ICTS Moodle Page

    The schedule of courses for Jan-Apr 2021 semester is given below

    1. Advanced Classical Electromagnetism - Core (PHY-207.5)

      Instructor: Loganayagam R

      Venue: Online

      Class timings: Thursdays & Saturdays: 11:00-2:30 pm (Tutorials on Wednesdays: 2:00-3:30 pm)

      First meeting: Thursday (10:00 - 13:00 Hrs), 11th February, 2021

      Course description: Please click here

      The grading policy: will be based on the following weightage

      – Assignments : 35% for PhD students, 40% for I.PhD students

      – Mid term Exam : 30%

      – End term Exam : 30%

      – Term paper (a thorough review of a topic in electromagnetism not covered in textbooks below, see below for suggestions) : 5% Extra credit (Compulsory for PhD Students) Note that Assignments form a central part of this course, since one of the main aims of this course is to train students to solve problems


    2. Advanced Classical Mechanics - Core (PHY-204.5)

      Instructor: Abhishek Dhar

      Venue: Online

      Class timings: 11 am-12:30 pm on Wednesdays & Fridays

      First meeting: 15th January 2021

      TA: Saurav Pandey, saurav.pandey@icts.res.in

      Course description:

      1. Recap of basic ideas of Newtonian mechanics

      2. Central force problem

      3. Small oscillations

      4. Dynamical systems theory basics

      5. Lagrangian and Hamiltonian formulation of classical mechanics

      6. Poisson brackets and symplectic structure

      7. Hamilton Jacobi theory

      8. Rigid body motion

      9. Integrability, Chaos, and Nonlinear-dynamics

      Prerequisites:

      First course in classical mechanics; Ability to write simple programs in any language (c, python, fortran, etc.)

      Books:

      (a) Goldstein: Classical Mechanics (b) Reichl: The Transition to Chaos (c) Saletan and Jose: Classical Dynamics

      Course evaluation: Assignments – 50 %; Mid-term and Final Exam – 50 %


    3. Lab Course - Core (PHY-108.5)

      Instructor:

      (i) Vishal Vasan and Amit Apte: Atmospheric sciences module

      (ii) Abhishek Dhar: Active matter module

      (iii) Pallavi Bhat and P. Ajith: Astrophysics module

      Venue:Online

      Course goals:

      Due to the current pandemic, the version of the experimental methods course offered will differ from the traditional one. In this course you will be introduced to several different areas of physics where experimental data play a key role. In particular you will be exposed to datasets as gathered by experimentalists working in the lab and from observation studies. You will learn how to do simple analysis & visualisation, investigate the nature and sources of systematic and random errors, and verify theoretical predictions against experimental data.

      Course structure and evaluation:

      The course is split into three modules: Atmospheric science, Active matter and Astrophysics. Each module will be between 2 weeks to 4 weeks long. In each module you will be introduced to some experimental methods and datasets related to that particular sub-field in physics. All modules will focus on the comparisons of theory and experiment introducing the student to subtle issues of validating a model from data. At the end of each module, students will submit a written report based on their findings. Class participation is crucial. Discussions form an essential part of science and class participation will be part of the final grade. Note: the course involves data analysis and thus a significant part of the course will involve programming in a language (most likely Python). Though prior experience with programming is not necessary, it will certainly be beneficial.

      Topics:

      (i) Atmospheric science: Dispersive waves, Fourier series and the FFT. Waves in atmosphere and ocean as seen in temperature, pressure, clouds and other similar datasets. Precip-itation.

      (ii) Active matter: Brownian motion and detection of such motion experimentally. Active matter and deviation from Brownian motion.

      (iii) Astrophysics: TBA.

      Evaluation: Students will be evaluated on the following basis

      (i) (60%=3×20%) Written report for each module

      (ii) (30%) Homework assignments

      (iii) (10%) Class participation

      Class timings:

      The course will begin with the atmospheric science module and classes will be held twice a week on tue/thur at 2:30-3:30pm. Note the timings for the remaining modules may change and you will need to check with your instructors!


