2018

COMPLEX SYSTEMS

Ralf Eichhorn (Nordita)

Complex systems, a.k.a. dynamical systems, refer to mathematical models describing the time evolution of systems by means of equations of motion and initial values. It is the solutions rather than the systems, or the models of the systems, that display complex features. Examples of such features are various ordered processes and structures, such as nonlinear oscillations and waves, as well as disordered chaotic processes and fractal structures. The models are formulated in terms of coupled nonlinear differential equations or, in the discrete case, as iterated maps. Nonlinearity is essential and key concepts are bifurcations, sensitive dependence on initial values, attractors and chaos. There are applications to physics, biology, chemistry, engineering and other areas.

The course deals with analytical and numerical methods for the analysis of nonlinear models based on a small number of independent variables.

Credits: This is a 7.5 point (ECTS) course, given by KTH Royal Institute of Technology (SI2540).

Course format: The course consists of 15 lectures, 2 hours each.

Examination: Home assignments and an oral examination (the latter only for PhD students).

Course home page:   www.kth.se/student/kurser/kurs/SI2540

First lectures: Thursday, 28 March 2018, 10:15 - 12:00.

Place: 112:028 (Nordita South building, Roslagstullsbacken 11).

MATHEMATICAL METHODS IN PHYSICS, ADDITIONAL COURSE

Johan Hellsvik (Nordita), Stefan Clementz (KTH)

Mathematical Methods in Physics, Additional Course (SI1142) Spring 2018 P4

The course mathematical Methods in Physics, Additional Course (SI1142) is suitable for students who have taken course SI1200 or similar. We will go more depth into modern theoretical physics and introduce formalism that will facilitate the transition from classical mechanics to quantum mechanics. On the curriculum are:

• Tensor and vector analysis in general spaces. Tangent and dual vectors. The metric tensor.
• Lagrange's and Hamilton's formulations of classical mechanics. Noether's theorem, constants of motion.
• Hamilton's formulations of classical mechanics

Credits: This is a 3.0 point (ECTS) course, given by KTH Royal Institute of Technology (SI1142).

Course format: The course consists of 6 lectures, and 6 exercise sessions, 2 hours each.

Course home page:   www.kth.se/student/kurser/kurs/SI1142

First lectures: Tuesday, 20 March 2018, 10:00—12:00, in FP21 (Roslagstullsbacken 33).

Place: FP21, FB41, FB51, FB54 (AlbaNova campus).

ASTROPHYSICAL MAGNETOHYRDRODYNAMICS IN 24 HOURS

Dhrubaditya Mitra (Nordita)

I assume that you have had a short course on fluid dynamics, typically the gas dynamics course given in the fall semester by Stephan Rosswog. But this is not mandatory. What is mandatory, however, is to have a good knowledge of classical mechanics, electrodynamics and statistical mechanics as is expected in any advanced graduate student. Although the course is called "astrophysical" masters and PhD students in physics are welcome. See the course home page for syllabus and Course Materials

Credits: This is a 7.5 point (ECTS) course, given by Stockholm University, see  www.astro.su.se/english/education/courses-and-programmes/courses/astrophysical-mhd-as7019-7-5-hp-1.257227

Course format: The course consists of 24 lectures, 1 hours each, but fortunately not delivered without a break: they will be spread over 10 weeks in the spring semester of 2018.

Examination: Homework (40%) and Written examination (60%)

Course home page:   www.nordita.org/~dhruba/teach/MHD

First lecture: Thursday, 16 January, 2018, 10.00-11.00

Place: 122:026 (Nordita West building, Roslagstullsbacken 17).

2017

MODERN FLUID MECHANICS:
From Viscous Electronics in Graphene to Conformal Invariance and Anomalies in Turbulence

Gregory Falkovich (Weizmann Institute)

This introductory course is intended for those who does not know the subject and for those who think they do. Syllabus:

• Hydrodynamics as collective description, equations and conservation laws, added mass as the first renormalization in physics.
• Ideal hydrodynamics and reversibility paradox, drag and quasi-momentum.
• Aristotelian world of viscous flows, gauge theory and swimming bacteria, emerging viscous electronics in graphene.
• Boundary layer and separation phenomenon, wake and finite drag and lift.
• Instabilities, laminar-turbulent transition in linearly unstable and stable systems, new concept of probabilistic transition.
• Turbulence and the first anomaly in physics. Anomalous scaling and statistical conservation laws. Turbulence in two dimensions, mysterious conformal invariance.
• Acoustics, linear and nonlinear, Burgers equation. Linear and nonlinear waves, solitons and wave collapses.

