HRI conducts an M.Sc. and a Ph.D. program in physics. The M.Sc. program is open to students with a bachelors degree in science or engineering, while the Ph.D. program is open to students with an M.Sc. degree in physics. Duration of the M.Sc. program is two years. The Ph.D. program consists of course work and projects for the first three semesters, followed by research work leading to a Ph.D. degree.

For information about admissions to these programs in physics at HRI, click here.

The M.Sc. program consists of four semesters of course work. The course work for the Ph.D. program lasts for three semesters. Each semester is roughly of four months duration. The students are taught basic as well as advanced courses in physics and they also get to work on projects. Follow the links below for the course schedule and syllabus.

The students enrolled for the Ph.D. program are expected to start working on their thesis soon after the completion of their course work and projects. Follow the links below for the various aspects related to thesis work.

The courses that are to be taken by M.Sc. and Ph.D. students are listed below semester-wise.

- Advanced Statistical Mechanics
- Mathematical Methods II
- Quantum Field Theory I
- Research Methodology and Numerical Methods
- Elective I

Elective I is to be chosen between Quantum Mechanics III and General Theory of Relativity

Elective II and III are to be chosen between Astrophysics, Condensed Matter Physics II, Particle Physics, Quantum Field Theory II and Quantum Information and Computation.

- Classical Mechanics
- Mathematical Methods I
- Quantum Mechanics I
- Research Methodology and Numerical Methods
- Laboratory I

- Classical Electrodynamics
- Electronics
- Quantum Mechanics II
- Statistical Mechanics
- Laboratory II
- Project

- Condensed Matter Physics I
- Mathematical Methods II
- Quantum Field Theory I
- Quantum Mechanics III
- Elective I

Elective I is to be chosen between Advanced Statistical Mechanics, Fluid Dynamics, General Theory of Relativity, Nonlinear Dynamics and Quantum Information and Computation I.

Elective II and II are to be chosen between Astrophysics, Condensed Matter Physics II, Cosmology, Introduction to Electronic Structure, Quantum Field Theory II, Quantum Information and Computation II, Quantum Optics, Soft Matter and Ultra cold Atoms.

A brief outline of the syllabus of the various courses is given below. The courses are listed in alphabetical order.

- Background: order parameters, mean field theory, phase transitions, Landau-Ginzburg theory, estimating fluctuations. The scaling hypothesis.
- Renormalisation group in classical systems: Hubbard-Stratonovich transformation, gaussian functional integrals, rederiving mean field theory, self-consistent field approximation. Real space RG: Kadanoff construction, application to the Ising model. Momentum shell RG: diagrammatic perturbation theory - first and second order, epsilon expansion, fixed points. Two dimensional solids, XY model.
- Renormalisation group in quantum systems: path integrals for fermions. One dimension: quartic perturbations, RG at tree level, RG at one loop. RG in higher dimensions: the one loop beta function, fixed points, Kohn-Luttinger effect. 1/N expansion and Fermi liquid theory.
- Equilibrium dynamics: conserved and broken symmetry variables, spin systems, hydrodynamics of simple fluids, dynamic critical phenomena.
- Non equilibrium phenomena: Boltzmann equation, Langevin and Fokker-Planck descriptions.
- Stochastic thermodynamics: non-equilibrium work theorems (Jarzynski, Crooks..), non- equilibrium steady states, stochastic heat engines, examples from colloidal particles, molecular motors.

- Introduction to celestial objects, coordinates and the concept of time. Radiation transfer. Equations of radiation transfer, Black-body/thermal radiation, Opacity and optical depth, solutions of the radiation transfer equations in limiting cases, Rosseland mean opacity.
- Thermal Bremsstrahlung emission, synchrotron emission. Self absorption and the emergent spectrum. Thomson scattering. Compton and Inverse-Compton scattering. Scattering in a region with magnetic field, Faraday rotation Introduction to fluid dynamics. Convection instability and transfer of energy from cores of stars. Supersonic motion, shocks.
- Introduction to Magneto-hydro dynamics, flux freezing, Generation and amplification of magnetic fields in astrophysical situations.
- Stellar structure. Mass-radius relation for main sequence stars, Minimum and maximum mass for nucleosynthesis, Hertzsprung-Russell diagram, Evolution of a star on the HR diagram. Novae and Supernovae, End points of stellar evolution. Interstellar medium. Phases of interstellar medium. Thermal, photoionisation, chemical and pressure equilibrium, Star formation, feedback and the evolution of ISM.
- Orbits around massive bodies, Tidal disruption, restricted 3 body problem, Roche limit. Orbits in external potentials, potential-density pairs. An overview of models for galaxies. Accretion of matter on to a point mass, spherical accretion, Eddington limit.
- Introduction to Cosmology, Friedmann models, equations. Hubble's law. A brief overview of the thermal history of the universe.