    4. Research Methodology and Ethics - Core (PHY-200.5)

      Instructor: Loganayagam R

      Venue: Online

      Class timings: Mondays 5:30-6:30 pm & Thursdays 4:00-5:30 pm

      First meeting:Thursday 4:00-5:30 pm, 11th Feb, 2021.

      Course description: Please click here

      The grading policy: There will be no drop test for this course.

      The grading policy: will be based on the following weightage

      – Class participation/presentations : 50%

      – Written Assignments : 50%


    5. Geometry and Topology in Physics - Topical (PHY-403.5)

      Instructor: Joseph Samuel

      Venue: Online

      Class timings: 11 am-12:30 pm on Mondays and Tuesdays

      First meeting: 12 January 2021

      Course description:

      Prerequisites:

      Advanced Classical Mechanics, Quantum Mechanics, Statistical Mechanics, (all at the level of Landau and Lifshitz), complex analysis, group theory.

      Textbooks:

      There are no fixed textbooks for the course. We will be drawing on many sources from the published literature and the internet.

      Structure of the course:

      The course will cover a number of applications of geometry and topology in the context of physical examples. The emphasis will be on the examples rather than on rigour. This course will be complementary to mathematics courses on geometry and topology.

      Exposure to such courses will be helpful, but not a prerequisite to follow the course.

      What students will gain from the course:

      An appreciation of the commonality between different areas of physics; the unifying nature of geometric and topological ideas in physics.

      How the course will achieve its goals:

      We will take specific examples of systems from different areas of physics and analyse them from a geometric perspective. Make connections wherever possible between the different examples. The course will start with simple examples and graduate to more advanced ones. The choice of examples will depend on the feedback I get from the students.

      Assessment:

      Some classes will include a twenty-minute quiz, in which students are asked to answer simple questions related to the class discussion. For example, filling in missing steps in the derivation; consideration of special cases etc. This will be 40% of the assessment. There will also be regular assignments, which the students will have to turn in on time. These will count as 30%. The remaining 30% is for the final exam. It is not presently clear if the pandemic will permit in-person classes. We hope that the situation will improve by Jan 2021. If this does not happen, classes will be conducted online. In this case, students taking the course will be required to have a good internet connection. If you need help in this regard, please contact the ICTS and consult your appointment letter for more details.


    6. Introductory Fluid Mechanics - Topical (PHY-402.5)

      Instructor: Rama Govindarajan

      Venue: Online

      Class timings: 9 am-10:30 am on Tuesdays and Wednesdays

      First meeting: 12th January 2021

      Course description: Following is a course summary but is subject to change depending on students' interests:

      1. Continuum formulation of fluid mechanics, limitations

      2. Lagrangian and Eulerian perspectives

      3. Conservation of mass (the continuity equation)

      4. Similarity transforms

      5. Stream functions, Angular momentum, Velocity gradient tensor – Symmetric and Antisymmetric parts etc.

      6. Conservation of Momentum – Euler and Navier-Stokes Equations

      7. Dynamic similarity – Buckingham Pi theorem

      8. Kelvin’s Circulation theorem

      9. Couette and Poiseuille Flow

      10. Introduction to Turbulence – Scaling laws, and energy budget equation

      11. Fully developed turbulence – K41 hypothesis

      12. Singular Perturbation Theory

      13. Bernoulli’s function and principle

      14. Boundary layer theory

      15. Flow past a plate, Blasius equation

      16. Vortex Dynamics

      17. Use of complex techniques for inviscid, incompressible vortex and mass source induced velocity fields.

      18. Method of images

      19. Potential flow past a cylinder

      20. Blasius theorem – Force and torque on a solid body in a fluid (inviscid, incompressible)

      21. Conformal Mapping

      22. Flow instabilities – Study of Linearized equations for stability

      23. Rayleigh Plateau instability

      24. Orr-Sommerfeld equation

      25. Benard Problem

      26. Taylor problem on centrifugal instability

      27. Reynolds-averaged Navier-Stokes Equations

      Evaluation: Homeworks, one midterm and one final exam.