The course is based on the book: G. Falkovich, Fluid Mechanics: A Short Course for Physicists (Cambridge University Press, 2011).

Prize for the best question! An author copy of the book will be given out as a present for the best question asked during the course.

Course home page:   www.nordita.org/~zarembo/FluidDynamics2017

Schedule: 1-12 September 2017.
Lecture 1. Monday, September 4, 10:15-12:00 (FB55)
Lecture 2. Tuesday, September 5, 10:15-12:00 (FB53)
Lecture 3. Wednesday, September 6, 10:15-12:00 (FD5)
Lecture 4. Thursday, September 7, 10:15-12:00 (FD42)
Lecture 5. Friday, September 8, 10:15-12:00 (FD41)
Lecture 6. Monday, September 11, 10:15-12:00 (FB42)
Lecture 7. Tuesday, September 12, 10:15-12:00 (FB42)

COMPLEX SYSTEMS

Ralf Eichhorn (Nordita)

Complex systems (dynamical systems) are mathematical models describing the time evolution of systems by means of equations of motion and initial values. Models are typically formulated in terms of coupled nonlinear differential equations (continuous time) or iterated maps (discrete time). Even for models with relative simple mathematical structure, the solutions may show surprisingly complex features, such as nonlinear oscillations, fractal structures and chaotic behavior.

The course gives an introduction to the analysis of such complex systems and their behavior. Key concepts are, amongst others, the phase space perspective, attractors, sensitive dependence on initial conditions, chaos, bifurcations, Poincare maps, and numerical solutions.

Credits: This is a 7.5 point (ECTS) course, given by KTH Royal Institute of Technology (SI2540).

Course format: The course consists of 15 lectures, 2 hours each.

Examination: Home assignments and an oral examination (the latter only for PhD students).

Course home page:   www.kth.se/social/course/SI2540/

First lectures: Wednesday, 29 March 2017, 10:15 - 12:00.

Place: 112:028 (Nordita South building, Roslagstullsbacken 11).

2016

COMPLEX SYSTEMS

Ralf Eichhorn (Nordita)

Complex systems (dynamical systems) are mathematical models describing the time evolution of systems by means of equations of motion and initial values. Models are typically formulated in terms of coupled nonlinear differential equations (continuous time) or iterated maps (discrete time). Even for models with relative simple mathematical structure, the solutions may show surprisingly complex features, such as nonlinear oscillations, fractal structures and chaotic behavior.

The course gives an introduction to the analysis of such complex systems and their behavior. Key concepts are, amongst others, the phase space perspective, attractors, sensitive dependence on initial conditions, chaos, bifurcations, Poincare maps, and numerical solutions.

Credits: This is a 7.5 point (ECTS) course, given by KTH Royal Institute of Technology (SI2540).

Course format: The course consists of 15 lectures, 2 hours each.

Examination: Home assignments and an oral examination (the latter only for PhD students).

Course home page:   www.kth.se/social/course/SI2540/

First lectures: Thursday, 30 March 2016, 13:15 - 16:00.

Place: 112:028 (Nordita South building, Roslagstullsbacken 11).

ASTROPHYSICAL MAGNETOHYRDRODYNAMICS IN 24 HOURS

Dhrubaditya Mitra (Nordita)

I assume that you have had a short course on fluid dynamics, typically the gas dynamics course given in the fall semester by Stephan Rosswog. But this is not mandatory. What is mandatory, however, is to have a good knowledge of classical mechanics, electrodynamics and statistical mechanics as is expected in any advanced graduate student. Although the course is called "astrophysical" masters and PhD students in physics are welcome. See the course home page for syllabus and Course Materials

Credits: This is a 7.5 point (ECTS) course, given by Stockholm University, see  www.astro.su.se/english/education/courses-and-programmes/courses/astrophysical-mhd-as7019-7-5-hp-1.257227

Course format: The course consists of 24 lectures, 1 hours each, but fortunately not delivered without a break: they will be spread over 10 weeks in the spring semester of 2016.

Examination: TBA

Course home page:   www.nordita.org/~dhruba/teach/MHD

First lecture: Thursday, 19 January, 2016, 10.00-11.00

Place: 122:026 (Nordita West building, Roslagstullsbacken 17).

