ଜାତୀୟ ବିଜ୍ଞାନ ଶିକ୍ଷା ଏବଂ ଗବେଷଣା ପ୍ରତିଷ୍ଠାନ

राष्ट्रीय विज्ञान शिक्षा एवं अनुसंधान संस्थान

NATIONAL INSTITUTE OF SCIENCE EDUCATION AND RESEARCH

P474 Introduction to Cosmology

P474**Course: **UG-Elective, PG-Elective

**Approval: **42 Lectures + 14 Tutorials

**Credit: **8

**Outcome: **This course teaches the students important concepts and methods in introductory cosmology, with the aim to build their background for future research work in this area.

**Prerequisite: **P457 (General Theory of Relativity & Cosmology)

**Syllabus:**

- The cosmic history and inventory
- A sketch of general Relativity.
- The expanding Universe
- Friedmann Equations and Cosmological Models
- The Standard cosmological model.
- The inflationary Universe.
- Primordial nucleosynthesis and the thermal history of the Universe.
- Perturbations in an expanding Universe.
- Growth of perturbations
- Dark Matter Halos.
- Statistical description of gravitational clusteing.
- Special Topics: Fluctuations in the CMB, Lensing, Cluster Cosmology, The Lyman-alpha Forest, Reionization, Halo Model, Redshift Space Distortions.

Reference Book

- Introducing Einstein’s General Relativity by Ray D’inverno
- The Early Universe by E. W. Kolb andM. S. Turner
- Introduction to Cosmology by BarbaraRyden
- Modern Cosmology by ScottDodelson
- Principles of Physical Cosmology by P. J. E. Peebles
- Large Scale Structure of the Universe by P. J. E.Peebles
- Structure Formation in the Universe by T.Padmanabhan

P475 Relativistic Nucleus-Nucleus Collision & Quark-Gluon Plasma

P475**Course: **UG-Elective, PG-Elective

**Approval: **42 Lectures + 14 Tutorials

**Credit: **8

**Outcome: **This course provides the basic background for relativistic nuclear scattering processes and physics of quark gluon plasma.

**Prerequisite: **P307 (Nuclei and Particle Physics), P304 (Special Theory of Relativity), P302 (Statistical Mechanics), P201 (Classical Mechanics-I)

**Syllabus:**

- Introduction to high energy heavy ion collisions and Quark-Gluon-Plasma, comparison of big bang and the little bang
- Thermodynamics: Relativistic gas (hadrons, quarks and gluons) and its statistical and thermodynamical properties, MIT Bag model, Hagedorn gas, phase diagram of QCD
- Relativistic Kinematics: four vectors notation, rapidity variables, pseudo rapidity variables, light cone variables, relativistic invariants, Dalitz plot, cross sections
- Collision Dynamics: initial state of nuclear collisions, fluid dynamical evolution, kinetic transport model, freeze-out and particle production
- Experiments: a general overview of different experimental setup related to search for QGP and relevant observables
- Signatures of QGP: collective flow, J/Ψ suppression, strangeness enhancement, jet quenching, electromagnetic probes, Hanbury-Brown-Twiss measurement
- Recent progress

Reference Book

- Hadrons and QGP by Letterssier and Rafelski
- Introduction to High Energy Heavy Ion Collissions by C. Y. Wong
- Phenomenology of Ultra Relativistic Heavy Ion Collissions by W Florkowski
- Ultra relativistic heavy ion collisions by R. Vogt
- Introduction to relativistic heavy ion collisions, by L. P. Csernai
- A Short Course On Relativistic Heavy Ion Collission by A. K. Chaudhuri
- Extreme states of matter in strong interaction physics by Helmut Satz
- Relativistic Hydrodynamics by L. Rezzolla and O. Zanotti
- Finite Temperature Field Theory by J. I. Kapusta and C. Gale
- The Early Universe by Kolb and Turner
- Fantastic Realitis by Frank Wilczek
- Research Reports in Physics, Quark Gluon Plasma, Invited lectures of Winter School, Published by Springer Verlag, Editors - B. Sinha, S. Pal and S. Raha
- The Physics of Quark Gluon Plasma, Introductory lectures, Lecture Notes in Physics 785, Publisher - Springer, Editor - S. Sarkar, H. Satz and B. Sinha
- Quark Gluon Plasma - From big bang to little bang, K. Yagi, T. Hatsuda, Y. Miake, Cam- bridge Monograms on Particle Physics, Nuclear Physics and Cosmology
- Quark Gluon Plasma: Theoretical Foundations, An annotated reprint collection - J. Ka- pusta, B. Muller and J. Rafelski, Publisher - Elsevier Science