- Special theory of relativity and electrodynamics: Lorentz transformation of electromagnetic fields, Lorentz covariant formulation of electrodynamics; gauge invariance, Maxwell equations from action principle.
- The electrostatic limit of Maxwell equations, multipole expansion, uniqueness, boundary value problems, solution of Poisson equation.
- The magnetostatic limit of Maxwell equations, applications.
- Electrodynamics: motion of charges in external fields; electromagnetic waves in vacua and propagation through continuous media; energy-momentum of electromagnetic field and Poynting theorem.
- Advanced and retarded Green functions; Lienard-Wiechert potentials; dipole radiation and Larmor's formula; spectral resolution and angular distribution of radiation from a relativistic point charge; synchrotron radiation; Rayleigh and Thomson scattering; collision problems; Bremsstrahlung and Cerenkov radiation.
- Scattering of electromagnetic waves: Rayleigh and Thomson scattering, radiation damping.

- A rapid review/summary of Newtonian mechanics
- Calculus of variations: Concept of variation - Euler equation - Applications - Variation subject to constraints and Lagrange multipliers.
- The Lagrangian formulation: Generalised coordinates and velocities - The principle of least action and the Lagrange equations of motion - Extension to constrained systems.
- Conservation laws: Symmetries and Noether's theorem.
- Integration of the Lagrange equations of motion: Motion in one dimension - The two body problem, reduced mass and the equivalent one-dimensional problem - Motion in a central field - Kepler's problem - Scattering.
- Small oscillations: Free, damped and forced oscillations in one dimension - Resonance - Damped and forced oscillations - Parametric resonance.
- Rigid body motion: Angular velocity - The inertia tensor and angular momentum of a rigid body - The equations of motion- Eulerian angles - Motion of tops - Motion in a rotating frame - Coriolis force.
- The Hamiltonian formulation: Hamiltonian and Hamilton equations - Poisson brackets - Dynamics in the phase space - Hamilton-Jacobi equation - Separation of variables and solutions - Action-angle variables - Adiabatic invariants.
- Elements of non-linear dynamics: Differential equations as dynamical systems - Lyapunov exponents.

- The building blocks - atoms to solids: atomic physics, Coulomb effects, crystal fields in solids, local moments and band electrons, lattice vibrations, electron-lattice coupling, electron-electron interactions.
- Structure: characterising structures - crystalline/amorphous/liquids, classification of periodic structures, reciprocal space, x-ray and neutron diffraction.
- Electronic structure: free electrons - spectrum, density of states, thermodynamics, band electrons - nearly free electron and tight binding limits, consequences for thermodynamics and transport.
- Physics of metals: specific heat, susceptibility, impurity scattering, basic transport theory. Response to magnetic fields: Landau quantization, quantum Hall effect.
- Phonons: Debye and Einstein model, spectrum of a real lattice, thermodynamics of phonons, anharmonic effects, Debye-Waller factor.
- Magnetism: spin paramagnetism, itinerant-vs-localised electrons, Stoner and Heisenberg models, mean-field theory, spin waves.
- Superconductivity: phenomenology, pairing interaction, BCS theory, Ginzburg-Landau theory and type II superconductors.

The course will consist of any two of A-D.

- Foundation: Low dimensional systems: Quantum Wells, Wires and Quantum Dots, one and two dimensional heterostructures, coupled wells and super- lattices. Density of states in low dimensional systems
- Charge Transport: Transmission and its relation to conductance, Landauer theory of coherent charge transport - phenomenology as well scattering theory. Transmission function and its relation to S matrix and Greens function. Non-equilibrium Greens function and its relation to Landauer-Buttiker theory. Noise in Charge transport: Thermal and Shot Noise in Mesoscopic conductors. Scattering theory of Shot noise and its application.
- Spintronics: 1: Introduction to spintronics.(Datta-Das spin transistor) 2: Spin currents: Equilibrium and non-equilibrium spin currents and their measurement and its relation to spin-Hall effect, generalized Landauer-Buttiker theory for coupled charge and spin transport. 3: Tunnel Magneto-resistance and spin currents 4: Spin Shot Noise, Entanglement generation and its detection.

