Courses for Sep - Dec 2021

  1. The Quantum Phases of Matter - Topical (PHY-431.5)

    Instructor: Prof. Subir Sachdev

    ICTS Course no.: PHY-431.5

    TIFR Course no.: PHY-431.1

    TIFR-H Course no.: PHY-431.7

    Venue: Online

    Class timings: Mondays and Wednesdays from 6:30 PM to 8:00 PM (with Fridays optional for extra classes)

    First meeting: Starting September 1. Classes will run till mid-December.

    Course description:

    1. Introduction to the phases of modern quantum materials

    2. Boson Hubbard model: superfluids, insulators, and other conventional phases

    3. Electron Hubbard model: antiferromagnets, metals, d-wave superconductors, and other conventional phases

    4. Mott insulators, resonating valence bonds, and the Z2 spin liquid

    5. Gapless spin liquids, and emergent SU(2) and U(1) gauge theories.

    6. Kondo impurity in a metal

    7. Kondo lattice: the heavy Fermi liquid, and the fractionalized Fermi liquid (FL*). Violations of the Luttinger theorem using emergent gauge fields.

    8. The pseudogap metal of the cuprates: FL* theories

    9. SYK model of metals without quasiparticles, and emergent gravity

    10. Fully connected random models of strong correlation

    11. Quantum criticality of Fermi surfaces

    Grading policy:

    1. Assignments

    2. Term paper

    3. Presentation of the term paper

    The percentages are to be decided soon.

    More details: http://qpt.physics.harvard.edu/qpm

    For additional information, TIFR students may contact the local tutors on their campus:

    ICTS: Subhro Bhattacharjee

    TIFR Colaba: Kedar Damle

    TIFR-H: Kabir Ramola


  2. Advanced Quantum Mechanics (Core)

    Course No.: PHY-206.5

    Instructor: Prof. Subhro Battacharjee

    Venue: Online

    Class timings: Tuesdays and Thursdays 09:15 AM to 10:45 AM 

    First meeting: 20th September, 2021

    Course description:

    • Mathematical preliminaries of quantum mechanics: Linear Algebra; Hilbert spaces (states and operators) 
    • Heisenberg and Schrodinger pictures
    • Symmetries: Role of symmetries and types (space-time and internal, discrete and continuous); Symmetries and quantum numbers; Simple examples of symmetry (Translation, parity, time-reversal); Rotations and representation theory of Angular momentum; Creation and annihilation operator formalism for a simple harmonic oscillator.
    • Perturbation Theory
    • Scattering

    We will also study some additional topics, including some elements of quantum information theory.

    Textbook:

    Modern Quantum Mechanics by Sakurai.

    Course evaluation:

    Assignments (typically one every two weeks): 60 % 

    2 month Term paper + presentation at the end of the semester (topics to be listed after the course starts): 20 %

    End sem exam (in-class if situation permits): 20 %


  3. Statistical Mechanics (Core) 

    Course No.: PHY-205.5

    Instructor: Prof. Anupam Kundu and Prof. Abhishek Dhar

    Venue: Online

    Class timings: Wednesdays and Fridays 4:00 PM to 05:30 PM 

    First meeting: 15th September, 2021

    Course description: 

    • Recap of Fundamentals of thermodynamics, Probability, distributions 
    • Foundations of equilibrium statistical mechanics —- Liouville’s equation, microstate, macrostate, phase space, typicality ideas, (Little on irreversible evolution of macrostate), Kac ring, equal a priori probability, ensembles as tools in statistical mechanics.
    • Partition functions, connection to thermodynamical free energies, Response functions
    • Examples: Non-interacting systems —— Classical ideal gas, Harmonic oscillator, paramagnetism, adsorption, 2 level systems, molecules, more non-standard examples.
    • Formulation of quantum statistical mechanics —— Quantum microstates, Quantum macro-states, density matrix.
    • Quantum statistical mechanical systems —— Dilute polyatomic gases, Vibrations of solid, Black body radiation
    • Quantum ideal gases —— Hilbert space of identical particles —— Fermi gas, Pauli paramagnetism —— Bose gas, BEC —— Revisit phonons, photons —— Landau diamagnetism 
    • Introduction to simulation methods
    • Interacting classical gas —— Virial expansions —— Cumulant expansions —— Liquid state physics —— Van-der Waals equation
    • Introduction to Phase transitions and Critical phenomena, universality, mean field theory, some exactly solvable models. 

    Textbooks:

    • M. Kardar, Statistical Physics of Particles
    • R. K. Pathria, Statistical mechanics
    • K. Huang, Statistical mechanics
    • J. M. Sethna, Statistical Mechanics: Entrop, Order Parameters and Complexity
    • M. Kardar, Statistical Physics of fields
    • Landau & Lifshitz, Statistical mechanics
    • + some other books and papers, references of which will be provided in the class.

    Course evaluation: 

    50% Assignment + 25% mid sem exam + 25% end sem exam

     

  4. Introduction to General Relativity (Reading)

    Course No.: PHY-487.5

    Instructor: Bala Iyer

    Venue: Online

    Class timings: Tuesday 4 - 5.30 and Friday 2 - 3.30

    First meeting: TBA

    Course description:

    Reading course based on Ray D'Inverno book Introducing Einstein's Relativity.

    Following Chapters:

    5. Tensor Algebra
    6.Tensor Calculus
    7. Integration, Variation, Symmetry
    9. Principles of General Relativity
    10. Field Eqns of General Relativity
    12. Energy Momentum Tensor
    14. The Schwarzschild Solution
    15. Experimental Tests of GR
    16. Non-Rotating Black Holes
    19. Rotating Black Holes
    20. Plane Gravitational Waves
    21. Radiation from Isolated Source
    22. Relativistic Cosmology
    23. Cosmological Models

    Format: Two sessions a week each of 90 minutes with students presenting. Problems on the chapter for tutorials.

     

  5. Multiphase Flows: Applications to Atmospheric Problems (Reading)

    Course No.: PHY-499.5

    Instructor: Samriddhi Sankar Ray

    Venue: Online

    Class timings: Saturdays 10 to 12 and Fridays 5 to 7 for one on one tutorials

    Class structure: Weekly problem-solving sets/reading assignments followed by classroom discussions/presentations of the same

    Course description:

    1. Basic thermodynamics: Ideal gas laws, thermodynamics of vapour etc

    2. Basic Fluid Mechanics: Equations of motion, instabilities

    3. Coupling of scalar fields in multiphase flows

    4. Evaporation and condensation

    5. Buoyancy

    6. Droplet dynamics

    7. Collisions and coalescences

    8. Smoluchowski equation, kernels and coagulation models

    9. Application of ideas to model clouds

    Text Books:

    1. White, Fluid Mechanics

    2. Pope, Turbulent Flows

    3. Reif, Fundamentals Of Statistical And Thermal Physics

    4. Yau and Rogers, A Short Course in Cloud Physics

    5. Pruppacher and Klett, Microphysics of Clouds

    These will be supplemented by research and review papers as and when necessary.

    Course evaluation: Continuous assessment based on weekly assignments [70%] + End Term Presentation [30%]

     

  6. Physics at ICTS sessions (Core)

    Venue: Online

    Class timings: Mondays 11 to 12:30

    First meeting: TBA

    Outline: These sessions are compulsory for all first-year physics students (PhD as well as IPhD). Each session will be given by one faculty member about the work done in their groups. Students are supposed to interact and discuss this with the speaker. For each class, 2 students will be assigned to submit a short one page summary of what was discussed.