2015

RENORMALISATION GROUP METHODS IN CONDENSED MATTER PHYSICS

John Hertz (Nordita)

The course is meant to give an overview of renormalisation group (RG) methods in various areas of condensed matter physics. It is expected that students have a general knowledge of statistical mechanics and know something about field-theoretic methods. The course should make them able to apply RG methods to problems in their own research.

Texts: For the most part, the course will follow the book ?Scaling and renormalisation in statistical physics? by John Card (Cambridge U Press). The plan is provisionally to base the material on fermion systems on the article ?Renormalisation-group approach to interacting fermions? by R Shankar (Rev Mod Phys 66, 129-192 (1994). Recent papers on topics of current interest will also be used.

Credits: This is a 7.5 point (ECTS) course, given by KTH Royal Institute of Technology.

Course format: The course consists of 9 lectures, 2 hours each.

Examination: TBA

Course home page:   www.kth.se/en/studies/innovate/rgcourse-1.557047

First lecture: Thursday, 16 April 2015, 14.00-16.00

Place: 122:026 (Nordita West building, Roslagstullsbacken 17).

COMPLEX SYSTEMS

Ralf Eichhorn (Nordita)

Complex systems (dynamical systems) are mathematical models describing the time evolution of systems by means of equations of motion and initial values. Models are typically formulated in terms of coupled nonlinear differential equations (continuous time) or iterated maps (discrete time). Even for models with relative simple mathematical structure, the solutions may show surprisingly complex features, such as nonlinear oscillations, fractal structures and chaotic behavior.

The course gives an introduction to the analysis of such complex systems and their behavior. Key concepts are, amongst others, the phase space perspective, attractors, sensitive dependence on initial conditions, chaos, bifurcations, Poincare maps, and numerical solutions.

Credits: This is a 7.5 point (ECTS) course, given by KTH Royal Institute of Technology (SI2540).

Course format: The course consists of 12 lectures, 2 hours each.

Examination: homework assignments and an oral examination (by Jack Lidmar).

Course home page:   www.kth.se/social/course/SI2540/

First lectures: Thursday, 26 March 2015, and Friday, 27 March, both 10:00 - 12:00.

Place: 122:026 (Nordita West building, Roslagstullsbacken 17).

ADVANCED TOPICS IN CONDENSED MATTER PHYSICS

Alexander Balatsky (Nordita), Edwin Langmann (KTH), Konstantin Zarembo (Nordita)

The course is aimed at introducing a number of topics in Condensed Matter Theory through the formalism of Green's functions. Topics will include: Green's functions, Linear response theory, Electron-phonon interactions, Elements of Fermi liquid theory, Green's functions at finite temperature, Electrons in random potential, and Superconductivity.

The course is based on a set of problems taken from the book L. S. Levitov and A. V. Shytov, "Green's functions. Theory and practice" . Ideally, this should be a reading course, where all the problems are solved in class. So pick a problem of your like and prepare to give a presentation on its solution along with an introduction to the underlying theory. You are encouraged nevertheless to solve all other problems on your own.

Credits: This is a 7.5 point (ECTS) course, given by KTH Royal Institute of Technology (FSI3215).

Course format: The course consists of 9 lectures, 2 hours each.

Examination: homework assignments.

Course home page:  www.nordita.org/~zarembo/CondMat2015/

First lecture: Wednesday, 25 March 2015, 13:15 - 15:00.

Place: FB41 (AlbaNova main building, Roslagstullsbacken 21.).

2013

RELATIVITY THEORY

Konstantin Zarembo (Nordita), Alexander Krikun (Nordita)

Credits: This is a 7.5 point (ECTS) course, given by Stockholm University (FSI3035)

Course format: The course consists of 15 lectures, 2 hours each. Homework assignments will be provided.

Course home page:  www.nordita.org/~zarembo/Courses/GR2013

First lecture: Tuesday, 22 October 2013, 13:15

Place: FB51, and later in other lecture rooms in the AlbaNova main building, Roslagstullsbacken 21.

CONFORMAL FIELD THEORY

Eddy Ardonne (Nordita)

This course will start from the basics. The topics which will be covered are: Motivation and introduction to conformal invariance; The Virasoro algebra; Free bosons and fermions; Minimal models; Singular vectors and differential equations for correlation functions; CFT on the torus: Modular invariance and the Verlinde Formula; Extended symmetries: current algebras and the Knizhnik-Zamolodchikov equation.

No previous knowledge of conformal field theory is assumed, even if some basic knowledge about quantum field theory will definitely be helpful.