- Physics at low dimensions: surface physics--surface states, reconstructions, adsorption on surfaces; atomic wires and clusters
- Electron-electron interactions: Hartree-Fock approximation, the electron gas; Density functional theory.
- Anharmonic effects in crystals: Thermal expansion, lattice thermal conductivity, Umklapp precesses.
- Phonons in Metals: Kohn anomaly, dielectric constant, temperature dependence of electrical resistivity.
- Dielectric properties of insulators: plasmons, magnons etc.

- Quantum Hall effect
- Quantum dots and quantum wires, Kondo effect
- Fermi liquid theory and Non-Fermi liquids
- Bosonisation and Luttinger liquids
- Quantum spin systems

- Mott physics: electron localisation, magnetic order, doped phase, physics in the cuprates.
- Kondo systems: physics of the single impurity, dense systems
- Kondo and Anderson lattice, heavy fermions, quantum criticality.
- Metallic magnets: ferromagnetism in strongly repulsive systems, the transition metals, spin-fermion systems, the double exchange model, the classical Kondo lattice.
- Electron-phonon coupling: the classical theory, polaron formation, many electron systems, polaron ordering, physics in the manganites.
- Superconductivity: the BCS-BEC crossover, superconductivity in repulsive systems, competition with magnetism, effect of disorder.

- Friedman-Robertson-Walker metric, Friedman equation and stress tensor conservation, equation of state: matter, radiation, cosmological constant, experimental evidence for dark matter and dark energy.
- Age of the universe, cosmological horizon, expansion rate.
- Thermal history of the universe, formation of hydrogen and origin of CMBR, decoupling of neutrinos, nucleosynthesis, recombination
- The horizon problem, possible resolution via inflation, slow roll condition and slow roll parameters, reheating, inflationary origin of density perturbation
- Early history, electroweak baryogenesis via leptogenesis, dark matter.
- Theory of cosmological perturbations: gauge invariant scalar and tensor perturbations, spectral index, ratio of tensor to scalar fluctuation and Lyth bound, transition from quantum to classical perturbation: horizon exit and reentry, from density fluctuation to CMB fluctuations via Boltzmann transport equation, origin of the acoustic peak, origin of CMB polarisation, E and B modes.

- Circuit theory: lumped circuit approximation, circuit elements, Kirchoff's current and voltage laws, resistive networks, node and loop analysis, Thevenin and Norton's theorem, time domain response of RL, RC and RLC circuits, frequency domain response, impedance, filters and transfer function.
- Analog electronics: discrete devices, characteristics and operation - diode, Zener diode, LED, photodiode. Simple diode circuits. Bipolar junction transistor (BJT): biasing, h parameters, small and large signal response, amplifiers. Field effect transistors. Operational amplifiers - device properties, integrator, differentiator, RC active filter, negative and positive feedback, oscillators.
- Digital electronics: logic gates, truth table, multiplexer, combinatorial circuits, flip-flop, counters, programmable logic devices, microprocessors.

- Ideal Fluids: Euler equation, hydrostatics, Bernoulli equation, conservation laws, incompressible fluids, waves, irrotational flows, inviscid fluids and vorticity.
- Viscous Fluids: Viscosity, Navier-Stokes equation, Reynolds number, laminar flow, exact solution to the eq. of motion.
- Turbulence: Stability of flows, instabilities, quasi-periodic flows, Strange attractors, turbulent flows, jets, free shear layers, wakes, boundary layers.
- Thermal Conduction in fluids: eq. of heat transfer, conduction in incompressible fluid, law of heat transfer, convection, convective instability in static fluid.
- Compressible flows
- Relativistic Fluid dynamics: eq. of motion, energy-momentum tensor, eq. for flow with viscosity and thermal conduction.