P476 Non-equilibrium Statistical Mechanics

P476**Course: **UG-Elective, PG-Elective

**Approval: **42 Lectures + 14 Tutorials

**Credit: **8

**Outcome: **This course provides the basic background of non-equilibrium statistical mechanics and out of equilibrium dynamics.

**Prerequisite: **P302 (Statistical Mechanics)

**Syllabus:**

- Kinetic theory of gases, Bolzmann distribution and its implications.
- Bolzmann equation, H Theorem, Conservations laws and Hydrodynamics
- Linear response, fluctuation dissipation theorem,Green-Kubo formula
- Markov Processes: Conditional probabilities, Markov processes, Chapman-Kolmogorov equation, Master equation, Fokker Planck equation, Random walk processes,Ising Glauber Model
- Stochastic differential equations: Langevin equation, stochastic integration, Ito calculus, Stratonvich integrals
- Diffusion equations, first passage problems, driven diffusive systems
- Applications: Aggregation,Fragmentation,Phase ordering Kinetic,Exclusion processes

Reference Book

- Stochastic Methods by C. Gardiner
- A Kinetic View of Statistical Physics by P. L. Kaprivsky, S. Redner and E. Ben Naim
- Statistical Physics 2- Nonequilibrium Statistical Mechanics by R. Kubo, M. Toda and N. Hashitsume
- Stochastic Processes in Physics and Chemistry by N. G. Van Kampen.
- Theory and Applications of Stochastic Processes by Z. Schuss
- A Guide to First Passage Processes by S. Redner

P477 Special Topics in Quantum Mechanics

P477**Course: **UG-Elective, PG-Elective

**Approval: **42 Lectures + 14 Tutorials

**Credit: **8

**Outcome: **This course teaches advanced topics in quantum mechanics which provides the much needed background in concepts and technique in present day research in interface of the area of quantum mechanics, many body physics and information theory.

**Prerequisite: **P303 (Quantum Mechanics II)

**Syllabus:**

PART I: Quantum entanglement & applications:

- Density matrices
- Tensor product and entangled states coherent and squeezed states; Bell basis
- Quantum teleportation
- EPR and Bells inequalities
- Shannon entropy: Qbits, introduction to quantum computing principles; measurement and decoherence

PART II: Introduction to many particle QM:

- Creation/ Annihilation operators; Symmetization/Antisymertization; many body operators, Boson/Fermion coherent states, Grassmann algebra and Gaussian integrals using coherent states.
- Dynamical variables and dynamics of identical particles
- Applications to many body systems: Angular momentum of system of identical particles, first order perturbation in many body systems, introduction to Hartree-Fock methods.

PART III: Symmetries in QM

- Group representation, Point group symmetry, Lie Groups; Schur lemma, orthogonality theorems, irreducible representations, accidental degeneracies; Irreducible tensor operators and direct product representations, Wigner Eckart theorem
- Applications including molecular orbitals, space time symmetries of Bloch states; normal model of vibrations; characters of angular momentum states; SU(2), SU(3) representations