    7. Open Quantum Systems - Topical (PHY-405.5)

      Instructor: Manas Kulkarni

      Venue: Online

      Class timings: 4:00 pm-5:30 pm on Tuesdays and Fridays

      First meeting: 15th January 2021

      Course description:

      1. Dissipation in Quantum Mechanics: General setup and various approaches

      2. Damped Quantum Harmonic Oscillator, two time averages and quantum regression

      3. Spin Boson Model (Dephasing) and some generalizations

      4. Dissipative two-level and multi-level systems

      5. Cavity-Quantum Electrodynamics (cavity-QED): Exact solutions of the Jaynes-Cummings Model (JCM)

      6. Dispersive limit of the JCM and its generalizations (reduction to Bose-Hubbard systems)

      7. Dissipative process in cavity-QED systems

      8. Driven-Dissipative Quantum Systems and applications (driven JCM)

      9. Dicke Model and phase transitions

      Prerequisites:

      Quantum Mechanics, Statistical Physics

      Textbooks: Below are some suggested books. I will also be making additional notes.

      1. Howard Carmichael, Statistical Methods in Quantum Optics 1. Master Equations and Fokker-Planck Equations (Springer)

      2. Girish S. Agarwal, Quantum Optics (Cambridge University Press)

      3. Heinz-Peter Breuer and Francesco Petruccione, The theory of open quantum systems (Oxford University Press)

      Term paper topics: Below are suggested topics for the term paper (report + presentation). The suggested references for each of them will be updated. Students will need to pick a topic (latest by February 15, 2021) and make a report and then give a presentation (at the end of the semester).

      1. Non-Hermitian Random Matrices

      2. Quantum Dot circuit-QED systems

      3. Optomechanical Systems

      4. Self-trapping, localization in Non-Hermitian Systems

      5. Parity-Time Symmetric Systems

      Grading Policy:

      Homework – 40 %

      Term paper (report and presentation) – 30 %

      Final Exam – 30 %


    8. Physics of Compact Objects - Topical (PHY-404.5)

      Instructor: Parameswaran Ajith & Bala Iyer

      Tutor: Shasvath Kapadia

      Venue: Online

      Class timings: Wednesdays from 3:30 pm-5:00 pm & Fridays from 2:15pm-3:45pm

      First meeting: 13th January 2021

      Plan: 15 lectures + 15 tutorials (each 90 mins; 45 contact hrs)

      Course description:

      This course aims to provide a general introduction to the physics and astrophysics of compact objects, and compact-object binaries. We will start with introductory topics and will end by surveying some of the current research. We will draw content from several textbooks and review articles.

      Stellar structure, evolution and collapse - 3 lectures

      • Hydrostatic equilibrium, Equations of stellar structure, Solutions to equations of stellar structure, Stellar evolution, Gravitational collapse and supernovae.

      White dwarfs - 3 lectures

      • Electron degeneracy pressure, Structure of white dwarfs, Chandrasekhar limit, Mass-radius relation of white dwarfs.

      Neutron stars - 3 lectures

      • Equation of state at higher densities, Structure of neutron stars, Mass limit of neutron stars, Mass-radius relation of neutron stars, Pulsars.

      Black holes - 3 lectures

      • Schwarzschild solution, Particle and photon orbits in Schwarzschild geometry, Kerr solution, Astrophysical black holes, x-ray binaries, galactic nuclei.

      Exotic compact objects - 1 lecture

      • Exotic objects and their possible observational signatures.

      Compact object binaries - 2 lectures

      • Compact binary evolution, Binary pulsars, Compact binary coalescence, their gravitational-wave signatures.