- Review of Lorentz transformations and special theory of relativity.
- Tensors and their transformation laws; Christoffel symbol and Riemann tensor; geodesics; parallel transport along open lines and closed curves; general properties of the Riemann tensor.
- Equivalence principle and its applications: gravity as a curvature of space-time; geodesics as trajectories under the influence of gravitational field; generalisation to massless particles; gravitational red-shift; motion of a charged particle in curved space-time in the presence of an electric field; Maxwells equation in curved space- time.
- Einsteins equation, Lagrangian formulation, Einstein-Hilbert action.
- Schwarzschild solution: construction of the metric and its symmetries; motion of a particle in the Schwarzschild metric; Schwarzschild black hole; white holes and Kruskal extension Schwarzschild solution: construction of the metric and its symmetries; Motion of a particle in the Schwarzschild metric; precession of the perihelion; bending of light; horizon, its properties and significance.
- Precession of the perihelion; bending of light; radar echo delay.
- Initial value problem; extrinsic curvature; Gauss-Codacci equations.
- Linearised theory, gravitational waves, field far from a source, energy in gravitational waves, quadrupole formula.
- Elementary cosmology: principles of homogeneity and isotropy; Friedman-Robertson- Walker metric; open, closed and flat universes; Friedman equation and stress tensor conservation, equation of state, big bang hypothesis and its successes.

- Review of QM: variational method, identical particles, many fermion wave functions.
- First-principles Hamiltonian and Born-Oppenheimer approximation.
- Treating electron-electron interactions: Hartree-Fock approximation, exchange energy, correlation energy.
- Density functional theory: Thomas-Fermi method, Hohenberg-Kohn theorems, Levy constrained search formulation, Kohn-Sham formulation, exchange-correlation energy, LDA and GGA functionals, spin density functional theory.
- Solution of the Kohn-Sham equations, basis sets - LCAO: STO-NG, 4-31G, 6-31G etc, quality of basis sets, polarisation functions, spin-restricted calculations, Roothan equations. Spin unrestricted calculations. Plane wave basis set.
- Pseudopotentials and PAW in conjunction with plane waves.
- Structure optimisation, Hellman-Feynman theorem.
- Simple practical applications: band structure of standard solids, metals and semiconductors, optimisation of lattice constants, cohesive energies and other simple properties.
- Possible advanced topics: hybrid functionals, van der Waals interactions, density functional perturbation theory, phonon band structure, electron-phonon coupling. CI,CCSD methods, QMC.

- Forced Oscillations-Pohl's Pendulum
- Coupled Pendula and Chaotic oscillator
- Photoelectric effect
- Normal and Anomalous Zeeman Effect
- Michelson Interferometer
- Mach-Zehnder Interferometer
- Faraday Effect
- Millikan Oil-drop Experiment
- Electron Diffraction
- Fine Structure

- Coupled Oscillator Circuits
- Thermal Equation of State and Critical point.
- Lock-in Amplifier and Signal Processing.
- OpAmps I: Amplifiers and Negative Feedback
- OpAmps II: Limitations and Applications
- Diodes: Clamps, Rectifiers, Power supplies
- Transistors I: Switch, Common Emitter Amplifier, Push-pull Follower
- Transistors II: Characteristics, Comparators, MoSFET, CMoS Inverter
- Logic Gates: NAND gate, OR, AND, NOT; Adder, Oscillator
- Flip-flops: as Memory element, Shift Register, Counters
- Microcontroller I: Programming to MCU, using the port for input
- Microcontroller II: Some Applications, Seven Segment Display

- Ferro to Para Electric Phase Transition(or its Magnetic analogue)
- Raman Spectroscopy
- ESR
- Earth's field NMR gradient
- Bragg Diffraction by Microwaves
- Hall Effect
- G-M counter, Counting Statistics, Gamma ray absorption cross section
- Gamma ray Spectroscopy
- STM with Graphene, HOPG, Gold, Semiconductors and CDW
- Measurement of Speed of Light

- Vector Analysis: operations with vectors, scalar and vector fields, gradient, curl and divergence. Line, surface, and volume integrals, Curvilinear coordinate systems, Elements of tensors.
- Vector Spaces, linear transformations, scalar product and dual space, bases, linear operators, eigenvalues and eigenfunctions, unitary and hermitian operators.
- Complex Analysis: functions of a complex variable, analytic functions, integral calculus, contour integrals, Taylor and Laurent series, singularities, residues, principal values, Riemann surfaces, conformal mapping, analytic continuation.
- Ordinary differential equations: linear ODEs, Green functions, second order differential equations: classification of singularities and local solutions, special functions.
- Elements of statistics: probability, random walk. Probability distributions.