Reference Book

- Part-I
- Entangled systems by Jurgen Audretsch
- Density Matrix Theory and Applications by Karl Blum
- Quantum Mechanics by Leonard Susskind
- Modern Quantum Mechanics by J. J Sakurai
- Part-II
- Quantum Mechanics Merzbacher (Chapters 21 and 22)
- Quantum many particle systems J. W. Negele and H. Orland (Chapter 1)
- Quantum Mechanics Schiff (Chapter 14)
- Elements of Advanced Quantum Theory by J. M. Ziman (Chapters 1,2 and 5)
- Modern Quantum Mechanics by J. J Sakurai
- Part-III
- Group Theory by M Tinkham
- Group Theory by Hamermesh
- Lie Algebras in Particle Physics: from Isospin To Unified Theories by Howard Geogie
- Group theory and Chemistry by Bishop
- Topics in Condensed Matter Theory by Michele Cini
- Elements of Advanced Quantum Theory by J. M. Ziman (chapter 7)
- Solid State Physics by Ashcroft and Mermin

P601 - Classical Mechanics

P601**Course: **PG-Core

**Approval: **

**Credit: **4

**Outcome: **

**Prerequisite: **

**Syllabus:**

- Two-body Central force problem (reduced mass), planet orbits,Virial theorem.
- Collisions and scattering, CM and lab frames, scattering cross section.
- Motion in non-inertial frames, Coriolis force.
- principle of virtual work, constraints, D Alemberts principle.
- Generalized coordinates, velocities and momenta, Lagranges formulation.
- principle of list action, fomulation by Maupertuls, Euler, Hamilton, Liouvilles theorem.
- Hamilton's equations, poisson brackets.
- Canonical transformation, Hamilton-Jacobi equation, Generating functions, Symetries and conservation laws.
- Small oscillations, Normal modes.
- Rigid body dynamics, Euler angles, Euler equations (should solve up to rotation of a top) .

Reference Book

- H.Goldstein-Classical mechanics
- Morion and Thorton- Introduction to classical mechanics.
- Landau & lifshitz-Mechanics
- John R Taylor- classical mechanics

P602 – Mathematical methods

P602**Course: **PG-Core

**Approval: **

**Credit: **4

**Outcome: **

**Prerequisite: **

**Syllabus:**

- Vectors and Tensors (index notation,vector analysis in curvilinear coordinates. Cartesian tensors and four vectors, General tensors).
- Review of Linear Algebra with emphasis on applications to physical problems (linear transformations + Matrix representations, Eigen values + Eigen Vectors, Innner product spaces).
- Review of complex analysis with applications (Cauchy-Riemann equations, Complex integration, Cauchy theorems, Contour integration, Branch points and branch cuts, Applications to integrals, series etc.)
- Hilbert Space methods, special functions (hilbert space, Orthonormal series expansions in Hilbert space especially Fourier series, Special functions
- Ordinary and partial differential equations (Analysis of second order OFE’s Sturm-Liouville system, Boundary value problems for Laplace Diffusion (Heat) and wave equations)
- Integral transforms, its applications and generalized functions (Laplace and Fourier transform, Dirac delta and other generalized functions, Green’s functions of ODE and PDE)
- Group theory (introduction using various groups occuring in physics, its algebra, Representation of groups, Characters)
- Probability and Statistics (probability distributions, Stochastic processes like Brownian motion, Error analysis for experiments, Statistical inference)

Reference Book

- Arfken and Weber, Mathematical Methods
- C.Harper, Mathematical methods
- T L Chow, Mathematical method for physicists.

P603- Electromagnetism

P603**Course: **PG-Core

**Approval: **

**Credit: **4

**Outcome: **

**Prerequisite: **

**Syllabus:**

- Electrostatics in vacuum, force, field, potentials and enegry.(4 hrs)
- Electrostatic boundary conditions and conductors. (2 hrs)
- Solution of Laplace's equation in one, two and three dimensions, uniqueness theorem, methods of images, separation of variables, multipole expansion.(12 hrs)
- Dielectrics(4 hrs)
- Current distributions, magnetic fields and magnetostatic boundary conditions(4 hrs)
- Motion of charges in E & B fields, energy and momentum of electromagnetic fields(8 hrs)
- Maxwell's equations, EM waves and their propagation in free space and in media(12 hrs)
- Potential formulation, Coulomb and Lorentz gauge, radiation from an accelerated charge, dipole radiation (10 hrs)

