UROP Project
Random walk through a critical landscape
Understanding the fate of a random walker couples to degree of freedom which is at criticality
Research Mentor: Sandeep Joy,
Department, College, Affiliation: Physics/National High Magnetic Field Laboratory , Arts and Sciences
Contact Email: sj24u@fsu.edu
Research Assistant Supervisor (if different from mentor):
Research Assistant Supervisor Email:
Faculty Collaborators:
Faculty Collaborators Email:
Department, College, Affiliation: Physics/National High Magnetic Field Laboratory , Arts and Sciences
Contact Email: sj24u@fsu.edu
Research Assistant Supervisor (if different from mentor):
Research Assistant Supervisor Email:
Faculty Collaborators:
Faculty Collaborators Email:
Looking for Research Assistants: Yes
Number of Research Assistants: 1
Relevant Majors: Open to all majors
Project Location: On FSU Main Campus
Research Assistant Transportation Required: Remote or In-person: Fully Remote
Approximate Weekly Hours: 5-10 hours, Flexible schedule (Combination of business and outside of business. TBD between student and research mentor.)
Roundtable Times and Zoom Link:
Not participating in the roundtable
Number of Research Assistants: 1
Relevant Majors: Open to all majors
Project Location: On FSU Main Campus
Research Assistant Transportation Required: Remote or In-person: Fully Remote
Approximate Weekly Hours: 5-10 hours, Flexible schedule (Combination of business and outside of business. TBD between student and research mentor.)
Roundtable Times and Zoom Link:
Not participating in the roundtable
Project Description
This project aims to understand the long-time behavior of a random walker coupled to a degree of freedom undergoing a phase transition. In a conventional random walk, the long-time behavior is diffusive. Here, we consider a model in which the 'spin' of the random walker is coupled to the spins of an underlying lattice. The lattice is modeled as an Ising system, where spins tend to align due to energetic favorability, but fluctuate at finite temperatures.In the zero-temperature limit, all lattice spins are aligned, and the random walker effectively does not experience their presence. At very high temperatures, the lattice spins are uncorrelated and random, again rendering the walker insensitive to the background on average. However, near the critical point of the Ising model, long-range spin correlations emerge. In this regime, the walker’s spin becomes entangled with the lattice spins, and these critical correlations may significantly alter its diffusive dynamics.
This project is partially motivated by the work presented here: https://journals.aps.org/prl/abstract/10.1103/ff28-tt6c.
Research Tasks: 1) Understanding the basic of random walks
2) Implementing simulation on Python or equivalent coding languages
3) Analyze the data and understand it intuitively
4) Summarize, present and publish the work
Skills that research assistant(s) may need: Open to learning
Mentoring Philosophy
The most important shared value is that the mentor and mentee support each other and serve as mutual resources. We strive to cultivate and maintain a 'culture of tolerating ignorance,' where members feel comfortable expressing what they do and don’t understand—without fear of judgment or scorn. Everyone is encouraged to listen, teach, and learn from one another whenever possible.(Adapted from Prof Brian Skinner's website, https://sites.google.com/view/skinner-physics/group-values-and-expectations)