- Integral transforms, Fourier transforms, inversion and convolution, Laplace transforms.
- Advanced topics in ODE, Partial differential equations: classification of second order PDEs, Laplace and Poisson equations, applications to electrostatics, Heat equation, Wave equation.
- Group theory, definitions and examples of groups. Homomorphism, isomorphism and automorphism, Permutation groups.
- Group representation: reducibility, equivalence, Schur's lemma. Lie groups and Lie algebras, SU(2) and SU(3). Representations of simple Lie algebras, SO(n), Lorentz group. Symmetries in physical systems, Young Tableau.

- Long time behaviour of the solutions of a system of ordinary nonlinear differential equations, fixed points and their classification according to stability.
- Periodic orbit for conservative systems, periodic orbits for dissipative systems ( limit cycles ) and their stability, Bifurcations and centre manifolds
- Different kinds of perturbation theory for calculating periodic orbits, Renormalisation group aided perturbation theory, Poincare Bendixon theorem, chaos and strange attractors.
- Maps, fixed points, cycles and stability, bifurcations, period doubling, intermittency and quasi periodicity, universal behavior at the onset of chaos, renormalization group and scaling behaviour.
- Partial differential equations, patterns, Galerkin truncations and reduction to dynamical systems.

- Experimental methods: fixed target and collider experiments, particle detectors.
- Role of symmetries: charge conjugation, parity, time reversal, isospin and SU(2), quark model and SU(3).
- Introduction to relativistic kinematics: Mandelstam variables, phase space, calculation of cross-sections and decay widths.
- Basics of quantum electrodynamics: electron-positron annihilation, electron-muon scattering, Bhabha scattering, Compton scattering.
- Deep inelastic scattering: Bjorken scaling, parton model, scaling violation, introduction to quantum chromodynamics and tree level processes.
- Introduction to weak interactions: parity violation, V-A theory, pion and muon decay, neutrino scattering.
- Standard Model: Glashow-Salam-Weinberg model, neutral current, physics of W, Z and Higgs, CKM mixing and CP violation.
- Neutrino physics, neutrino oscillation.

All regular as well as the integrated Ph.D. students are expected to do two projects with the faculty members. The students are advised to choose projects so that, at least one of them will eventually lead to the topic of their thesis.

- Non-relativistic quantum field theory: quantum mechanics of many particle systems; second quantisation; Schrodinger equation as a classical field equation and its quantisation; inclusion of inter-particle interactions in the first and second quantised formalism
- Irreducible representations of the Lorentz group, connection to quantum fields.
- Symmetries and conservation laws: examples in non-relativistic and relativistic field theories; translation, rotation, Lorentz boost/Galilean transformation and internal symmetry transformations; associated conserved charges.
- Free Klein-Gordon equation: classical action and its quantisation; spectrum; Feynman rules for computing n-point Green functions of elementary and composite operators.
- Interacting Klein-Gordon field; Feynman rules for computing Green functions; physical mass of the particle from the analysis of two point Green functions; S-matrix and its computation from n-point Green functions; relating S-matrix to cross-section.
- Quantisation of free Dirac fields: spectrum; Feynman rules.
- Quantisation of free electromagnetic field: role of gauge invariance; gauge fixing; physical state condition; spectrum; Feynman rules.
- Quantum electrodynamics: coupling Dirac field to electromagnetic field; gauge invariance; quantisation; Feynman rules for computing Green functions; Spectrum and S-matrix from the Green functions.

- Path integrals for scalar and fermionic fields: generating functional, Feynman rules, loop diagrams.
- Renormalisation of scalar and Yukawa theories: power counting, regularisation, renormalisable and non-renormalisable theories, Green functions at 1 loop of some prototypical theories, basics of renormalisation group (running coupling), 1PI effective actions.
- Spontaneous symmetry breaking and Goldstone's theorem.
- Path integrals for the Maxwell field, gauge fixing.
- Renormalisation of QED: 1 loop diagrams, Landau pole.
- Non-abelian Gauge Theories: Classical theory of non-abelian gauge theories, Quantization of non-abelian gauge theories by path integral methods, Non-abelian gauge theories at one loop and asymptotic freedom, Spontaneous symmetry breaking in non-abelian gauge theories.