      References (not exclusive):

      1. Saul Teukolsky and Stuart L. Shapiro. Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects (Wiley-VCH; 1983).

      2. T. Padmanabhan, Theoretical Astrophysics: Volume 2, Stars and Stellar Systems (Cambridge 2001).

      3. Bernard F. Schutz, A First Course in General Relativity (Cambridge, 2009).

      Evaluation: 70% based on assignments and homework. 30% based on final term paper.


    9. The Black Hole Information Paradox - Topical (PHY-412.5)

      Instructor: Suvrat Raju

      Venue: Online

      Class timings: 6:30 pm -8 pm on Wednesdays and Thursdays

      First meeting: 13th January 2021

      Course description:

      This is an advanced elective course covering recent developments in our understanding of the black-hole information paradox. We will emphasize the broader lessons that puzzles about black-hole evaporation and the black-hole interior hold for theories of quantum gravity. The topics that we plan to cover include the following:

      1. Hawking's original formulation of the information paradox.

      2. Paradoxes involving the black-hole interior and the monogamy of entanglement.

      3. The principle of holography of information.

      4. Quantum extremal Islands.

      5. Paradoxes involving large AdS black holes

      6. Construction of the black-hole interior in AdS/CFT

      7. State dependence

      8. Fuzzballs, firewalls and other proposals for horizon structure

      We will use the recent review "Lessons from the Information Paradox" as a guide for the lectures.

      Click here

      Prerequisites:

      Quantum field theory, general relativity, familiarity with black-hole thermodynamics and quantum fields in curved spacetime.

      Lecture details:

      The course will be entirely virtual.

      We will have 2 virtual lectures per week starting the week of 11 January and continuing till mid-April. Each lecture will be 1.5 hours. In addition, we will have office-hours/tutorials each week for questions and discussion.

      Lecture timings will be fixed later based on the convenience of the students attending.


    10. Introduction to Dynamical Systems Theory (IISc course: MA 278; ICTS course: MTH 216.5)

      Instructor: Amit Apte

      Venue: google-meet, see link below for the google-classroom

      Class timings: TBA

      First meeting: 23rd February 2021 (10-11 am)

      To join: https://bit D.O.T ly SLASH 3bg0P2l (hope you know what I mean!)

      Course description:

      Linear stability analysis, attractors, limit cycles, Poincare-Bendixson theorem, relaxation oscillations, elements of bifurcation theory: saddle-node, transcritical, pitchfork, Hopf bifurcations, integrability, Hamiltonian systems, Lotka-Volterra equations, Lyapunov function & direct method for stability, dissipative systems, Lorenz system, chaos & its measures, Lyapunov exponents, strange attractors, simple maps, period-doubling bifurcations, Feigenbaum constants, fractals. Both flows (continuous-time systems) & discrete-time systems (simple maps) will be discussed. Assignments will include numerical simulations.

      Prerequisites, if any:

      familiarity with linear algebra - matrices, and ordinary differential equations

      Desirable:

      Ability to write codes for solving simple problems.

      Suggested books and references:

      1. S. Strogatz, Nonlinear Dynamics and Chaos: with Applications to physics, Biology, Chemistry, and Engineering, Westview, 1994.

      2. S. Wiggins, Introduction to applied nonlinear dynamics & chaos, Springer-Verlag, 2003.

      3. K. Alligood, T. Sauer, & James A.Yorke, Chaos: An Introduction to Dynamical Systems, Springer-Verlag, 1996.

      4. M.Tabor, Chaos and Integrability in Non-linear Dynamics, 1989.

      5. L. Ya. Adrianova, Introduction to Linear Systems of Differential Equations, AMS 1995.

      6. Morris W. Hirsch, Robert L. Devaney, Stephen Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press 2012.

      Academic Events for this course:

      Sr. No.