Credits: This is a 7.5 point (ECTS) course, given by Stockholm University

Course format: The course will consist of lectures (once a week, 2 times 45 minutes), as well as exercises which will be provided.

Course home page:   www.nordita.org/~ardonne/cft-course.html

First lecture: Wednesday, 12 September 2013, 15:15 - 17:00

Place: Nordita Astrophysics seminar room, 122:026 (Roslagstullsbacken 17)

ADVANCED ASTROPHYSICAL FLUID DYNAMICS

Axel Brandenburg (Nordita, and Astronomy Department, Stockholm University)

The goal of the course is to understand: (a) fluid dynamics and magnetohydrodynamics (MHD), (b) waves and instabilities, (c) global and local helioseismology, (c) shocks, solar wind, accretion, (d) fundamental aspects of turbulence and convection, (e) dynamo theory, and (f) numerical techniques for MHD and turbulence.

Credits: This is a 7.5 point (ECTS) course, given by Stockholm University

Course format: The course consists of 13 lectures, 4 tutorials, plus the student presentations. Exercises which will be provided.

Course home page:  http://www.nordita.org/~brandenb/teach/AstroFluids/schedule/2013_Feb.html

First lecture: Wednesday, 13 February 2013, 10:15 - 12:00

Place: Nordita Astrophysics seminar room, 122:026 (Roslagstullsbacken 17)

2012

LATTICE BOLTZMANN METHODS FOR SIMULATION OF COMPLEX PHENOMENA ACROSS SCALES

Sauro Succi (Istituto Applicazioni Calcolo, CNR, Roma, Italy)

The lattice Boltzmann equation (LBE) is a minimal form of Boltzmann kinetic equation, which is meant to simulate the dynamic behaviour of fluid flows without directly solving the equations of continuum fluid mechanics. In this series of lectures, after expounding the basic notions behind LB theories, we shall discuss selected applications from current cutting-edge research in the field, such as the modeling of fluid turbulence, the rheology of soft-glassy materials and wave propagation.

Course home page:  www.nordita.org/lbe2012

First lecture: Monday, 14 May 2012,

Place: Nordita Astrophysics seminar room, 122:026 (Roslagstullsbacken 17)

ASTROPHYSICAL HYDRO- AND MAGNETOHYDRODYNAMICS

Axel Brandenburg (Nordita, and Astronomy Department, Stockholm University)

The goal of the course is to understand: (a) the equations of magnetohydrodynamics (MHD), (b) waves and instabilities, (c) shocks, solar wind, accretion, (d) fundamental aspects of turbulence and convection, (e) dynamo theory, and (f) numerical techniques for MHD and turbulence.

The course consists of 12 lectures plus 5 tutorials. Exercises which will be provided. This is a 7.5 point (ECTS) course.

Course home page:  www.nordita.org/~brandenb/teach/MHD/schedule/2012_Jan.html

First lecture: Tuesday, 17 January 2012, 10:15 - 12:00

Place: Nordita Astrophysics seminar room, 122:026 (Roslagstullsbacken 17)

2011

CONFORMAL FIELD THEORY

Eddy Ardonne (Nordita)

This course will start from the basics. The topics which will be covered are: Motivation and introduction to conformal invariance; The Virasoro algebra; Free bosons and fermions; Minimal models; Singular vectors and differential equations for correlation functions; CFT on the torus: Modular invariance and the Verlinde Formula; Extended symmetries: current algebras and the Knizhnik-Zamolodchikov equation.

No previous knowledge of conformal field theory is assumed, even if some basic knowledge about quantum field theory will definitely be helpful.

The course will consist of lectures (once a week, 2 times 45 minutes), as well as exercises which will be provided. It will be a 7.5 point (ECTS) course

Course home page:   www.nordita.org/~ardonne/cft-course-2011.html

First lecture: Wednesday, 2 September 2011, 15:15 - 17:00

Place: Nordita Astrophysics seminar room, 122:026 (Roslagstullsbacken 17)

2010

INTRODUCTION TO SCIENTIFIC COMPUTATION

Dhrubaditya Mitra (Nordita)

This 7.5 point PhD course for 5 weeks. Each week consists of three 1.5 hr lecture. Each lecture will be roughly 30 minutes of lecture and 1 hour of hands on session. The main topic is scientific computation. The method of teaching will use fortran 90 heavily. You can use any other language (e.g., C, C++) you wish (but not packages software e.g, mathematica or matlab). Also includes a guest lecture by Chi-Kwan Chan on computations in graphics processors (gpu )