- Quantum formalism: states, evolution, measurements.
- Multipartite quantum systems: description and manipulation of bipartite systems and beyond.
- Entanglement: quantification and detection in bipartite and multipartite systems
- Quantum communication: no-cloning theorem, quantum teleportation, quantum dense coding, multipartite communication protocols.
- Quantum cryptography: essential classical cryptography, BB84, B92, Ekert, and secret sharing protocols.
- Quantum computation: quantum algorithms, universal gates.
- Interface of quantum information with other sciences.
- Experimental realisations

- General evolution and Decoherence theory.
- Master equations (Markovian and Non-Markovian, Various measure of nonmarkovianity).
- Advanced entanglement theory (GM, GGM, newly proposed measures etc)
- Quantum Correlation Beyond Entanglement (Quantum Discord, Geometric discord, Work-Deficit etc)
- Resource theory in QI (Entanglement, Quantum Coherence, Reference Frame, Asymmetry etc).
- Quantum Thermodynamics.
- Advanced topics in quantum channels.
- Quantum information and condensed matter systems.

- Basic notions: states, operators, time evolution.
- One-dimensional problems: harmonic oscillator, periodic potential, Kronig-Penny model; Three-dimensional problems: central force potential, the hydrogen atom.
- Charged particle in an electromagnetic field: gauge invariance, Landau levels.
- Symmetries and conservation laws in QM: Degeneracies, Discrete symmetries.
- Angular momentum in quantum mechanics: raising and lowering operators, angular momentum addition, Clebsch-Gordon coefficients; Tensor operators and Wigner-Eckart theorem.
- Time-independent perturbation theory: non-degenerate and degenerate cases, Stark and Zeeman effects.
- Semiclassical (WKB) approximation and variational methods

- Scattering theory and applications.
- Schrodinger and Heisenberg pictures; postulates of quantisation.
- Time dependent perturbation theory, Interaction picture, Fermi golden rule
- Path integrals: propagators, amplitudes as path integrals, Semiclassical methods revisited.
- Quantum mechanics of many particles, identical particles and symmetries of the wave- function, scattering of identical particles.
- Relativistic quantum mechanics, Klein-Gordon and Dirac equations and their solutions, gyromagnetic ratio of the electron, relativistic corrections to the Schrodinger equation.
- Entangled states and Bell inequalities.

- Atomic physics: One electron atoms - spin-orbit interaction, fine structure, Lamb shift, Zeeman effect, Stark effect. Two electron atoms: spin wave functions, approximate handling of electron-electron repulsion. Coupling of angular momenta, multipletstructure, gyromagnetic effects. Hyperfine and nuclear quadrupole interactions. Many electron atoms: central field approximation, Thomas-Fermi and Hartree-Fock methods.
- Molecular physics: Born-Oppenheimer approximation, molecular structure, rotation and vibration of diatomic molecules, hydrogen molecular ion, vibrational-rotational coupling, effect of vibration and rotation on molecular spectra. Electronic structure- molecular orbital and valence bond theories.
- Atoms and light: transition rates, dipole approximation, Einstein coefficients, radiative damping, optical absorption, ac Stark effect.
- Cold atoms: Doppler cooling, magneto-optical trap, ion traps, dipole force, evaporative cooling, optical lattice. Collective effects - Feshbach tuning of interactions, Bose condensation of alkali atoms, BCS-BEC crossover, the unitary Fermi gas. Imaging cold atoms.
- Computing with atoms: qubits and their properties, entanglement, quantum logic gates, decoherence and error correction.

- Introduction: Quantization of the electromagnetic field, Fock states, coherent states, squeezed states, basic atom-photon interaction, density-matrix formalism.
- Theory of coherence; Semiclassical theory of atom-photon interaction.
- Quantum theory of atom-photon interaction.
- Quantum theory of dissipation.
- Quantum information in continuous variable systems; Quantum state engineering.
- Quantum operations based on beam splitters, mirrors, squeezing and homodyne and heterodyne measurements and nonlinear operations such as parametric down converters.
- Photon addition and subtraction operations; Elements of cavity QED.

- Research Methodology including quantitative methods, communication skills, seminar presentation and review of research papers.
- Introduction to programming languages: F77, F90 or C.
- Errors in numerical calculations.
- Numerical linear algebra, eigenvalue and eigenvectors.
- Interpolation techniques.
- Generation and use of random numbers.
- Sorting and searching.
- Differentiation and Integration (including Monte Carlo techniques)
- Root finding algorithms
- Optimisation, extrema of many variable functions.
- ODEs and PDEs: including FFT and finite difference methods, integral equations.

