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Path integrals in statistical mechanics with applications in soft and hard condensed matter physics (2015)

Name of course:
Path integrals in statistical mechanics with applications in soft and hard condensed matter physics.


ECTS credits:
5


Course parameters:

Language: English

Level of course: PhD course

Time of year: Q3 2015

No. of contact hours/hours in total incl. preparation, assignment(s) or the like:

 

6 hours weekly distributed between lectures, student talks, and theoretical exercises.

8 hours weekly preparation and self-study.

40 hours preparation for oral presentation.


Capacity limits

15 participants


Objectives of the course:

This course is intended to introduce the students to the theory of path integrals in statistical mechanics with applications in soft and hard condensed matter physics. The content is chosen such that the students will be well prepared for future research in the field.

Specifically, the course will cover the following subjects:

- Field theories, critical phenomena, momentum shell renormalization group.

- Solution of stochastic equations: the Langevin equation, the Fokker Planck equation.

- Applications to soft matter, Partition functions of polymers and membranes.

- Path integrals for many-body systems. Coherent states and Grassman numbers.

- Mean-field theory and the stationary phase approximation. Fluctuations.

- Renormalization group for quantum many-body systems: Fermi liquid theory and ferromagnetism.


Learning outcomes and competences:

At the end of the course, the student should be able to:

Apply the path integral technique to a broad range of physical problems, in particular, s/he should be able to

- Use the path integral and the renormalization group theory to find the critical behavior of physical models.

- Find the formal solution of stochastic equations.

- Derive the thermodynamic properties of soft matter systems.

- Express the partition function of a quantum system in terms of a path integral.

- Derive mean-field theory as well as fluctuation corrections from the path integral.

- Use the renormalization group to analyze correlated quantum systems.


Course contents:

- Field theories, critical phenomena, momentum shell renormalization group.

- Solution of stochastic equations: the Langevin equation, the Fokker Planck equation.

- Applications to soft matter, Partition functions of polymers and membranes.

- Path integrals for many-body systems. Coherent states and Grassman numbers.

- Mean-field theory and the stationary phase approximation. Fluctuations.

- Renormalisation group and quantum many-body systems: Fermi liquid theory and ferromagnetism.


Prerequisites:

Three years of study including quantum mechanics and statistical physics.


Name of lecturers:

Georg Bruun

Alberto Imparato


Type of course/teaching methods:

Lectures, student talks, and exercises


Literature:

P. M. Chaikin, T. C. Lubensky “Principles of Condensed Matter Physics”

Altland & Simons, “Condensed Matter Field theory”

Hagen Kleinert, “Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets”

R. Shankar, Rev. Mod. Phys. 66, 129 (1994).

Notes and review articles


Course homepage:

Will be set up later.


Course assessment:

The students will be required to give an oral presentation of a chosen subject, relevant to the course. The presentation will be restricted to 1/2 hour. The students will be graded based on their presentation on a pass/non-pass basis. Grading on the usual scale will be available on request in advance.  Students are expected to attend all presentations of their fellow students.


Provider:

Department of Physics


Registration:

Deadline for registration is 19 January 2015


If you have any questions, please contact:

Georg M. Bruun, e-mail: bruungmb@phys.au.dk

Alberto Imparato, e-mail: imparato@phys.au.dk

Comments on content: 
Revised 16.05.2017