Reference Book

- David Griffith, "Introduction to electrodynamic"
- Reitz, Milford, Christy, "Foundation of electromagnetic theory"
- J.D.Jackson, "Classical Electrodynamics"
- M.H Nayfeh, M.K Brussel, "Electricity and magnetism"

P612 – Introduction to Condensed Matter

P612**Course: **PG-Core

**Approval: **

**Credit: **4

**Outcome: **

**Prerequisite: **

**Syllabus:**

- Hydrogen atom including 1.s coupling and hyperfine interaction.
- helium atom introduction to exchange and correlation; variational calculation of ground and exited-states.
- Introduction to the idea of effective potentials for electrons in many-electron atoms (Hartree theory and idea of self-consistency); use of Clementi-Roetti wave-function.
- One-electron atomic systems in an elecromagnetic field; dipole approximation and associated section rules; Stark and Zeeman effect (Note: Instructor will have to introduce the students to time-dependent perturbation theory here).
- Einisteins A and B coefficients, population inversion, laser action, derivation of A and B coefficient from-semi-classical treatment of light-atom interaction.
- Molecular formation: Discussion of atom-atom interaction, van der waals force, ionic interaction and covalent bold .
- Molecular structure: Hydrogen molecule MO and VB picture; importance of correlations.
- Molecular spectra (restricted to two atom molecules) electronic, rotational and vibrational.
- Some lectures left for interesting current topic.

Reference Book

- Elementary Atomic structure -G.K Woodgate
- Atomic Physics: C.J Foot
- Atoms, molecules and Photons: W. Demtroder
- The Theory of atomic Spectra: Condon and Shortley
- Topics in Atomic Physics: C.E Butkhardt and J.L Leventhal

P614-Statistical Mechanics

P614**Course: **PG-Core

**Approval: **

**Credit: **4

**Outcome: **

**Prerequisite: **

**Syllabus:**

- Review of thermodynamics, thermodynamic potentials, thermodynamic equilibrium and stability
- Gibbs distribution: Ensembles, classical and quantum free particles, systems with continuous and discrete spectrum, degenerate Fermi systems, Bose-Einstein condensation.
- Interacting system: Cluster an Virial expansions, radial distribution function.
- Introduction to response, fluctuation and noise, Einstein formula.
- Phase transition: phenomenology of first order and continuous phase transitions, order parameters, 1D Ising model, Iniversality and scaling, Ginzburg-Wilson theory, Spontaneous symmetry breaking.
- Fundamentals of statical mechanics: phase space, Liouville theorem, statistical distribution theorem.
- Probability theory: Probability densities, cumulants and correlations, central limit theorem, laws of large numbers.
- Brownian motion, Langevin equation, Markov process and Fokker Planck equation.

Reference Book

- Kerson Huang - Introduction to statical mechanics
- Reif - Statistical physics
- M. Kardar- Statistical physics of particles
- H.E Stanley - Introduction to phase transitions and critical phenomena

P615 – Quantum mechanics

P615**Course: **PG-Core

**Approval: **

**Credit: **4

**Outcome: **

**Prerequisite: **

**Syllabus:**

- HIlbert space (states, operators, evolution)
- One dimensional problems & Harmonic oscillator, delta & periodic pots
- Bound states vs scattering states
- The central force problem
- The hydrogen atom, hard and soft sphere
- Time-independent perturbation theory, WKB approximation, variational method
- Time-dependent perturbation theory, Heisenberg and interaction represtations
- Dirac equation
- Scattering theory/semi classical theory of radiation/identical particles/ angular momentum/ path integrals(depending of available time))

Reference Book

- R. Sankar-principles of Quantum Mechanics
- Cohen-Tannoudji, Diu and Laloe- Quantum Mechanics I & II
- J.J Sakurai-Modem Quantum mechanics
- David Griffiths-Intruduction to Quantum mechanics
- S.Gasiorowicz-Quantum Physics
- Eugen Merzbacher-Quantum mechanics
- Bransden and joachain-Quantum mechanics
- Richard Liboff-Introductory quantum mechanics