## Course Detail

 Course Name Statistical Mechanics Course Code 22PHY505 Semester 7 Credits 4

### Syllabus

##### Unit 1

Learning objective
Review of Thermodynamic potentials
Introduce various probability distribution functions and their property

Thermodynamics Review: Review of thermodynamic variables and thermodynamic potentials. Review of probability functions- random walk problem.

##### Unit 2

Learning objective

Canonical ensemble and definition of inverse temperature
Introduce partition function and its computation

Canonical Ensemble: Micro canonical ensemble – phase space – trajectories and density of states – Liouville’s theorem – canonical and grand canonical ensembles-partition function – calculation of statistical quantities – Energy and density fluctuations.

##### Unit 3

Learning objectives
Classical and Quantum statistical distribution function
Application of MB, FE and BE distribution functions
Classical and Quantum Statistics: Maxwell- Boltzmann, Fermi Dirac and Bose Einstein statistics, properties of ideal Bose and Fermi Gases, Bose-Einstein condensation

##### Unit 4

Learning Objectives
Phase diagram of single simple systems
Phase transition – Paramagnetic to ferromagnetic system
Landau theory of phase transition
Bose Einstein Condensation

Phase Transition and Critical Phenomena: Phase transitions, phase diagram for a real gas, Analogy of fluid and magnetic Systems, Cluster expansion of classical gas, Landau theory of phase transition, critical indices, scale transformation and dimensional analysis-Bose Einstein Condensation.

##### Unit 5

Learning g objectives
Intro to Non-equilibrium statistics
Stochastic and Markov Process
Langevin equation

Non-equilibrium Statistical Mechanics: Introduction to non-equilibrium processes, diffusion, transport, Brownian motion, review of probability distributions, stochastic processes, Markov processes, master equation, Fokker-Planck equation, Langevin equation, normal and anomalous diffusion, Levy flights and fractional Brownian motion

### Objective & Outcomes

Pre-requisites: Mathematics 1 &2, Thermal and Statistical Physics
Course objective: To expose the students to Statistical mechanics- both classical and quantum and introduce various applications.
Course outcomes
CO1: Review thermodynamics with specific reference to thermodynamic potentials and co-ordinates and various relationship
CO2: Understand canonical ensemble and arrive at expression for partition function and its computation
CO3: Apply classical and quantum probability distribution functions to various systems
CO4: Understand the Phase transition phenomena and study various theory explaining phase transitions.
CO5: Introduce Non –linear equilibrium statistics

Skill: Analytical and problems solving skill to apply principles of statistical physics to various system in thermal equilibrium.

 POs PO1 PO2 PO3 PO4 PO5 PSO1 PSO2 PSO3 CO1 3 3 3 3 CO2 3 3 3 3 CO3 3 3 3 3 CO4 3 3 3 3 CO5 3 3 3 3

### References

1. F Reif, Foundations of Statistical and Thermal Physics, Tata McGraw-Hill, IE, 2011.
2. Silivio R.A. Salinas, Introduction to Statistical Physics, Springer, 2010.
3. R.K. Pathria, Paul D. Beale, Statistical Mechanics, Elsevier, 3rd Edition, 2011.
4. L.D. Landau and E.M. Lifshitz, Statistical and Thermal Physics, Butterworth-Heinemann; 3rd Edition, 1996.
5. Daniel J Amit and Yosef Verbin, Statistical Physics- An Introductory course, World Scientific Co Pvt Ltd, 1999.
6. V Balakrishnan, Elements of Non- Equilibrium Statistics, ANE Books- New Delhi, 2009

### Evaluation pattern

CO-PO Mapping

 Assessment Internal External Semester Periodical 1 (P1) 15 Periodical 2 (P2) 15 *Continuous Assessment (CA) 20 End Semester 50

*CA – Can be Quizzes, Assignments, Projects, and Reports.

Justification for CO-PO Mapping

 Mapping Justification Affinity level CO1-CO5 to PO2 and PSO 1 This is course with objective of building basic analytical skills to formulate problems and solve using techniques developed. There for it has highest affinity towards  PO2 and PSO1. 3 CO1-CO5-PO3 and PSO2 This course develops problem solving skills and form a core course in Physics which will help student to formulate research problems – hence has strong affinity towards PO3 and PSO 2 3

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