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(52424) Computational Science: Computational Nanoscience

 

Summer term 2016

Prof. F. Evers, Dr. R. Korytár

Lectures:
Tuesday, 13:30—15:00, Room: PHY 5.0.20
Friday, 10:15—11:45, Room: PHY 7.1.21
Exercises:
Thursday, 15:15—18:00,
Room: CIP-Pool PHY2 (PHY 9.2.08)

The fist lecture starts on April 12
Reminder: No lecture on June 24!
Reminder: No lecture on July 8!


Requirements:

Lecture:
basic quantum mechanics & solid state physics
Practice:
some basic knowledge of programming

Molecular devices
 

Exercise sheets

Sheet 0, discussion: April 8, download also the Cheat sheet
Sheet 1, discussion: April 14, download also the python script
Sheet 2, discussion: April 21
Sheet 3, discussion: April 28
Sheet 4, discussion: Monday, May 9, 15:15—16:45 CIP-Pool PHY2
Solution: Sheet 4 / Problem 2 (Lanczos algorithm)
Sheet 5, discussion: May 12
Sheet 6, discussion: May 19
Sheet 7, discussion: June 2
Quick guide to FHI-AIMS; you can also download the AIMS lecture, given on May 20
Sheet 8, discussion: June 9, BenzeneExample.xyz,  pentacene.geometry.in
Sheet 9, discussion: June 16
New location of FHI-AIMS files and executables: /temp/ccmt/software/
The old location is obsolete.
Sheet 10, discussion: June 23
Sheet 11, discussion: June 30 in an extra-ordinary location PHY 1.0.02
Sheet 12, discussion: July 7 (this is the last sheet)

Final Exam

Take-home final exam: Exam sheet

Important information

  • Deadline for submission of numerical results: August 12

    Results should be submitted in a single .pdf file by e-mail to Dr. Daniel Hernangómez Pérez. You can use your favorite document preparation tool (LaTeX recommended). Please make an effort so that the document is clear and readable (sections, subsections etc.), label all plots accordingly and add the most important parts of your code integrated into the solutions with comments and explanations.
    Note: if e-mail submission is impossible for you, we can arrange hard copy submissions by request.

  • Oral exam: September 26, 9:30 (sharp!) - 11:00, Room PHY 4.1.13

    Oral examination will be held individually and will have an approximate duration of 20 minutes. Please, be on time to your scheduled appointment. Best of luck!

    • Hubert Beck, 9:30 - 9:50
    • Andreas Hauke, 9:50 - 10:10
    • Thomas Karl, 10:10 - 10:30
    • Fabian Stöger, 10:30 - 10:50

Contact person: Dr. Daniel Hernangómez Pérez, daniel.hernangomez(at)ur.de, office PHY 3.1.24

Contents

The advent of powerful algorithms – like Krylov-subspace methods, the Kernel-polynomial method or recursive Green's function methods, ...– together with the improving computer power has opened up a completely new route to test existing concepts and to obtain new insights into broad classes of physical systems. Nowadays, computational tools are well established in all branches of theoretical sciences and make unique and indispensable contributions. Indeed, often they provide the only route for systematic studies and improved understanding.
This lecture offers an introduction into basic computational techniques and the conceptual ideas behind. The pedagogical approach of the lecture will be to start from a fundamental example, usually taken from the physical sciences, and then develop a numerical approach starting from there. In exercises practical implementations with Python for scientifically relevant examples will be given.
The lecture will proceed along the following roadmap:

1. The Gas of Non-interacting Fermions

1.1 Free fermions, state counting, band structure
1.2 Tight binding models – graphene
(Fast fourier transformation)
1.3 Excursion: Topologically non-trivial materials

2. Beyond Band Structure Physics

2.1 Broken translational symmetries – Hofstadter butterfly
(Full matrix routines, LAPACK)
2.2 Disorder effects
(General purpose numerics: iterative methods, linear solvers)
2.3 Wavepacket propagation in nanostructures
(Sparse matrix methods: Krylov subspace technology)
2.4 Ground states
(Lanczos and Davidson methods)

3. Interaction Effects - Mean Field Theories

3.1 Briefing: Fermi-Liquid-Theory
3.2 Hartree-Fock method (HF)
(Self-consistent iteration schemes)
3.3 Thermodynamics
(Kernel-Polynomial Method and stochastic trace evolution)
3.4 Interaction effects on quantum dynamics – Time dependent HF and random phase approximation
(Kubo-formalism and theory of linear response)
3.5 Superconductivity: BCS and Boguliubov-deGennes theory
(Topological superconductors, Majorana edge modes, Kitaev models)

4. Density Functional Theory (DFT)

4.1 Basic idea and Levi's proof
4.2 Exact properties
4.3 Exensions of DFT: Spin-DFT, time dependent DFT etc.
4.4 Approximate functionals
4.5 Beyond DFT: GW-theory

5. Statistical and Transport Physics

5.1 Hydrodynamics and classical transport
(Partial differential equations, difference equations, boundary problems)
5.2 Quantum transport
(Transfer matrix technique and Landauer formalism)
5.3 Molecular Electronics
(Non-equilibrium Green's functions)
5.4. (Thermal) phase transitions – Ising transition
(Monte-Carlo simulations and finite size scaling)
5.5 Quantum phase transitions - Anderson transition
(Fractal and Multifractal analysis)

6. Strongly Correlated Electron Systems

6.1 Briefing: Kondo effect
6.2 The numerical renormalization group
6.3 Briefing: Luttinger liquid
6.4 The density matrix renormalization group method

 

Literature: Computational Methods

  1. Computational Physics,
    J.M. Thijsen,
    Cambridge university Press (2007) 

  2. An introduction to Computational Physics,
    Tao Pang
    Cambrdige University Press (2006) 
  3. Matrix Computations
    G. H. Golub, C. F. van Loan
    The Johns Hopkins University Press, Baltimore London (1996) 

Literature: Conceptual framework of modern condensed matter physics 

  1. Principles of condensed matter systems
    P. M. Chaikin and T.V. Lubensky,
    Cambridge, University Press (1995) 
  2. Condensed Matter Field Theory,
    A. Altland and B. Simons
    Cambridge University Press (2010)
  3. Quantum Theory of the Electron Liquid
    G. Giuliani G. Vignale
    Cambridge, University Press (2005) 
  4. Basic notions of Condensed Matter Physics,
    P.W. Anderson, 'Frontiers in Physics'
    Benjamin / Cummings Publishing Company (1984) 

 

 
Last modified: 17th Jul, 2018 by Daniel Hernangomez