Advanced Statistical mechanics PHY613

Transcription

1 Advanced Statistical mechanics PHY613 Instructor: Amit Dutta Module 1: Critical Phenomena and Renormalization Group Lect. 30 hrs Basics of Phase transitions, mean field theory, concepts of scaling, application of real space and momentum space renormalization group techniques to magnetic and non-magnetic classical critical systems. Epsilon-expansion, large n methods and non-linear sigma models are to be used. Books: 1. Chaikin and Lubesnky 2. S. K. Ma: Critical Phenomena 3. Nigel Goldenfeld Module 2: Quantum Phenomena: Lect: 20 hrs Quantum phase transitions, Bose Einstein Condensation, An introduction to superfludity, Bogoliubov theory, coherent states, An introduction to superconductivity: BCS theory, Bogoliubov-Degennes theory, Quantum coherence: Flux and charge qubits. Books: 1. Annet: superconductivity superfluidity and condensates 2. Tinkham: Superconductivity Topic may be added/dropped/rearranged/reorganized based on the progress of the course and student feedback. Book for all the topics: Condensed Matter field theory: Altland and Simons Required: Phy412: Statistical Mechanics, PHY543 (Preferrably) Evaluation based on Examination and term paper presentation.

2 Indian Institute of Technology, Kanpur Department of Physics PHY 615: Non equilibrium Statistical Mechanics Part: I : Thermodynamics of irreversible processer near equilibrium Entropy production, coupled processes and energy transduction; endo- reversible Thermodynamics; Thermal and chemical engines with finite cycle time; modes of operation; efficiency at maximum power. Part II : Equations for describing time evolution of non- equilibrium systems: (1) Fokker- Planck equation: Diffusion equation, examples of solutions with different initial and boundary conditions, diffusion equation with drift; relation with Schrödinger equation and exact solutions in one dimension. (2) Master equation: Random walk and diffusion; relation between Liouville equation and master equation illustration with Kac ring model; relation with quantum master equation- Pauli equation (3) Langevin equation: theory of Brownian motion; derivation of generalized Langevin equation form Hamilton s equation. Part III: Time evolution form non equilibrium initial states to equilibrium final state: (1) Critical slowing down: illustration with interacting Ising model. (2) Kramers theory of the decay of metastable states- reaction rate theory; Application of WKB approximation. (3) Becker Doering theory: homogeneous nucleation in metastable state. (4) Domain growth and phase ordering form unstable initial states: dependence on symmetry and conservation; Allen- Cahn and Cahn- Hilliard laws; formation of ordered patterns. (5) RG for dynamic exponent & for domain growth. Part IV : Cyclic processes and non equilibrium steady- states far from equilibrium: Stochastic resonance and Brownian ratchet; beating second law with energy pumping. Interacting self driven particles: TASEP; boundary- induced phase transitions; application to intracellular molecular motor transport. Part V: Modern fluctuation theorems, foundations of statistical mechanics and applications: Taming Maxwell s DEMON!! Instructor : Prof. D. Chowdhury.

3 PHY681 (Quantum Field Theory) Instructor: Dipankar Chakrabarti. [ , 1st semester] It will be an introductory course on Quantum Field Theory(QFT). Students should have knowledge on quantum mechanics. The plan of the course is as outlined below: 1. Preliminaries of QFT. 2. Space-time in QFT, Lorentz invariance. 3. Action principle, Euler-Lagrange equations, Noether s theorem. 4. Canonical quantization of fields : (a) scalar fields: real and complex scalar fields (b) Dirac fields and (c) gauge fields 5. S-matrix, Wick s theorem. 6. Feynman diagram, Feynman rules. 7. Tree level calculations in QED. Books: 1. Quantum Field Theory- Peskin and Schroeder 2. Quantum Field Theory - Lahiri and Pal 3. Quantum Field Theory - Mandl and Shaw.

4 Course Title: Coherence and Quantum Entanglement Course Number: PHY690 G; Semester-I, Instructor: Anand Kumar Jha Office: Faculty Building 351 Lab: CL 104 D/E Ph: (+91) (Off); (+91) (Mobile) ; Course content: This course will have two main parts. The first part, which will cover about 1/3 rd of the course, will discuss the concept of coherence; the remaining part of the course will focus on Quantum Entanglement. (1) Coherence: Spectral properties of stationary random processes, Wiener-Khintchine theory, Angular spectrum representation of wavefields, Introduction to the second-order coherence theory, Propagation of coherence, The van Cittert-Zernike theorem, Coherent mode representation of sources and fields. (2) Quantum Entanglement: Basics of nonlinear optics, Two-photon field produced by parametric down-conversion, EPR paradox, Bell inequalities and its experimental violations, Quantum theory of higher-order correlations, Two-photon coherence and two-photon interference effects. Two-photon entanglement in the following variables: time-energy, position-momentum, and angle-orbital angular momentum; Introduction to Quantum Information: Quantum Cryptography, Quantum Dense Coding, Quantum Teleportation, Quantum Imaging. (3) Additional topics (may be covered during the course or given out as small projects): Photoelectric detection of light, The Hanbury Brown-Twiss experiment, Photon-bunching and antibunching, Photon Statistics, Squeezed states of light. Reference books: 1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge university press, New York, 1995). 2. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, New York, 2008). 3. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University Press, New York, USA, 2000). 4. M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University Press, Cambridge, 1999). 5. Feynman R, Leighton R, and Sands M. The Feynman Lectures on Physics, Volume III. Evaluation: 25% Homework; 30% Mid-term exam (or project); 45% Final exam (or project). Office Hours: There will be no office hours. You could see me in my office/lab with questions/concerns as and when I am available there. Alternatively, you could /phone me to setup a meeting time.

