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Statistical Physics of Non-Interacting and Interacting Systems

By Prof. Saurabh Basu   |   IIT Guwahati
Learners enrolled: 468   |  Exam registration: 24
ABOUT THE COURSE:
The course introduces the reason to study statistical mechanics when thermodynamics yields an equilibrium description of the systems. The basic concepts of the subject are explained from a formal viewpoint that deals with the concept of ensembles and ergodic hypothesis. Quantum statistical mechanics appears as an upgradation of the classical ideas that incorporates the indistinguishability of the particles, and thus is applicable to the ‘microscopic world’ of bosons and fermions. Several examples are discussed in this context, such as Bose-Einstein condensation, magnetism of fermionic systems. Besides, there are special topics, such as, Chandrasekhar limit, thermodynamics of black holes etc Further, as interacting systems are ubiquitous in nature, and hence require an introduction to the masters and the PhD students. Different examples of interacting systems are discussed through Ising model, Heisenberg model etc and specialized techniques such as Bethe ansatz are discussed.

INTENDED AUDIENCE: Senior undergraduate, Masters’ students, PhD students, researchers of condensed matter physics, teachers in colleges and universities.

PREREQUISITES: Preferably Quantum Mechanics and Classical Mechanics at the introductory level

INDUSTRY SUPPORT: Data analysis for complex systems
Summary
Course Status : Completed
Course Type : Elective
Language for course content : English
Duration : 12 weeks
Category :
  • Physics
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 22 Jul 2024
End Date : 11 Oct 2024
Enrollment Ends : 05 Aug 2024
Exam Registration Ends : 16 Aug 2024
Exam Date : 03 Nov 2024 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.


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Course layout

Week 1:  Introduction, Why study Statistical Physics, Review of Thermodynamics, Entropy, Gibb’s paradox, concept of Temperature, Free energies and their interrelationships, Legendre transformation, Maxwell’s relations, Micro and Macrostates, Examples.

Week 2: Ensembles, Different Ensembles: Microcanonical, Canonical and Grand Canonical Ensembles, concept of Phase Space, Phase Space density, Liouville’s Theorem, Lagrange’s undetermined multipliers, Partition Function.

Week 3: Application of ensemble theory to classical ideal gas, non-interacting spins in a magnetic field, Magnetization, Curie’s law, Classical Harmonic Oscillators, Specific Heat, concept of Negative Temperature, Realization of negative temperature in lab, Cold atomic systems.

Week 4: Quantum Statistics: Distribution functions for indistinguishable particles, occupation numbers, Quantum Ideal Gases, Ideal Bose and Fermi systems, resolution of Gibb’s paradox.

Week 5: Ideal Bose Gas, Bose-Einstein Condensation (BEC), properties of an ideal Bose gas, Black Body Radiation, Specific heat of solids, Einstein’s and Debye’s theories.

Week 6: Ultracold atomic systems, Recent experiments on achieving negative temperature in labs, liquid Helium, Superfluidity

Week 7: Non-interacting Fermions, Pauli Exclusion Principle, Slater determinants, Free Fermi Gas, Fermi surface and Fermi temperature of Metals, Shubnikov de Haas and de Haas van Alphen (dHvA) oscillations

Week 8: Electronic Specific heat, Magnetic Properties of Solids, Pauli paramagnetism, Semiconductors, Law of mass action.

Week 9: Special topics: White dwarfs, Chandrasekhar limit, classical and quantum black hole thermodynamics, Temperature and surface gravity.

Week 10: Interacting Systems, Formalism, Virial equation of state, Virial coefficients, different kinds of interparticle interactions, introduction to linked cluster expansions.

Week 11: Ising model in one dimension, Exact solutions, Transfer matrix, Mean field theory, Bragg-William’s approximation

Week 12: Renormalization Group, Phase transitions, fixed points, Two-dimensional Ising Model, Bethe Anstaz.

Books and references

  1. Statistical Mechanics, by R.K. Pathria
  2. Statistical Mechanics, by D. A. Mcquarrie
  3. Introduction to Physics, by S. Salinas
  4. Statistical Mechanics, by K. Huang
  5. Introduction to Modern Statistical Mechanics, by D. Chandler
  6. Equilibrium Statistical Mechanics, by M. Plischke and B. Bergersen

Instructor bio

Prof. Saurabh Basu

IIT Guwahati
Prof. Saurabh Basu is currently a professor at the Department of Physics, Indian Institute of Technology Guwahati. Saurabh does research in theoretical Condensed Matter Physics with a focus on graphene, Quantum Hall effect, topological insulators and ultracold atoms. The current projects include Edge states in adatom decorated graphene and other two dimensional Dirac materials, transmission through spin-orbit coupled Nano-junctions, phase diagram and tunneling dynamics of bosons in optical lattices, non-Hermitian systems, higher order topology, skyrmions etc. He has offered several courses in MOOCS, such as, Advanced Condensed Matter Physics, Advanced Quantum Mechanics with Applications, A brief course on Superconductivity, Numerical Methods and Simulation Technique in Science and Engineering, Quantum Hall effect etc. which have received tremendous attention from the students, teachers and researchers.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 
03 November 2024 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Guwahati .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team


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