      Event

      From

      To

      1

       First meeting

       23.02.2021 (10:00-11:00)

      2

       Course Registration

       22.02.2021

      05.03.2021

      3

       Course Dropping without mention in the Transcripts

       06.03.2021

      26.04.2021

      3

       Course Dropping without mention in the Transcripts

       27.04.2021

      26.05.2021

      4

       Last date for Instruction

       28.05.2021

      5

        Terminal Examination -- sometime between the dates of 02 to 11 June (exact date TBD)

       02.06.2021

      11.06.2021

      The course time will be adjusted in the first meeting based on any clashes that may arise, so those interested in registering should attend the first meeting without fail.

      The mode of instruction will be completely online at least until 31st March. Further decisions will be announced in class.

      Note:IISc semester schedule will be followed. Interested ICTS students, please contact the instructor for registration; Interested IISc students, please contact the IISc maths department for registration process (note: IISc students need to register for IISc course number MA 278).

      google classroom link is https://classroom.google.com/u/0/c/Mjc1OTY1MTk3OTIw?cjc=jt67mhlp>

      It is also mentioned on http://math.iisc.ac.in/course-schedule.html


    11. Probability in High Dimensions (IISc course: MA 363; ICTS course: MTH 217.5)

      Instructor: Anirban Basak

      Venue: TBA

      Class timings: TBA

      First meeting: tentatively first week of March (so the course will be from March to around mid-June), exact dates TBA

      Course description:

      Prerequisites:

      This is a graduate level topics course in probability theory. Graduate level measure theoretic probability will be useful, but not a requirement. Students are expected to be familiar with basic probability theory and linear algebra. The course will be accessible to advanced undergraduates who have had sufficient exposure to probability and linear algebra.

      Course outline:

      This course will be aimed at understanding the behavior of random geometric objects in high dimensional spaces such as random vectors, random graphs, random matrices, and random subspaces, as well. Topics will include the concentration of measure phenomenon, non-asymptotic random matrix theory, empirical processes, and some related topics from geometric functional analysis and convex geometry. Towards the latter half of the course, depending on students' interests, a few applications of the topics covered in the first half will be considered such as community detection, covariance estimation, randomized dimension reduction, and sparse recovery problems.

      Suggested books and references:

      1. Roman Vershynin, High-dimensional probability: An introduction with Applications in Data Science, Cambridge Series in Statistical and Probabilistic Mathematics (Series Number 47), 2018.

      2. Roman Vershynin, Introduction to the non-asymptotic analysis of random matrices, Compressed sensing, 210-268, Cambridge University Press, 2012.

      3. Stéphane Boucheron, Gábor Lugosi, and Pascal Massart, Concentration Inequalities: A nonasymptotic theory of independence, Oxford University Press, 2013.

      4. Michel Ledoux and Michel Talagrand, Probability in Banach spaces, Springer Science & Business Media, 2013.

      5. Avrim Blum, John Hopcroft, and Ravindran Kannan, Foundations of Data Science, Cambridge University Press, 2020.

      6. Joel Tropp, An Introduction to Matrix Concentration Inequalities, Foundations and Trends in Machine Learning, Vol. 8, No. 1-2, pp 1-230, 2015.

      Weekly schedule will be posted later.

      Grading:

      Students taking this course for credit are required to do a (reading) project, submit a report, and give a presentation on the same at the end of the semester. Depending on the number of registered students the grading scheme may change.

      Email: anirban.basak@icts.res.in

      Course webpage: Link

      Office hours: By email appointment.

      Note: IISc semester schedule will be followed (the start date and duration to be decided). Interested ICTS students, please contact the instructor for registration; Interested IISc students, please contact the IISc maths department for registration process (note: IISc students need to register for IISc course number MA 363).


  • Physical Sciences
    • ICTS Moodle Page

      The schedule of courses for September - December 2020 are given below

      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 micro states , 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 11am 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.

