ICTS Graduate Courses for Sep - Dec 2020

  1. Advanced Quantum Mechanics (Core)

    Instructor: Subhro Bhattacharjee

    Venue: Online

    Class timings: Tuesday and Friday from 11:45 Noon to 13:15 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.

  2. Advanced Statistical Mechanics (Core)

    Instructor: Anupam Kundu

    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: 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.

  3. Modern Theory of Turbulence (Topical)

    Instructor: Samriddhi Sankar Ray

    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.

  4. Mechanics (Topical)

    Instructor: Pranav Pandit

    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.

    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.

    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.

  5. Introduction to General Relativity (Reading)

    Instructor: Bala Iyer

    Venue: Online

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

    First meeting: 7th September 2020

    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.

  6. Physics at ICTS sessions (Core)

    Venue: Online

    Class timings: Saturdays 11 am to 12:00 noon

    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.

  7. Conformal Field Theory (Reading)

    Instructor: Rukmini Dey

    Venue: Online

    Class timings: TBA

    First meeting: TBA

    Course description: TBA

  8. Instability in Shear Flow (Reading)

    Instructor: Rama Govindarajan

    Venue: Online

    Class timings: TBA

    First meeting: TBA

    Course description: TBA