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 Friday 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:

For additional information, TIFR students may contact the local tutors on their campus:
ICTS: Subhro Bhattacharjee
TIFR Colaba: Kedar Damle
TIFR-H: Kabir Ramola

ICTS Course no.: MTH 122.5

Venue: Online

Class timings: Tuesdays and Thursdays from 11:00 AM to 12:30 AM (1 hr tutorial once a week, tutorial timings to be announced later)

First meeting: 10th August 

Course description: 

Topology: Homotopy, retraction and deformation, fundamental group, Van Kampen theorem, covering spaces and their relations with the fundamental group, universal coverings, automorphisms of a covering, regular covering. 

Geometry: Differential geometry of curves and surfaces, mean curvature, Gaussian curvature, differentiable manifolds, tangent, and cotangent spaces, vector fields and their flows, Frobenius theorem, differential forms, de Rham cohomology.   

Grading policy:

20% assignments,  40% midterm,  40% final.

ICTS Course no.: MTH 247.5

Venue: Online

Class timings: Mondays and Wednesdays 2:00-3:30 (Additional tutorial TBD).

First meeting: 30th August 2021, last lecture in the second week of December. 

Course description: 

This course is aimed at students and researchers working in the field of nonlinear PDEs. We will focus on semilinear evolution equations (mostly scalar-valued) with the emphasis on (a) the mathematical theory behind such equations, (b) how this theory informs the development of numerical methods. Selected topics include: transform techniques for linear equations; spectral methods for evolution PDEs; wellposedness theory for nonlinear PDEs. Additional topics as per the interest of the instructor and students.

Prerequisites: Interested individuals should have prior experience with nonlinear PDEs and numerical methods (through coursework or research). A course in the real and complex analysis will be useful but not essential. Students should consult the instructor before registering.

Course structure: 50% Homework + 20% Report + 30% Final viva exam.

T Tao Nonlinear Dispersive Equations: local and global analysis
R Temam Infinite dimensional dynamical systems in mechanics and physics
C Doering Applied analysis of Navier-Stokes
selected papers to be distributed in class

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.

TextbookModern 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 %

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. 

    • 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

Venue: Online
Class timings: Tuesday 4:00 - 5:30 PM and Friday 2:00 - 3:30 PM
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.


Presentation of Lectures - 40%
Problem sheet - 30%
Final viva - 30%

Venue: Online
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%]

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.