    The schedule of ICTS courses for Jan - Apr 2020 are given below:

    1. Condensed Matter Physics-1 (Elective)

      Instructor:  Chandan Dasgupta and Subhro Bhattacharjee

      Venue: Chern Lecture Hall, ICTS

      Class Timings: Monday and Wednesday 5-6.30 PM

      First Meeting: 2nd January 2020, 3:15 pm

      Course Description:This course is aimed to introduce the basics of condensed matter physics. These ideas and techniques form the building blocks for studies in quantum many-body physics and a large class of quantum field theories that form the basis of our present understanding of materials around us. A detailed outline is available on the ICTS website. Students interested in aspects of quantum many-body physics are strongly encouraged to credit/audit the course.

      Prerequisites:Quantum Mechanics II, Statistical Mechanics I

      For more details: Click here

    2.  

    3. Statistical mechanics (Core)

      Instructor:  Anupam Kundu

      Venue: Emmy Noether Seminar Hall

      Class Timings: Wednesday 03:30 PM - 05:00 PM Chern lecture hall and Friday 04:00 PM - 05:30 PM Chern lecture hall

      First Meeting: Wednesday 08 Jan 05:00 - 06:30

      For more details: Click here

    4.  

    5. Classical Electromagnetism Course (Core)

      Instructor:  Loganayagam R

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Class Timings: Tuesday and Fridays, 11:00-12:30 AM(Tentative)

      Tutorials on Wednesday: 3:00-4:00 PM(Tentative)

      First Class (Introduction): Friday (02:00 pm - 05:00 pm), 3rd January, 2020
      Emmy Noether Seminar Hall (Note unusual venue/timing for the first class.)

      For more details: Click here

    6.  

    7. Basics of Nonequilibrium Statistical Physics (Elective)

      Instructor:  Abhishek Dhar

      Venue: Emmy Noether Seminar Hall, ICTS
      On 3rd Feb ARC seminar Room
      on 29th Jan and 5th Feb S N Bose meeting room

      First Meeting: First Meeting: Friday, Jan 3, 4 PM Chern lecture hall, ICTS Campus, Bangalore

      Class Timings: 11:00 to 12:30 PM Monday and Wednesday

      The topics to be covered are:
      (i) Basics of random walks
      (ii) Basics of Markov processes.
      (iii) Brownian motion, classical and quantum Langevin equations
      (iv) Fokker Planck equations and quantum master equations
      (v) Linear response theory

      The course will be aimed at understanding the formalism through examples.
      Requirements: Students should have a solid basic knowledge of statistical physics and quantum physics

      Books:
      (i) Stochastic processes in physics and chemistry: van Kampen
      (ii) Nonequilibrium Statistical Physics: Noelle Pottier

    8.  

    9. Geometry and Topology in Physics (Elective)

      Instructor:  Joseph Samuel

      Class Timings: Wednesday 02:00 PM - 03:30 PM Chern lecture hall and Thursday 11:00 AM - 12:30 PM Chern lecture hall

      First Meeting: 2nd January 2020, 11:00 am Feynman

      Prerequisites: Advanced Classical Mechanics, Quantum Mechanics, Statistical Mechanics. (all at the level of Landau and Lifshitz), basic complex analysis and group theory.

      Textbooks: There are no fixed textbooks for the course. We will be drawing on many sources from the published literature and the internet.

      Structure of the course: The course will cover a number of applications of geometry and topology in the context of physical examples. The emphasis will be on the examples rather than on rigour. This course will be complementary to mathematics courses on geometry and topology. Exposure to such courses will be helpful, but not a prerequisite to follow the course. What students will gain from the course: an appreciation of the commonality between different areas of physics; the unifying nature of geometric and topological ideas in physics. How the course will achieve its goals: We will take specific examples of systems from different areas of physics and analyse them from a geometric perspective. Make connections wherever possible between the different examples. The course will start with simple examples and graduate to more advanced ones. The choice of examples will depend on the feedback I get from the students.

      Assessment: Some classes will include a fifteen-minute quiz, in which students are asked to answer simple questions related to the class discussion.