5 DEPARTMENTAL ELECTIVE PHY 690 M Advanced General Relativity and Black Holes Pre requisite: PHY 407 STR/GTR or equivalent. Course Contents: 1. Differential Geometry and Summary of Connection, Curvature, Killing vectors and Symmetries. Energy Momentum Tensor. 2. Geodesic Congruences, Energy conditions, Frobenius Theorem and Raychuadhuri Equation. 3. Hypersurfaces, Gauss-Stokes Theorem and Gauss-Codazzi Equations. Israel Junction Conditions. 4. Lagrangian Formulation of General Relativity. Action and Einstein Field Equation. 5. Schwarzschild Black Holes, Horizon, Singularity, Eddington Finkelstein Cordinates and Kruskal Diagrams, 6. Carter-Penrose Diagrams, de-sitter and Anti de Sitter ( AdS) space time. Einstein Static Universe. 7. Reissner Nordstrom Black Holes: Horizon, Singularity, Killing Vectors and Penrose Diagrams. 8. Kerr and Kerr -Newman Black Holes: Horizon, Singularity, Killing Vectors and Penrose Diagrams. 9. Elements of Black Hole Thermodynamics. ( If Time Permits)

6 Course Title: Principles of Lasers and Detectors Course Number: PHY690P/PSE 602 Units: Pre-requisite: None Level: PG Course Description: This course provides an introduction to the fundamental principles governing the operation and design of coherent light sources and detection tools. Course Topics: Introduction to light sources, Lasers, principle of lasing Optical cavities, longitudinal, transverse modes, Stability Interaction of radiation with matter, Spontaneous emission Absorption and stimulated emission, line broadening mechanisms Population inversion, absorption and gain coefficients Pumping schemes (Rate equation based Lasing model) Three- and four- level lasers CW and pulsed lasers, Q-switching and mode-locking Detection of optical radiation: photomultiplier tubes, semiconductor photodiodes, avalanche photodiodes, Single photon detectors,dark current, thermal noise, shot noise Measurement systems: Spectroscopy (Spectral and Temporal measurement systems), CCD, monochromater, pulse width measurement References: 1. Laser Physics, Peter W. Milonni and Joseph H. Eberly, Wiley, 2nd edition, Lasers, Anthony E. Siegman, University Science Books; 1st edition, Laser Electronics, Joseph T. Verdeyen, Prentice Hall; 3rd edition, Laser spectroscopy, W. Demtroder, 3rd edition, Lasers, Theory and Applications, K. Thyagarajan and A.K. Ghatak, Macmillan India Ltd., Principles of Lasers, O. Svelto and D. C. Hanna,5th edition, 2010

7 Introduction to High Performance Computing for scientists and engineers Course No: PHY 690X level (MODULAR course) About the course: This is an introductory course on parallel programming on scientific applications that will enable the students to write and analyse parallel programs. The focus would be on general parallel programming tools, specially MPI and OpenMP programming. These tools would useful to all students irrespective of their branch. We expect the specific departments or group of departments to teach more advanced courses like Parallel Computational Fluid Dynamics, Parallel Molecular Dynamics, etc. The proposed course would enable the students to take advanced courses on parallel computing. Departments from which students can take course for credit: Physics, Chemistry, Biological Science and BioEngineering, Aerospace engineering, Mechanical Engineering, Chemical Engineering, Computer Science and Engineering Units: [Modular course, 3 lectures, 5 credits] Prerequisite: Basic knowledge in computer programming Instructor: Mahendra Verma (PHY) Who can take the course: Ph. D., M. Sc., and Advanced UG students. Course Contents: 1. Introduction to HPC and scientific computing. Overview of major applications [1 lecture] 2. Supercomputing architecture; multicores; shared memory; switch etc. [3 lectures] 3. Review of basics of C/Fortran programming [3 lectures] 4. Programming in Message Passing Interface (MPI) [8 lectures] 5. Programming in OpenMP [3 lectures] 6. Case study on one major application [2 lectures] Textbooks and References: 1. P. S. Pacheco, An Introduction to Parallel Programming, Elsevier (2011) 2. M. Quinn, Parallel Programming in C and OpenMP, McCraw Hill Education (India) (2003) 3. A. Grama, A. Gupta, G. Karypis, and V. Kumar, Introduction to Parallel Computing, Pearson (2007)