**Venue:**Online

**Class timings:**Tuesday and Friday from 4:00 to 5:30 PM

**First meeting:**4th September 2020

**Course description:**

- Recap of Fundamentals of thermodynamics, Probability, distributions (single and multi variables), Conditional probability, moments, cumulants, moment generating functions, central limit theorems
- 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 -- Integer partitions -- Condensation phenomena in real space
- Basic discussions on large deviation principles in classical statistical mechanics.
- Introduction to simulation methods
- Interacting classical gas -- Virial expansions -- Cumulant expansions -- Liquid state physics -- Van-der Waals equation

**Textbooks:**

- M. Kardar, Statistical Physics of Particles
- R. K. Pathria, Statistical mechanics
- K. Huang, Statistical mechanics
- J. M. Sethna, Statistical Mechanics: Entropy, 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.

**Evaluation:**

**Venue:**Online

**Class timings:**Tuesday and Friday from 11:30 Noon to 13:00 PM

**First meeting:**4th September 2020

**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.

**Evaluation: **

The grading would be done on the basis of the following weightage :

**• **Assignments (every other week approximately): 50%

**⇒ ONLY **students who are crediting need to submit the assignments. Those who are auditing should be present in the tutorials and join the discussions to make sure that they have done the calculations correctly for the assignments.

**⇒ Delay in submission: ***Delay in the submission of the assignment beyond the **deadline would attract a penalty of 10% per day unless due to exceptional circumstances **with prior knowledge of the TA and/or Instructor. ***No assignment will be ac****cepted after the corresponding tutorial has been conducted by the TAs. **

**⇒ Collaborations in assignments: ***You are encouraged to discuss with your **classmates, but not copy. Any signatures of copying will be penalised by putting a **total score of zero for the relevant assignment.*

**• **End semester Exam (Take home, the details of the format to be decided): 40%

**⇒ Collaboration for the Exam: ***As will be elaborated in the question paper, NO collaborations are allowed in the exam. Any sign of copying would lead to cancellation of the exam (a zero will be recorded) and will be reported to the graduate studies cell.*

**• **Impromptu class test/quiz (typically once a month, to be announced at the beginning of the class): 10%

**⇒ **All students present would need to participate.

- Teacher: Subhro Bhattacharjee

**Venue:**Online

**Class timings:**Saturdays 11 am to 12:00 noon

**First meeting:**

**TBA**

**Course description:**

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: Samriddhi Sankar Ray

**Venue:**Online

**Class timings:**Wednesday and Friday from 02:00 to 03:30 PM

**First meeting:**2nd September 2020

**Course description:**

This is an introductory course on the foundations of mechanics, focusing mainly on classical mechanics. The laws of classical mechanics are most simply expressed and studied in the language of symplectic geometry. This course can also be viewed as an introduction to symplectic geometry. The role of symmetry in studying mechanical systems will be emphasized.

The core syllabus will consist of Lagrangian mechanics, Hamiltonian mechanics, Hamilton-Jacobi theory, moment maps, and symplectic reduction. Additional topics will be drawn from integrable systems, quantum mechanics, hydrodynamics, and classical field theory.

**Prerequisites:**

Calculus on manifolds; rudiments of Lie theory (the equivalent of Chapter 1, Chapter 2, and Section 4.1 of [AM78]).

**Textbook:**

The course will not follow any particular textbook.

**References:**

[AM78] Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978.

[Arn89] Vladimir I. Arnol’d, Mathematical methods of classical mechanics, Graduate Texts in Mathematics, vol. 60, Springer-Verlag, New York, 1989.

[CdS01] Ana Cannas da Silva, Lectures on symplectic geometry, Lecture Notes in Mathematics, vol. 1764, Springer-Verlag, Berlin, 2001.

[MR99] Jerrold E. Marsden and Tudor S. Ratiu, Introduction to mechanics and symmetry, second ed., Texts in Applied Mathematics, vol. 17, Springer-Verlag, New York, 1999.

**Evaluation:**

The final grade will be based on homework assignments (60% of the grade) and on two exams (40% of the grade). Both exams will carry equal weight.

- Teacher: Pranav Pandit

**Venue:**Online

**Class timings:**Tuesday and Thursday from 6:00 to 7:30 PM

**First meeting:**3rd September 2020

**Course description:**

- Introduction to basic fluid dynamics
- The Navier-Stokes equation: Analysis, Symmetries, Conservation Laws, Energy Budgets, etc
- Introduction to chaos
- Phenomenology of fully developed turbulence: Experiments
- Scaling laws: Connections with the Burgers equation
- The four-fifth law: Connections with the Burgers equation
- Anomalous scaling and dissipative anomaly: Mathematical Treatment
- Bifractal, beta and multifractal models: Implications for observed scaling laws
- Closure Models
- Special topics: 2D turbulence, cascade models, Burgers equation, rotating flows, passive-scalar advection, etc.

**Evaluation: **30% assignments, 30% mid semester and 40% term paper.

- Teacher: Samriddhi Sankar Ray

**Venue:**Online

**Class timings:**Monday and Thursday from 11:30 - 13:00 PM

**First meeting:**7th September 2020

**Course description:**

Following Chapters:

5. Tensor Algebra6.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