      For example, filling in missing steps in the derivation; consideration of special cases etc.
      This will be 40% of the assessment. The remaining 60% is from the final exam

    10.  

    11. An Introduction to GW Physics & Astronomy (Elective)

      Instructor:  P.Ajith and Bala Iyer

      Venue: Chern Lecture Hall, ICTS

      Class Timings: 10:00 - 11:30 am on Wed & Fri (to be confirmed after the first meeting)

      First Meeting: 10:00 am, Jan 17 (Fri)

      Prerequisites: General Relativity, exposure to Python and Mathematica

      Contents:

      • Theory of GWs
      • Detection of GWs
      • GW data analysis
      • GW source modeling
      • Astrophysics of GW sources

      Evaluation: 50% assignments + 50% written test.

      Books:

      • Bernard Schutz, A First Course in General Relativity (Cambridge)
      • Michele Maggiore, Gravitational Waves: Volume 1: Theory and Experiments (Oxford)
      • Jolien D. E. Creighton & Warren G. Anderson, Gravitational-Wave Physics and Astronomy: An Introduction to Theory, Experiment and Data Analysis (Wiley-VCH)
      • Nils Andersson, Gravitational-Wave Astronomy: Exploring the Dark Side of the Universe (Oxford)
      • Stuart L. Shapiro Saul A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (Wiley-VCH)

    12.  

    13. String theory II (Reading)

      Instructor:  Loganayagam R

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Class Timings: Tuesday and Friday, 02:30-4:00 PM(Tentative)

      First Meeting: Tuesday (02:30 PM), 7th Jan 2020

      For more details: Click here

    14.  

    15. Topics in Fluid Mechanics (Reading)

      Instructor:  Rama Govindarajan

    The schedule of ICTS courses for Aug - Nov 2019 are given below

    1. Introduction to General Relativity (Reading)

      Instructor:  Bala Iyer

      Venue: Amal Raychaudhuri Meeting room, ICTS Campus, Bangalore

      Class Timings: Monday 1:45-3:15 pm, Friday 1:45-3:15 pm

      First Class: Monday, 12 August, 2019

      Text Books:

      1. Introducing Einstein’s Relativity: Ray D’Inverno
      2. A first course in general relativity: B. Schutz

      Structure of the course:
      The reading course has three components:

      1. Weekly Presentation and Participation
      2. Problem solving
      3. Final Oral Exam/Seminar

      Presentations will be Twice a week (1.5 hrs each) where all students take turns in reading the assigned text and presenting them. I will start off the course with an Overview Lecture on GR and Information on Standard Texts they can consult. Problems on various modules will be evaluated by a TA. There will be an end-semester Oral Exam (which may be replaced by a Seminar)

      Final Grades will be based on:

      1. Class presentation/participation: 30%
      2. Problems: 30%
      3. End term Oral Exam (or Seminar): 40%
    2.  

    3. String Theory I (Reading)

      Instructor:  R.Loganayagam

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Class Timings: Wednesday and Friday, 11:00-12:30 AM(Tentative)

      First Class: Wednesday (10:00 am), 7th August, 2019

      Structure of the course: The reading course has three components : Presentation/Class participation, assignments and exams.

      Presentations will be twice a week (1.5-2hrs each) where all students take turns in reading the assigned text and presenting them. I will start off the course with a set of 6 to 8 lectures (i.e, 3 − 4 weeks) giving a brief survey at the level of basic textbooks mentioned below.

      Assignments will be a set of problems on various modules which need to be handed over by those who are crediting the course. Since I do not really have a TA for this course, I want the students who credit this course to grade each others’ assignments.

      There will be a mid-semester and an end-semester exam (the latter can be replaced by a term-paper, see below for details).

      The grading policy will be based on the following weightage :

      – Class presentation/participation : 20% – Assignments : 40%
      – Mid term Exam : 20%
      – End term Exam (or) Term paper : 20%

      For more details, see the PDF

    4.  

