Instructor:  

            Gil Refael
            164 WB,

            refael{at}caltech.edu
            Office Hours : 3-4pm, Friday

TA's:

Min-Feng Tu

mtu {at} caltech.edu
Office: 155 WB
OH: Tuesday 4pm-5pm @ room 57 WB

Feng Bi

fbbi {at} caltech.edu
Office: 52 WB
OH: Monday 3pm-4pm @ room 57 WB

Final exam

   Final exam front page - download any time to see the conditions, e.g., allowed materials.

   Final exam - download when you are ready to being and take the exam. 

Topics:

    1. Superfluidity.

    2. Vortices and the Kosterlitz-Thouless-Brezhinski transition.

    3. Imaginary time.

    4. Quantum phase transitions.

    5. Bosonization.

    6. Fluctuation-dissipation theorem.

    7. Jarzinski inequality (maybe..) 

Lecture Notes

    Week 1 - Superfluidity, and the Landau critical velocity.         

    Week 2 - Vortex physics.

    Week 3 - Kosterlitz-Thouless transition, and construction of RG flow

    Week 4 - Kosterlitz-Thouless analysis of RG flow. Imaginary time.

    Week 5 - Imaginary time path integral for an harmonic oscillator, and for a double well potential.

    Week 6 - Quantum phase transitions and the dimerized electronic chain.

    Week 7 - Bosonization.

    Week 8 - Interactions and the dimerization transition using bosonization. 

Reference on Bosonization and QPT's: Subir Sachdev, Quantum Phase Transitions.

also: Giamarchi, Quantum physics in one dimension

    Week 9 - Dynamics: Fluctuation dissipation theorem.

Homework

    PS 1 - due April 20th before class.   [Sol 1]

    PS 2 - due May 9th before class.   [Sol 2] 

    PS 3 - due May 23rd before class.   [Sol 3]

    PS 4 - due June 1st, noon, Gil's mailbox.    [Sol 4]

 Supplements

           You-tube on helium:

              http://www.youtube.com/watch?v=2Z6UJbwxBZI

          And the fountain effect: 

              http://www.youtube.com/watch?v=kCJ24176enM