Course home page:  www.nordita.org/~dhruba/teach

Time: 1st Nov-17th Dec 2010

Place: Nordita Astrophysics seminar room, 122:026 (Roslagstullsbacken 17)

2009

SOLAR PHYSICS AND MAGNETOHYDRODYNAMICS

Axel Brandenburg (Nordita)

This 7.5 point PhD course provides an introduction to solar physics with emphasis on solar activity and magnetohydrodynamics. The course includes 4 computer exercises and 3 problem sheets will be handed out. The course syllabus covers solar/terrestrial connection, atmospheric waves, numerical techniques, helioseismology, convection, turbulence, winds and critical points, magnetic fields, coronal heating, reconnection, magneto-rotational instability, laminar and turbulent dynamos, magnetic helicity, and coronal mass ejections.

Course home page:  www.nordita.org/~brandenb/teach/solar

Time: 5-28 May 2009

Place: Nordita Astrophysics seminar room, 122:026 (Roslagstullsbacken 17)

INTRODUCTION TO LOOPS AND STRINGS

Diego Chialva, Kristina Giesel, and Alexander Wijns (Nordita)

This is a seminar series or journal club where we want to discuss approaches to quantum gravity. We will start by introducing loop quantum gravity (4 hours) and string theory (4 hours) to a non-expert audience. The focus will be on the basic ingredients that go into both approaches. We will also try to compare their shortcomings, success, common aspects, etc. Afterwards we can venture int various directions according to the preferences and expertise of the participants. The atmosphere surrounding these seminars is hoped to be rather informal.

Time: Tuesdays, 15:00-17:00. The four introductory lectures are

• 21 April, LQG I (KG)
• 28 April, LQG II (KG)
• 5 May, ST I (DC)
• 12 May, ST II (AW)

Place: Nordita Astrophysics seminar room, 122:026 (Roslagstullsbacken 17)

2008

CONFORMAL FIELD THEORY

Eddy Ardonne (Nordita)

This course will start from the basics. The topics which will be covered are: Motivation and introduction to conformal invariance; The Virasoro algebra; Free bosons and fermions; Minimal models; Singular vectors and differential equations for correlation functions; CFT on the torus: Modular invariance and the Verlinde Formula; Extended symmetries: current algebras and the Knizhnik-Zamolodchikov equation.

No previous knowledge of conformal field theory is assumed, even if some basic knowledge about quantum field theory will definitely be helpful.

The course will consist of lectures (once a week, 2 times 45 minutes), as well as exercises which will be provided. It will be a 7.5 point (ECTS) course

Course home page:   www.nordita.org/~ardonne/cft-course-2008.html

First lecture: Wednesday, 24 September 2008, at 13:15 to 15:00.

Place: Quantum Chemistry seminar room, 122:026 (Roslagstullsbacken 17)

ADVANCED QUANTUM FIELD THEORY

Ulf Lindström (Nordita and the Physics and Astronomy Department at Uppsala University)

Course home page:  www.teorfys.uu.se/people/lindstrom/qft.html

Time: 1 April to 15 May 2008

Place: Uppsala

2007

SUPERSYMMETRY

Ulf Lindström (Nordita and the Physics and Astronomy Department at Uppsala University)

The course is aimed at beginning PhD-students in physics. Good background is some knowledge of relativistic quantum field theory and a little familiarity with Lie-groups and Lie-algebra.

I will discuss the possible symmetries of a relativistic quantum field theory, the concept of bose-fermi symmetry and define superalgebras. Supersymmetry will be illustrated in the context of simple field theories and sigma models. Emphasis will be give to efficient methods for packaging multiplets (i.e. superspace) and I will choose low dimensional examples to bring out the ideas as clearly a possible. The main body of the course will be basic supersymmetry and representations thereof. Advanced topics that I hope to touch upon towards the end of the course are the relation to complex geometry, supergravity, superstring theory et.c.

Time: Wednesdays and Thursdays from 10:15 to 12:00, between 24 October and 22 November 2007.

Place: Nordita seminar room

INTRODUCTORY LECTURES ON STRING THEORY

Paolo Di Vecchia (Nordita)

These lectures are for people who do not know anything about string theory and who want to know some basic elements. The first lectures will deal with (1) Why do we speak about string theory? (2) Introduction to the bosonic string and its physical spectrum.

First lecture: Thursday, 18 October 2007 from 10:00 to 11:00.

Place: Nordita seminar room