## Welcome to Statistical Mechanics

**PHGN 530 STATISTICAL MECHANICS**

Fall 2016, Prof. Susanta K. Sarkar, Dept. of Physics

12:30 PM – 1:45 PM, Tuesday and Thursday, Berthoud Hall 206

TA: Warren Colomb (wcolomb@mymail.mines.edu)

Office hours: Timberline 1 M‐F 10‐11 AM or email for extra hours

Email: ssarkar@mines.edu

__Textbook:__

Statistical Mechanics, Raj Pathria

__Accessories:__

Laptop with Microsoft Office, Word, EndNote, Mathtype.

Equivalent Mac versions are alright.

__Syllabus:__

__Module 1 and 2 (4 weeks)__

**NOTES1.1 Basic Thermodynamics and Statistical Mechanics**

1. Spontaneity (free energy), speed (activation barrier), phase transition (density of states).

How does one make a non-spontaneous process happen?

How does one trap a system in non-equilibrium state?

How does one speed up a reaction?

2. Assumptions and breaking points: ergodicity, arrow of time, and counting (Gibbs paradox).

3. Comparison of ensembles for small and large systems. Comparison of classical and quantum mechanics.

4. Liouville’s theorem: time evolution of probability. Simulations.

__Module 3 ____(2 weeks)__

**NOTES2.1 Violations of Second Law**

1. Violations of second law for small systems and other counter-intuitive aspects.

__Module 4 ____(2 weeks)__

**NOTES3.1 Poisson Process Approach to Statistical Mechanics**

1. Simulation, analysis, and applications of random processes.

In particular, Poisson process using Matlab.

Data analysis, accuracy, and precision.

__Module 5 ____(2 weeks)__

**NOTES4.1 Poisson Process Approach to Transport**

**NOTES4.2 Transport Notes for Final Exam**

1. Transport: Electron and phonon

__Module 6 ____(2 weeks)__

**NOTES5.1 Phase Transition and Collective Phenomena **

**NOTES5.2 Phase Transition without Broken Symmetry **

**NOTES5.3 Phase Transition in Finite Systems**

**NOTES5.4 Liquid Crystal for Final Exam**

**NOTES5.5 Reasons for 1-site for Ising Model Theory**

1. Phase transition:

Identify order parameters.

Write free energy as a function of order parameters.

Calculate experimentally measurable quantities.

__Learning outcomes:__

__Based on statistical mechanics__

1. Formulate and plan a thesis research-related project

2. Theoretically derive related thermodynamic properties

3. Compare and contrast their results with literature

4. Select and apply relevant course content to their thesis

5. Explain their research orally and in written form

6. Peer review, provide constructive suggestion, and respond

__Content resources:__

__For content of statistical mechanics, students may use__

1. Statistical Mechanics by Raj Pathria

2. Flipped video, lecture notes, papers, and in class lecture

3. Their professional contacts including advisor(s)

4. Materials available on the internet

__Learning assessments:__

__Students will__

1. Write the title, the abstract, and the introduction by Sept 30

2. Write about experiment, theory, and/or modeling by Oct 30

3. Write results and discussion by Nov 30

4. Produce an article in the format of Physical Review Letters

5. Teach part of every class discussing their projects

6. Provide feedback and respond using NSF-inspired rubric