    5. Classical Mechanics (Core)

      Instructor:  Manas Kulkarni  

      Class Timings: Wednesdays - 3:30 to 5:00 pm and Fridays – 4 pm to 5:30 pm

      Venue: Chern lecture hall, ICTS Campus, Bangalore

      First Class: Wednesday (4:00pm), 7th August, 2019

      Topics:

      1. Recap:
        -Recap of Newton's laws and their consequences
        -System of point masses, Rigid Bodies
        -Classical driven-dissipative systems
         
      2. Lagrangian Formulation:
        -Principle of least action
        -Noether's Theorem, Symmetries
        -Small Oscillations, Applications
         
      3. Rigid body motion:
        -Euler Angles
        -Tops
         
      4. Hamiltonian formulation:
        -Liouville's Theorem
        -Action-Angle variables
        -Hamilton-Jacobi Equations
         
      5. Classical Integrable Models and Field Theory:
        -Lax Pairs
        -Toda Model
        -Calogero Family of Models
        -Integrable Field Theories
        -Integrable Partial Differential Equations and applications in physics.
    6.  

      Books:

      1. Landau Lifshitz course on theoretical physics: Vol 1: Classical Mechanics
      2. Classical Mechanics by Herbert Goldstein, Charles P. Poole, John L. Safko
      3. Analytical Mechanics by Louis N. Hand, Janet D. Finch
      4. classical integrable finite-dimensional systems related to Lie algebras, M.A. Olshanetsky, A.M.Perelomov, Physics Reports, Volume 71, Issue 5, May 1981, Pages 313-400

       

    7. Physics of Living Matter (Elective)

      Instructor:  VijayKumar Krishnamurthy  

      Prerequisites: A first course on statistical physics

      Outline: Basic phenomenology of living systems. Bionumbers. Statistical physics in biology (active particles, chemical kinetics, feeding by diffusion, membrane potentials). Molecular machines (molecular motors, polymerases, synthases, enzymes, ion-pumps, mitochondria). Macromolecular assemblies (polymers, membranes). Sensing and signalling (receptor-ligand interactions, MWC model, biochemical pathways, physical limits to sensing). Hydrodynamics (Navier-Stokes, low Reynolds number flows, swimming, generalized hydrodynamics, active matter, physics of the actomyosin cytoskeleton). Pattern formation (morphogen gradients, Turing patterns, mechanochemical patterns)

      Time: Tuesdays and Thursdays 10:00 am - 11:30 am

      First Meeting: Thursday, 8th August 2019

      Venue: Feynman Lecture Hall, ICTS, Bangalore

      Webpage: https://biophysics.icts.res.in/teaching/physics-of-living-matter/

      Sign up: https://forms.gle/n5KDAzauZZBtXDbk8

    8.  

    9. Statistical Physics of Turbulent Flows (Elective)

      Instructor:  Samriddhi Sankar Ray  

      Venue: Feynman Lecture Hall, ICTS Campus, Bangalore

      Meeting Time: Wednesdays and Thursdays: 2.00 pm - 3:30 pm

      First Meeting: Wednesday, 7th August 2019

      Course Outline:

      1. Basics of Fluid Dynamics
      2. Fourier Analysis
      3. Isotropic Turbulence: Phenomenology of Three-Dimensional Turbulence
      4. Analytical Theories (closures, etc) and Stochastic Models
      5. Two-Dimensional Turbulence

    10.  

    11. Advanced Quantum Mechanics (Core)

      Instructor:  Suvrat Raju  

      Venue and Timings: 2:30 to 4:00 pm Feynman Lecture hall, Thursdays: 2:30 to 4:00 pm Chern Lecture hall

      Course Outline

      • 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.

    12.  

    13. Lab Course (Core)

      Instructors:   Abhishek Dhar, Vishal Vasan

      Timings for first meet: 2 pm Monday, 19th August 2019

      Venue: J C Bose Lab