometry experiments.

Light-Like Trajectories Around Neutral Gravitational Sources

General Relativity has been known to be a highly nonlinear theory. However, there are a class of important phenomena, for massless force carriers specifically, in which we can consider a linearized theory of gravity. In this exposition, we will focus on one of these phenomena, the deflection of a photon by a neutral (uncharged, stationary) gravitational source. Namely, we compute the angle of deflection of a photon with impact parameter b about a massive body with mass M: α = 4MG / bc2 . Furthermore, we derive a closed-form expression (in terms of elliptic integrals) to the preceding result by considering light-like trajectories performing an orbit about a Schwarzschild Black Hole. We conclude this by performing an expansion to linear order in rs/b, showing that this closed-form expression reduces to the initial answer of 4MG /bc2 in the large-b limit.

T-Duality and Gluon Scattering Amplitudes

A research review describing concepts related to a widespread string duality called T duality which can be used to compute planar gluon scattering in supersymmetric yang mills theories. The project explores the Alday-Maldacena prescription and the structure of D-branes, AdS/CFT and string scattering from HEPT papers.

## RESOURCES AND IDEAS

Berkeley also has a directed reading program in the mathematics department for students interested in doing pure mathematics. Please note that we still consider mathematical methods in physics to be a part of physics since there is a different conceptual emphasis when it's done by other physicists.

https://math.berkeley.edu/wp/drp/

## MENTEE F.A.Q.

Q1. I'm a freshman. Am I eligible?

Yes! Although seniority is a component of the overall application, we consider individuals based off their background, motivation to do a project and fit to a mentor.

Q2: I've just transferred. Am I eligible?

Yes! The coursework done at different college is completely valid. We look more at background than just courses taken.

Q3: I am not a physics major. Am I eligible?

Yes. We encourage people who are interested in the program to apply regardless of background. This will allow undecided majors to explore physics should we have mentors open for your particular topic.

Q4: When do we meet with our mentors?

Once paired to a mentor, you will decide as a group what is the most convenient time for your team.

Q5: Can we meet for more than one hour?

Yes. Mentors have to allow for a minimum of one hour per week however more can be done if both parties mutually agree.

Q6: Do we have a fund for physical copies of books?

As of Fall 2020, we do not. Perhaps in the future if enough interest is generated, we can generate a community fund for books. If you would like to make a donation and get such a fund started, please contact one of the organizers.

Q7: I want to learn a complex topic (e.g. topological string theory) but don't have the background. Can I still apply?

Yes. One of the primary goals of the program is to bridge the gap between having no background and a specific research area. It will be decided between you and your mentor how much background will be needed to be covered.

Q8: Where should my recommender send the letters of recommendation?

Please refer all recommendation letters to: andresfranco@berkeley.edu [temporary address as of July 2021]

Q9: Do I need to get a letter from the physics department?

No. It just has to be somebody who can give us a judgement of your character. It can be somebody from an unrelated department or even a friend. We encourage this part so that people have experience asking for letters of recommendations and others writing them.

Q10: Are international/exchange students allowed to apply?

Yes. As long as you are currently enrolled at UC Berkeley as an undergraduate, you may join. We check via your Berkeley email when you apply.