**ICTS Course no.: **PHY-422.5

**Venue:** Online

**Class timings:** Wednesdays and Fridays 11:00-12:30

**First meeting:** 21st January 2022

**Course description: **

- Random walks including method of generating functions and the first passage problem
- Basics of stochastic procceses and Markov processes.
- Brownian motion, classical and quantum Langevin equations.
- Path integral approaches and Fokker Planck equations
- Correlation Functions and Spectral Densities; the Wiener-Khintchine theorem; light spectra; noise in a gravitational-wave detector
- Linear response theory and fluctuation dissipation relations
- Interacting particle systems: Glauber dynamics and Monte-Carlo simulations.

The course will be aimed at understanding formalism through examples.

**Requirements:** Students should have a solid basic knowledge of statistical physics and quantum physics

**References:**

- Stochastic processes in physics and chemistry: van Kampen
- Nonequilibrium Statistical Physics: Noelle Pottier
- Random Walks and random environment: Barry D. Hughes (some relevant chapters)
- Stochastic processes in physics and astronomy, S. Chandrasekhar
- Brownian Functionals in physics and computer science, S. N. Majumdar
- Blandford and Thorne: Classical Physics: Chapter on Random Processes

Other relevant references will be provided during the course.

**Assessment:** Assignment (50%) + Examination (50%)

- Teacher: Abhishek Dhar