Advanced Statistical Mechanics
SPRING 2023
Course Number: PHYS 6210
(3 CREDITS, 3 CONTACT HOURS/WEEK)
Instructor: ARCHANA KAMAL (archana_kamal[AT]uml.edu)
Meeting Times: Tuesday/Thursday, 5:00 p.m. - 6:15 p.m.; Location: Olney 115
Prerequisites: Undergraduate Statistical Mechanics, Graduate Classical Mechanics, Graduate Quantum Mechanics (or special permission from the instructor).
Primary Textbooks:
Statistical Physics Vol. II, M. Kardar (Vol I may be referred to for some initial selected topics)
Quantum Field Theory and Condensed Matter, R. Shankar
Lectures on Phase Transitions and the Renormalization Group, N. Goldenfeld
Scaling and Renormalization in Statistical Physics, J. Cardy
Grading Scheme:
Homeworks - 90%
Attendance and class participation - 10%
Course Description: The aim of this course is to introduce graduate students to advanced concepts in collective phenomena, phase transitions, and renormalization group techniques. The course assumes familiarity with basic concepts of statistical physics such as kinetic theory of gases, partition functions, ideal classical and quantum gases.
Course Policy:
Students are expected to keep up with the reading of the textbook and/or assigned reading material. Even though this will not directly contribute towards the grade, it is imperative for both digesting the concepts and solving homework problems that employ extensions of concepts introduced in the lecture.
Homeworks: All problem sets will be posted in the shared course folder located on UML OneDrive. The students will get typically 2 weeks to submit their solutions. No late homeworks will be accepted.
To facilitate in-depth learning and maintain fairness, the students should avoid making use of online solutions to problems (if any exist!). Solutions to the homeworks will not be posted, but can be discussed with/requested from the instructor.
Absence Policy: Students are expected to attend class regularly, as regular attendance is one of the most important contributors to student success. In case a student occasionally needs to miss a lecture due to illness, emergency, or caring for a sick family member, the student is responsible for notifying the professor with as much advance-notice as possible of their absence and working with the professor to make up any missed work.
Students may not miss a submission deadline without prior permission from the professor, except in the case of a sudden emergency. If a student needs additional time to complete their homework, they must contact the professor as soon as possible to discuss their options.
Cell Phones: Use of cell phones is strictly prohibited during lecture hours, except in verifiable cases of emergencies. Use of laptops and electronic tablets is limited to the instances when required for in-class exercises or running simulations explicitly provided during the course of the lectures.
Students who prefer to take notes on electronic writing pads or tablets, should contact the professor and seek prior permission to do so.
Food and Drinks: No eatables are allowed during the lecture hours. If there is a compulsive need to eat, the students should excuse themselves and leave the classroom (or turn off their video/audio in case of zoom) to finish their meal. The exception to this rule is only permitted in case of a medical requirement. The only drink allowed during the lectures is water (students should feel free to keep themselves hydrated!). Consumption of alcoholic drinks during the lecture is not allowed.
Academic Integrity: Collaboration with other students on homeworks and formation of study groups are encouraged. However, the collective wisdom developed in the process should not preclude individual comprehension. Each student should hand in separate homeworks, written independently of the other group members.
Any suspected cheating or other instance of academic dishonesty will be dealt with as per the university policy (please read: https://www.uml.edu/Catalog/Graduate/Policies/Academic-Integrity.aspx).
Student Mental Health and Well-being: We are a campus that cares about the mental health and well-being of all individuals in our campus community, and recognize that personal health and well-being of students can impact their success in this course. Students sometimes experience mental health concerns or stressful experiences that interfere with academics and have a negative impact on everyday life. If a student or someone they know are experiencing mental health challenges at UMass Lowell, they should contact Counseling (information below). Their services are free and confidential, and same day appointments are available.
Students can also reach out to any one of a wide range of campus resources, including:
Counseling Services provides crisis intervention, assessment, referrals, short-term individual counseling, group therapy, and on-call clinicians outside of business hours. They are located at University Crossing Suite 300 and their 24/7 phone number is 978-934-6800.
UMatter2 is a university-wide initiative to support students and promote mental health. The office may be reached at 978-934-6671.
Consider also reaching out to a friend, faculty or a trusted family member for getting connected to the support that can help.
Health and Safety: The safety and health of the UMass Lowell community is our shared priority. In seeking to provide the fullest academic and campus life experience possible, UMass Lowell will rely on all members of our community to act responsibly. For the latest updates on UMass Lowell’s health advisory, please visit https://www.uml.edu/student-services/health/advisories.aspx
UMass Lowell has implemented reasonable health and safety protocols in accordance with national and state public health guidelines. These standards apply to anyone who is physically present on campus or participating in a UMass Lowell-sponsored activity.
Vaccination: COVID-19 vaccination is no longer required for students, though strongly recommended for all members of campus community. Please visit Mass. Vaccine Finder to find vaccine locations.
Face Coverings: Face coverings are no longer required outdoors or in indoor common spaces including classrooms, instructional laboratories, meeting rooms, work areas, break rooms, hallways, elevators and restrooms. Nonetheless, guided by personal discretion, students are encouraged to use them especially if they are not vaccinated.
Disability Services: If a student a documented disability that will require classroom accommodation, they should notify the professor as soon as possible, so that appropriate arrangements can be made. The students should contact the professor during office hours or send an email. They are encouraged to visit the Student Disability Services webpage for further information.
Additionally, Student Disability Services supports software for ALL students. The university has literacy software that allows the student to read on-screen text aloud, research and check written work, and create study guides. Students can download the software from the IT Software webpage on the UML assistive technologies website.
Course Plan:
Phase Transitions: Mean-field theory, Landau-Ginzburg approach, scaling and critical exponents
Renormalization Group Theory: Idea of coarse graining, relevant and marginal perturbations, universality, finite-size scaling
Landau-Wilson model: Wilson-Fisher fixed point, epsilon-expansion, perturbative RG (conformal perturbations and operator product expansion)
Berezinskii-Kosterlitz-Thouless (BKT) transition: 2D degenerate systems, low and high temperature asymptotes for correlations, topological defects
Bardeen-Cooper-Schrieffer (BCS) Theory of Superconductivity
Quantum Phase Transitions: Path integral and partition function for a quantum system, 1D quantum XY model, 1D Josepshon junction array
Fluctuations and Linear Response Theory: Onsager relations, fluctuation-dissipation theorem and Kubo formula, Fokker-Planck and diffusion equations
Selected topics*: Random matrix theory, replica trick, rudiments of conformal field theory, gauge fields and fractionalization
*Chosen based on availability of time and instructor's discretion