**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:**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

**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.

- Teacher: Rukmini Dey

**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: **

**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.

**References**:

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

- Teacher: Vishal Vasan

**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 %

- Teacher: Subhro Bhattacharjee

**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

- Teacher: Abhishek Dhar
- Teacher: Anupam Kundu

**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.

**Evaluation:**

- Teacher: Bala Iyer

**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%]

- Teacher: Samriddhi Sankar Ray

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.

- Teacher: Pallavi Bhat