- Forces, energies and timescales in soft matter, van der Waals force, hydrophobic and hydrophilic interactions. Basic phenomenology of liquid crystals, polymers, membranes, colloidal systems. Phase behaviour, diffusion and flow, viscoelasticity.
- Order parameter, phase transitions: mean-field theory and phase diagrams, elasticity, stability, metastability, interfaces.
- Colloidal systems: Poisson-Boltzmann theory, DLVO theory, sheared colloids, stability of colloidal systems, measurement of interaction.
- Polymers: model systems, chain statistics, polymers in solutions and in melts, flexibility and semi-flexibility, distribution functions, self-avoidance, rubber elasticity, viscoelasticity, reptation ideas.
- Membranes: fluid vs. solid membranes, energy and elasticity, surface tension, curvature, de Gennes-Taupin length, brief introduction to shape transitions.
- Experimental tools and numerical approaches: Stokes limit, Rouse and Zimm Model for polymers, membranes, relaxation, computational studies, multiscale modelling.

- Basics: phase space, distributions, notion of equilibrium, ensembles, Boltzmann distribution, partition function, calculating observables.
- Non interacting classical systems: few level systems, ideal gases, oscillators.
- Non interacting quantum systems: method of second quantisation, electrons in metals, relativistic electron systems, electrons in a strong magnetic field, lattice vibrations and phonon physics, photons, blackbody radiation, Bose condensation.
- Interacting classical systems: non-ideal gases, van der Waals gas, cluster expansion, classical spin models - Ising and Heisenberg, outline of exact solutions.
- Phase transitions: symmetry breaking and long range order, mean field approach, Landau theory, 2nd and 1st order transitions, Landau-Ginzburg functional, illustrative examples, estimate of fluctuations.

- Spatial, time, and energy scales in cold atom physics.
- Experimental background: trapping and cooling, Feshbach resonance, optical lattices, cold atom spectroscopies.
- Basic theory: many particle physics, mean field theory, phase transitions, perturbation theory.
- Continuum bosons: bosons in free space, weak interactions, Bogoliubov theory, BEC in trapped systems, Gross-Pitaevski equation.
- Continuum fermions: fermions in free space, trapped fermions, Fermi liquid theory, weak attraction - BCS instability, strong attraction - BEC of pairs, the unitary Fermi gas, Stoner instability.
- Optical lattices: Hubbard model - Bose/Fermi cases, superfluid-Mott transition for repulsive bosons, BCS-BEC crossover for attractive fermions, Mott transition in repulsive fermions.
- Spin systems: quantum, S = 1/2, magnetism on unfrustrated and frustrated lattices.
- Entanglement in many body systems: pure states, mixed states, area laws, tensor network states.
- Special topics: population imbalance, Anderson localisation, gauge fields, quench dynamics.

The grading of the courses will be based on continuous assessment, a mid-semester and an end-of-semester exam.

- A student getting less than 50% fails the course, and would have to repeat the course and pass on the second attempt.
- To continue through the course work, a student should not fail in two or more courses at any given time.
- A student completing the course and the project requirements satisfactorily is said to clear the course work successfully.

Ph.D. students who are very confident of their mastery of the course material can ask the course instructor to give them a test at the start of the course. If they pass this test, they can be exempt from attending the course, further examinations, etc.. The request for an exemption test is not automatically granted, it depends on prior impression about the ability of the student and interaction between the student and course instructor. Even if an instructor does not allow test based exemption in a particular case, the instructor may allow the student to be absent from the regular lectures, but submit all assignments/projects, and take all the tests.

There are no course exemptions for M.Sc. students.

At HRI, research in physics is conducted in the following five areas:

- Astrophysics
- Condensed Matter Physics
- High Energy Phenomenology
- String Theory
- Quantum Information and Computation

For further details about the research carried out in physics at HRI, click here.

Ph.D. students are expected to choose their advisor by/before the end of their course work. For a student to officially enrol with a faculty member, the student has to have met the passing requirements of the course work and cleared the Oral General Comprehensive Exam (OGCE).

Students pursuing Ph.D. have to give a seminar before July 31 every year until they have submitted their thesis.

All students are expected to submit their thesis within five years of joining HRI.

Harish-Chandra Research
Institute

Chhatnag Road, Jhusi

Allahabad 211 019,
India

Phone: +91 (532) 2667 510,
2667 511, 2668 311, 2668 313, 2668 314

Fax: +91 (532) 2567 748,
2567 444

Physics Graduate Programme <physgradp at hri dot res dot in>

Updated: September 03, 2016 T22:25:33Z