Could someone provide feedback on this letter?? This is my first one and I am not confident.

Respected ---,

I am writing this letter to apply for Ph.D. position at the Condensed Matter Theory and Quantum Computing group at ---.

After I completed my schooling with highest grades in Physics, I received my Bachelor's degree in Physics where I was among the top 5% of the class. Following my interest further I pursued a Master's degree in Physics from --- where I performed fairly well in the class and was among the top 5 during the first year. My interest has always been on the theoretical side of subjects and during my second year of Master, I had the opportunity to do a reading project in one of the most fascinating field,Condensed Matter Physics where I got well versed with the formalism of Adiabatic Gauge Potentials (AGPs).

I learned about the notion of distance between wave functions and geomteric tensor of the system and how these abstract quantities can be related to actual dissipation in systems which is measurable via the concept of gauge potentials. Connecting geometric tensor to measurements is very important as it finds use in quantum information theory where it places a bound on the quantum speed limit, topological systems where it can be used to derive invariants such as Chern number helping in characterizing topological phases and understanding dynamical effcts such as Quantum Hall effect where generalized force derived from gauge potential is related to quantized chern number leading to quantized response of the system. Another useful notion stemming from gauge potentials is counter diabatic driving which finds use in reducing dissipation by following a particular state of the system and has great applications in quantum information theory. AGPs are also a very useful tool to find quantum phase transitions of system and another unexplored avenue is using them to detect quantum chaos in many body systems. I would be interested in exploring if these can be used to study phase transitions in systems such as topological insulators and superconductors. The techniques I learned to compute them can be used in many body systems to understand their topology and phase transitions. I would also like to study in detail fractional quantum hall effect and its excitations and see if it could be understood using gauge potential formalism.

The coursework in condensed matter physics I did has helped me strengthen my foundations of the subject as well as connected the basics to more recent developments in the field and helped me appreciate the depth as well as the breadth of this subject. I also has experience with numerical technqiues which I learned during the Computational Physics course and the methods of Quantum Field Theory which may prove useful and puts me on a strong footing to undertake research within the group. My marks in Quantum Field Theory suffered a big dip due to an illness I acquired during pandemic but I have covered it up by self learning and following various lectures later.

Later, I worked for my Master's thesis on the topic "Effective Fick-Jacobs description for diffusion under intermittent search strategies" where I studied the effects of resetting a Brownian particle stochastically in a geomterically constrained environment and modifications to its survival time due to this. The work helped me develop a research oriented thinking and now the work done is soon to be submitted for publication in a reputed journal.

After having some experience in statistical physics and condensed matter physics, I am convinced of my interest and motivation to pursue further research in the latter field. Research work done in the group is in a diverse range of topics and the knowledge I have gained in this field can be connected in many interesting ways to explore new avenues in this big field which makes me more excited to work within the group and my overall academic achievements and my research experience make me a suitable candidate for the position.

Thank you for considering my application, and I look forward to receiving your acceptance.

Sincerely yours,

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